Patent Publication Number: US-2023162219-A1

Title: Computer-readable recording medium storing information processing program, information processing method, and information processing system

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is based upon and claims the benefit of priority of the prior Japanese Patent Application No. 2021-191379, filed on Nov. 25, 2021, the entire contents of which are incorporated herein by reference. 
     FIELD 
     The embodiments discussed herein are related to a non-transitory computer-readable recording medium storing an information processing program, an information processing method, and an information processing system. 
     BACKGROUND 
     In the related art, a system called a supply chain is formed by an order receiving side that manufactures a product and an ordering side that requests the manufacture. There is a case where each of two parties of the order receiving side and the ordering side independently determines a price of the product to be sold to the ordering side and a quantity of the product requested to be manufactured by the order receiving side so as to maximize a profit. For example, there is a case where an order receiving side determines a price of a product to be sold to an ordering side so as to maximize a profit of the order receiving side, and the ordering side determines a quantity of the product requested to be manufactured by the order receiving side so as to maximize a profit of the ordering side. In this case, a situation called double marginalization in which it is difficult to maximize a profit of the entire supply chain is likely to occur. 
     Japanese National Publication of International Patent Application No. 2004-517378 and Japanese Laid-open Patent Publication No. 2004-035219 are disclosed as related art. 
     Li, Mengmou, et al. “Smooth dynamics for distributed constrained optimization with heterogeneous delays.” IEEE Control Systems Letters 4.3 (2020): 626-631 is also disclosed as related art. 
     SUMMARY 
     According to an aspect of the embodiments, a non-transitory computer-readable recording medium stores an information processing program causing a computer to execute a process including: acquiring a first order quantity from an order receiving side to an ordering side and a first profit amount distributed from the order receiving side to the ordering side, which are calculated by the order receiving side by using a first parameter including first confidential information owned by the order receiving side, from the order receiving side; acquiring a second order quantity from the order receiving side to the ordering side and a second profit amount distributed from the order receiving side to the ordering side, which are calculated by the ordering side by using a second parameter including second confidential information owned by the ordering side, from the ordering side; calculating a first penalty that acts to reduce a difference between the first order quantity and the second order quantity and a difference between the first profit amount and the second profit amount, based on the acquired first order quantity, the acquired first profit amount, the acquired second order quantity, and the acquired second profit amount; notifying the order receiving side to calculate the first order quantity and the first profit amount by using the first parameter including the calculated first penalty; and notifying the ordering side to calculate the second order quantity and the second profit amount by using the second parameter including the calculated first penalty. 
     The object and advantages of the invention will be realized and attained by means of the elements and combinations particularly pointed out in the claims. 
     It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory and are not restrictive of the invention. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG.  1    is an explanatory diagram illustrating an example of an information processing method according to an embodiment; 
         FIG.  2    is an explanatory diagram illustrating an example of an information processing system; 
         FIG.  3    is a block diagram illustrating a hardware configuration example of a management side apparatus; 
         FIG.  4    is a block diagram illustrating a hardware configuration example of an order receiving side apparatus; 
         FIG.  5    is a block diagram illustrating a hardware configuration example of an ordering side apparatus; 
         FIG.  6    is a block diagram illustrating an example of a functional configuration of an information processing system; 
         FIG.  7    is a block diagram illustrating a specific example of the functional configuration of the information processing system; 
         FIG.  8    is an explanatory diagram (part 1) illustrating a first operation example of the information processing system; 
         FIG.  9    is an explanatory diagram (part 2) illustrating the first operation example of the information processing system; 
         FIG.  10    is an explanatory diagram (part 3) illustrating the first operation example of the information processing system; 
         FIG.  11    is an explanatory diagram (part 4) illustrating the first operation example of the information processing system; 
         FIG.  12    is an explanatory diagram (part 1) illustrating a second operation example of the information processing system; 
         FIG.  13    is an explanatory diagram (part 2) illustrating the second operation example of the information processing system; 
         FIG.  14    is an explanatory diagram illustrating an example of effects obtained by the information processing system; 
         FIG.  15    is a flowchart illustrating an example of an order receiving side calculation process procedure; 
         FIG.  16    is a flowchart illustrating an example of an ordering side calculation process procedure; 
         FIG.  17    is a flowchart illustrating an example of a first penalty calculation process procedure; and 
         FIG.  18    is a flowchart illustrating an example of a second penalty calculation process procedure. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     As the related art, for example, there is a technique for obtaining an optimum configuration for a process in a supply chain model by considering an optimum condition for the supply chain model. For example, there is a technique for determining an improvement item in a supply chain when the supply chain is to be improved from profit and loss information of the entire supply chain. For example, there is a technique for causing a plurality of systems to calculate a formulated evaluation function and a constraint condition in a distributed manner, for an optimization problem. 
     Meanwhile, in the related art, it is difficult to maximize the profit of the entire supply chain. For example, without referring to concealed information owned by the order receiving side and concealed information owned by the ordering side, it is difficult to determine a price of the product sold to the ordering side and a quantity of the product requested to be manufactured by the order receiving side so as to maximize the profit of the entire supply chain. 
     According to one aspect, an object of the present disclosure is to maximize a profit in an entire system without disclosing confidential information. 
     Hereinafter, embodiments of an information processing program, an information processing method, and an information processing system according to the present disclosure are described in detail with reference to the drawings. 
     (Example of Information Processing Method According to Embodiment) 
       FIG.  1    is an explanatory diagram illustrating an example of an information processing method according to an embodiment. An information processing apparatus  100  is a computer for maximizing a profit in an entire predetermined system. The information processing apparatus  100  is, for example, a server, a personal computer (PC), or the like. 
     For example, the predetermined system is a system formed by an order receiving side and an ordering side. For example, the predetermined system is a supply chain. Ordering is to request a predetermined number of resources from the order receiving side. A resource is, for example, a physical resource. The physical resource is, for example, a product. The resource may be a human resource, a spatial resource, a calculation resource, or the like. The predetermined number is called, for example, an order quantity. 
     The order receiving side is, for example, a manufacturing side that manufactures a product. The ordering side is, for example, a requesting side that requests the manufacturing. For example, the ordering side is a retail side that purchases a product and sells the product to a consumer. The order receiving side may be a wholesaler, in some cases. The order receiving side may be a wholesaler and the ordering side is an intermediate wholesaler, in some cases. A profit of the entire predetermined system is, for example, a sum of a profit of an order receiving side and a profit of an ordering side that form the predetermined system. 
     There is a case where each of two parties of the order receiving side and the ordering side independently determines a price of the product to be sold to the ordering side and a quantity of the product requested to be manufactured by the order receiving side so as to maximize a profit. For example, there is a case where an order receiving side determines a price of a product to be sold to an ordering side so as to maximize a profit of the order receiving side, and the ordering side determines a quantity of the product requested to be manufactured by the order receiving side so as to maximize a profit of the ordering side. In this case, there is a problem that a situation called double marginalization in which it is difficult to maximize a profit of an entire supply chain is likely to occur. 
     Meanwhile, it is difficult to maximize the profit of the entire supply chain. For example, without referring to confidential information owned by the order receiving side and confidential information owned by the ordering side, a price of the product sold to the ordering side and a quantity of the product requested to be manufactured by the order receiving side may be determined so as to maximize the profit of the entire supply chain. The confidential information is information that is not preferable to be disclosed to others, from the viewpoint of protection of know-how, protection of personal information, or the like. 
     A method is conceivable in which an ordering side receives confidential information owned by an order receiving side and determines a price of a product sold to the ordering side and a quantity of products requested to be manufactured by the order receiving side so as to maximize a profit of the entire supply chain. According to this method, since the confidential information owned by the order receiving side is disclosed to the ordering side, the order receiving side is likely to suffer from disadvantages, which is not preferable. Another problem is that a risk occurs that the confidential information owned by the order receiving side is leaked from the ordering side. 
     In the same manner, another method is conceivable in which an order receiving side receives confidential information owned by an ordering side and determines a price of a product sold to the ordering side and a quantity of products requested to be manufactured by the order receiving side so as to maximize a profit of the entire supply chain. Also in this method, since the confidential information owned by the ordering side is disclosed to the order receiving side, the ordering side is likely to be disadvantageous, which is not preferable. Another problem is that a risk occurs that confidential information owned by the ordering side is leaked from the order receiving side. 
     Still another method is conceivable in which confidential information owned by an order receiving side and confidential information owned by an ordering side are provided to a neutral computation device that belongs to neither the order receiving side nor the ordering side. According to this method, the computation device determines a price of a product sold to the ordering side and a quantity of products requested to be manufactured by the order receiving side so as to maximize the profit of the entire supply chain. Also in this method, since the confidential information owned by the order receiving side and the confidential information owned by the ordering side are disclosed to the computation device, both the order receiving side and the ordering side are likely to suffer from disadvantages, which is not preferable. Another problem is that a risk occurs that the confidential information owned by the order receiving side and the confidential information owned by the ordering side are leaked from the computation device. 
     Accordingly, it is desirable that both the order receiving side and the ordering side do not disclose the confidential information, and the profit is maximized in the entire system. Therefore, in the present embodiment, an information processing method will be described with which it is possible to maximize a profit in an entire system without both an order receiving side and an ordering side disclosing confidential information. 
     As illustrated in  FIG.  1   , there are an order receiving side  101  and an ordering side  102 . For example, the ordering side  102  is a selling side that sells a product to a consumer. For example, the order receiving side  101  is a manufacturing side that manufactures a product and provides the manufactured product to the ordering side. 
     The order receiving side  101  has first confidential information. For example, the first confidential information includes a cost of a product, and an original profit obtained by the order receiving side. By using a first parameter including the first confidential information, the order receiving side  101  may execute a first calculation process of calculating a first order quantity q m  from the order receiving side to the ordering side and a first profit amount d m  distributed from the order receiving side to the ordering side. The first parameter may include a penalty. The first order quantity q m  is a provisional order quantity. For example, the first profit amount d m  is a provisional profit amount. 
     The ordering side  102  has second confidential information. For example, the second confidential information includes demand information of the product and an original profit obtained by the ordering side. By using a second parameter including the second confidential information, the ordering side  102  may execute a second calculation process of calculating a second order quantity q r  from the order receiving side to the ordering side and a second profit amount d r  distributed from the order receiving side to the ordering side. The second parameter may include a penalty. The second order quantity q r  is a provisional order quantity. For example, the second profit amount d r  is a provisional profit amount. 
     (1-1) The information processing apparatus  100  acquires, from the order receiving side  101 , the first order quantity q m  from the order receiving side  101  to the ordering side  102  and the first profit amount d m  distributed from the order receiving side  101  to the ordering side  102 , which are calculated by the order receiving side  101  using the first parameter. For example, the information processing apparatus  100  receives a first transposed matrix [q m  d m ] T  including the first order quantity q m  and the first profit amount d m  from the order receiving side  101 . 
     (1-2) The information processing apparatus  100  acquires, from the ordering side  102 , the second order quantity q r  from the order receiving side  101  to the ordering side  102  and the second profit amount d r  distributed from the order receiving side  101  to the ordering side  102 , which are calculated by the ordering side  102  using the second parameter. For example, the information processing apparatus  100  receives a second transposed matrix [q r  d r ] T  including the second order quantity q r  and the second profit amount d r  from the ordering side  102 . 
     (1-3) The information processing apparatus  100  calculates a first penalty µ based on the acquired first order quantity q m , first profit amount d m , second order quantity q r , and second profit amount d r . The first penalty µ acts to reduce various differences such as a difference between the first order quantity q m  and the second order quantity q r  and a difference between the first profit amount d m  and the second profit amount d r . For example, the first penalty µ acts to reduce various differences in each of the first calculation process and the second calculation process. 
     For example, by including the first penalty µ in the first parameter, the first penalty µ acts to enable calculation of the first order quantity q m  and the first profit amount d m  so as to reduce various differences in the first calculation process. For example, by including the first penalty µ in the second parameter, the first penalty µ acts to enable calculation of the second order quantity q r  and the second profit amount d r  so as to reduce various differences in the second calculation process. 
     For example, the information processing apparatus  100  calculates the first penalty µ by adding a difference value obtained by subtracting the second transposed matrix [q r  d r ] T  from the first transposed matrix [q m  d m ] T  and an integral value of the difference value. Therefore, the information processing apparatus  100  may obtain the first penalty µ serving as a guideline indicating how to adjust the first order quantity q m , the first profit amount d m , the second order quantity q r , and the second profit amount d r  without referring to the first confidential information and the second confidential information. 
     (1-4) The information processing apparatus  100  notifies the order receiving side  101  to calculate the first order quantity q m  and the first profit amount d m  by using the first parameter including the calculated first penalty µ. For example, the information processing apparatus  100  transmits a notification including the first penalty µ to the order receiving side  101 . Therefore, the information processing apparatus  100  may cause the order receiving side  101  to calculate the first order quantity q m  and the first profit amount d m  again so as to reduce the various differences. 
     (1-5) The information processing apparatus  100  notifies the ordering side  102  to calculate the second order quantity q r  and the second profit amount d r  by using the second parameter including the calculated first penalty µ. For example, the information processing apparatus  100  transmits a notification including the first penalty µ to the ordering side  102 . Therefore, the information processing apparatus  100  may cause the ordering side  102  to calculate the second order quantity q r  and the second profit amount d r  again so as to reduce the various differences. 
     Therefore, the information processing apparatus  100  may reduce various differences such as the difference between the first order quantity q m  and the second order quantity q r  and the difference between the first profit amount d m  and the second profit amount d r  without directly referring to the first confidential information and the second confidential information. For this reason, with the information processing apparatus  100 , the order receiving side  101  may avoid disclosure of the first confidential information, a risk of leakage of the first confidential information may be suppressed, and the order receiving side  101  may be less likely to suffer from disadvantages. In the same manner, with the information processing apparatus  100 , the ordering side  102  may avoid disclosure of the second confidential information, a risk of leakage of the second confidential information may be suppressed, and the ordering side  102  may be less likely to suffer from disadvantages. 
     Although the case where the information processing apparatus  100  calculates the first penalty µ once is described, the embodiment is not limited thereto. For example, the information processing apparatus  100  may repeatedly acquire the first order quantity q m  and the first profit amount d m  calculated by the order receiving side  101  and the second order quantity q r  and the second profit amount d r  calculated by the ordering side  102 , and repeatedly calculate the first penalty µ, in some cases. 
     For example, every time the information processing apparatus  100  makes a notification to the order receiving side  101 , the information processing apparatus  100  acquires the first order quantity q m  and the first profit amount d m  calculated by the order receiving side  101  in accordance with the notification. Every time the information processing apparatus  100  makes a notification to the ordering side  102 , the information processing apparatus  100  acquires the second order quantity q r  and the second profit amount d r  calculated by the ordering side  102  in accordance with the notification. Every time the first order quantity q m , the first profit amount d m , the second order quantity q r , and the second profit amount d r  are acquired, the information processing apparatus  100  calculates the first penalty µ and notifies the order receiving side  101  and the ordering side  102  of the first penalty µ. 
     Although the case where the information processing apparatus  100  operates alone is described above, the information processing apparatus  100  is not limited to this. For example, a function as the information processing apparatus  100  may be implemented by a plurality of computers, in some cases. For example, the function as the information processing apparatus  100  may be implemented by a cloud, in some cases. 
     Example of Information Processing System  200   
     Next, an example of an information processing system  200  to which the information processing apparatus  100  illustrated in  FIG.  1    is applied will be described by using  FIG.  2   . 
       FIG.  2    is an explanatory diagram illustrating an example of the information processing system  200 . As illustrated in  FIG.  2   , the information processing system  200  includes a management side apparatus  201 , an order receiving side apparatus  202 , and an ordering side apparatus  203 . 
     In the information processing system  200 , the management side apparatus  201  and the order receiving side apparatus  202  are coupled to each other via a wired or wireless network  210 . The network  210  is, for example, a local area network (LAN), a wide area network (WAN), Internet, or the like. In the information processing system  200 , the management side apparatus  201  and the ordering side apparatus  203  are coupled to each other via the wired or wireless network  210 . 
     The management side apparatus  201  is a computer that does not belong to an ordering side or an order receiving side. The ordering side is, for example, a selling side that sells a product to a consumer. The order receiving side is, for example, a manufacturing side that manufactures a product and provides the manufactured product to the ordering side. For example, the management side apparatus  201  corresponds to the information processing apparatus  100  illustrated in  FIG.  1   . 
     The management side apparatus  201  acquires the first order quantity q m  and the first profit amount d m  calculated by the order receiving side apparatus  202  by using a first parameter from the order receiving side apparatus  202 . The management side apparatus  201  acquires, from the order receiving side apparatus  202 , a first ratio π m (q m , d m )/t m  of a provisional profit π m (q m , d m ) to an original profit t m  of the order receiving side calculated by the order receiving side apparatus  202  by using the first parameter. 
     From the ordering side apparatus  203 , the management side apparatus  201  acquires the second order quantity q r  and the second profit amount d r  calculated by the ordering side apparatus  203  by using a second parameter. From the ordering side apparatus  203 , the management side apparatus  201  acquires a second ratio π r (q r , d r )/t r  of a provisional profit π r (q r , d r ) to an original profit t r  of the ordering side calculated by the ordering side apparatus  203  by using the second parameter. 
     Based on the acquired first order quantity q m , first profit amount d m , second order quantity q r , and second profit amount d r , the management side apparatus  201  calculates the commonization penalty µ. The commonization penalty µ corresponds to the first penalty µ illustrated in  FIG.  1   . The commonization penalty µ acts on the order receiving side and the ordering side so as to reduce a difference between the first order quantity q m  and the second order quantity q r  and a difference between the first profit amount d m  and the second profit amount d r . 
     Based on the acquired first ratio π m (q m , d m )/t m  and second ratio π r (q r , d r )/t r , the management side apparatus  201  calculates a profit ratio penalty v. The profit ratio penalty v acts on the order receiving side and the ordering side so as to reduce a difference between the first ratio π m (q m , d m )/t m  and the second ratio π r (q r , d r )/t r . 
     By using the first parameter including the calculated commonization penalty µ and profit ratio penalty v, the management side apparatus  201  notifies the order receiving side apparatus  202  to calculate the first order quantity q m , the first profit amount d m , and the first ratio π m (q m , d m )/t m . For example, the management side apparatus  201  transmits a notification including the commonization penalty µ and the profit ratio penalty v to the order receiving side apparatus  202 . 
     By using the second parameter including the calculated commonization penalty µ and profit ratio penalty v, the management side apparatus  201  notifies the ordering side apparatus  203  to calculate the second order quantity q r , the second profit amount d r , and the second ratio π r (q r , d r )/t r . For example, the management side apparatus  201  transmits a notification including the commonization penalty µ and the profit ratio penalty v to the ordering side apparatus  203 . 
     The management side apparatus  201  may repeatedly execute a series of processes described above. For example, the management side apparatus  201  repeatedly executes the series of processes described above until the first order quantity q m  and the first profit amount d m , the second order quantity q r  and the second profit amount d r , and the first ratio π m (q m , d m )/t m  and the second ratio π r (q r , d r )/t r  converge. The convergence is a state in which the first order quantity q m  and the second order quantity q r  coincide with each other, the first profit amount d m  and the second profit amount d r  coincide with each other, and the first ratio π m (q m , d m )/t m  and the second ratio π r (q r , d r )/t r  coincide with each other. 
     For example, the management side apparatus  201  is a server, a PC, or the like. The management side apparatus  201  may be implemented by a microcomputer, a programmable logic controller (PLC), or the like, in some cases. 
     The order receiving side apparatus  202  is a computer belonging to the order receiving side. The order receiving side apparatus  202  is used by an order receiving side user, for example. The order receiving side apparatus  202  has first confidential information to be used as a first parameter. For example, the first confidential information includes a cost of a product and the original profit t m  obtained by the order receiving side. The order receiving side apparatus  202  stores the commonization penalty µ and the profit ratio penalty v to be used as the first parameter. 
     The order receiving side apparatus  202  executes a first calculation process of calculating the first order quantity q m , the first profit amount d m , and the first ratio π m (q m , d m )/t m  by using the first parameter. The order receiving side apparatus  202  transmits the calculated first order quantity q m , first profit amount d m , and first ratio π m (q m , d m )/t m  to the management side apparatus  201 . The order receiving side apparatus  202  receives a notification including the commonization penalty µ and the profit ratio penalty v from the management side apparatus  201 . The order receiving side apparatus  202  updates the commonization penalty µ and the profit ratio penalty v included in the first parameter to the commonization penalty µ and the profit ratio penalty v included in the received notification. 
     Until the first order quantity q m , the first profit amount d m , and the first ratio π m (q m , d m )/t m  converge, the order receiving side apparatus  202  repeatedly executes a series of processes described above. For example, when the first order quantity q m , first profit amount d m , and first ratio π m (q m , d m )/t m  calculated in the previous time coincide with the first order quantity q m , first profit amount d m , and first ratio π m (q m , d m )/t m  calculated in the current time, the order receiving side apparatus  202  determines that the convergence is made. For example, the order receiving side apparatus  202  is a server, a PC, or the like. The order receiving side apparatus  202  may be implemented by a microcomputer, a PLC, or the like, in some cases. 
     The ordering side apparatus  203  is a computer belonging to the ordering side. The ordering side apparatus  203  is used by an ordering side user, for example. The ordering side apparatus  203  has second confidential information to be used as a second parameter. For example, the second confidential information includes demand information of a product and the original profit t r  obtained by the ordering side. The ordering side apparatus  203  stores the commonization penalty µ and the profit ratio penalty v to be used as the second parameter. 
     By using the second parameter, the ordering side apparatus  203  executes a second calculation process of calculating the second order quantity q r , the second profit amount d r , and the second ratio π r (q r , d r )/t r . The ordering side apparatus  203  transmits the calculated second order quantity q r , second profit amount d r , and second ratio π r (q r , d r )/t r  to the management side apparatus  201 . The ordering side apparatus  203  receives a notification including the commonization penalty µ and the profit ratio penalty v from the management side apparatus  201 . The ordering side apparatus  203  updates the commonization penalty µ and the profit ratio penalty v included in the second parameter to the commonization penalty µ and the profit ratio penalty v included in the received notification. 
     Until the second order quantity q r , the second profit amount d r , and the second ratio π r (q r , d r )/t r  converge, the ordering side apparatus  203  repeatedly executes a series of processes described above. For example, when the second order quantity q r , second profit amount d r , and second ratio π r (q r , d r )/t r  calculated in the previous time coincide with the second order quantity q r , second profit amount d r , and second ratio π r (q r , d r )/t r  calculated in the current time, the ordering side apparatus  203  determines that the convergence is made. For example, the ordering side apparatus  203  is a server, a PC, or the like. The ordering side apparatus  203  may be implemented by a microcomputer, a PLC, or the like, in some cases. 
     Application Example of Information Processing System 200 
     Next, an application example of the information processing system  200  illustrated in  FIG.  2    will be described. For example, the information processing system  200  may be applied to a case where an ordering side requests an order receiving side to provide a predetermined number of ordered physical resources. The physical resource is, for example, a product or the like. For example, the provision is selling. For example, the provision may be a loan, in some cases. Therefore, the information processing system  200  may appropriately adjust an order quantity of the physical resources to be provided by the order receiving side to the ordering side so as to maximize a profit of an entire supply chain. 
     For example, the information processing system  200  may be applied to a case where an ordering side requests an order receiving side to provide a predetermined number of ordered human resources. The human resource is, for example, an employee or the like. For example, the provision is a loan. Therefore, the information processing system  200  may appropriately adjust an order quantity of the human resources to be provided by the order receiving side to the ordering side so as to maximize a profit of an entire supply chain. 
     For example, the information processing system  200  may be applied to a case where an ordering side requests an order receiving side to provide a predetermined number of ordered spatial resources. The spatial resource is, for example, a warehouse or the like. For example, the provision is selling. For example, the provision may be a loan, in some cases. Therefore, the information processing system  200  may appropriately adjust an order quantity of the spatial resources to be provided by the order receiving side to the ordering side so as to maximize a profit of an entire supply chain. 
     For example, the information processing system  200  may be applied to a case where an ordering side requests an order receiving side to provide a predetermined number of ordered calculation resources. The calculation resource is, for example, a memory, a server, or the like. For example, the provision is selling. For example, the provision may be a loan, in some cases. Therefore, the information processing system  200  may appropriately adjust an order quantity of the calculation resources to be provided by the order receiving side to the ordering side so as to maximize a profit of an entire supply chain. 
     Hardware Configuration Example of Management Side Apparatus  201   
     Next, a hardware configuration example of the management side apparatus  201  will be described with reference to  FIG.  3   . 
       FIG.  3    is a block diagram illustrating the hardware configuration example of the management side apparatus  201 . In  FIG.  3   , the management side apparatus  201  includes a central processing unit (CPU)  301 , a memory  302 , a network interface (I/F)  303 , a recording medium I/F  304 , and a recording medium  305 . The respective components are coupled to each other through a bus  300 . 
     The CPU  301  controls the entire management side apparatus  201 . The memory  302  includes, for example, a read-only memory (ROM), a random-access memory (RAM), a flash ROM, and the like. For example, the flash ROM or the ROM stores various programs, and the RAM is used as a work area of the CPU  301 . The program stored in the memory  302  causes the CPU  301  to execute coded processes by being loaded into the CPU  301 . The memory  302  stores a profit ratio penalty and a commonization penalty. 
     The network I/F  303  is coupled to the network  210  through a communication line, and is coupled to another computer via the network  210 . The network I/F  303  controls an interface between the network  210  and internal components, and controls an input and an output of data from and to the another computer. The network I/F  303  is, for example, a modem, a LAN adapter, or the like. 
     The recording medium I/F  304  controls reading and writing of data from and to the recording medium  305  under the control of the CPU  301 . The recording medium I/F  304  is, for example, a disk drive, a solid-state drive (SSD), a Universal Serial Bus (USB) port, or the like. The recording medium  305  is a nonvolatile memory that stores data written under the control of the recording medium I/F  304 . The recording medium  305  is, for example, a disk, a semiconductor memory, a USB memory, or the like. The recording medium  305  may be detachable from the management side apparatus  201 . 
     In addition to the components described above, the management side apparatus  201  may include, for example, a keyboard, a mouse, a display, a printer, a scanner, a microphone, a speaker, and the like. The management side apparatus  201  may include a plurality of recording medium I/Fs  304  or a plurality of recording media  305 . The management side apparatus  201  may not include the recording medium I/F  304  or the recording medium  305 . 
     Hardware Configuration Example of Order Receiving Side Apparatus  202   
     Next, a hardware configuration example of the order receiving side apparatus  202  will be described with reference to  FIG.  4   . 
       FIG.  4    is a block diagram illustrating the hardware configuration example of the order receiving side apparatus  202 . In  FIG.  4   , the order receiving side apparatus  202  includes a CPU  401 , a memory  402 , a network I/F  403 , a recording medium I/F  404 , and a recording medium  405 . The respective components are coupled to each other through a bus  400 . 
     The CPU  401  controls the entire order receiving side apparatus  202 . The memory  402  includes, for example, a ROM, a RAM, a flash ROM, and the like. For example, the flash ROM or the ROM stores various programs, and the RAM is used as a work area of the CPU  401 . The programs stored in the memory  402  are loaded by the CPU  401  and cause the CPU  401  to execute coded processes. 
     The memory  402  stores an order receiving side parameter. For example, the order receiving side parameter corresponds to the first parameter described above. As the order receiving side parameter, for example, order receiving side confidential information is stored. For example, the order receiving side confidential information corresponds to the first confidential information described above. For example, the order receiving side confidential information includes a cost of a product and an original profit obtained by an order receiving side. As the order receiving side parameter, for example, a profit ratio penalty and a commonization penalty are stored. 
     The network I/F  403  is coupled to the network  210  through a communication line, and is coupled to another computer via the network  210 . The network I/F  403  controls an interface between the network  210  and internal components, and controls an input and an output of data to and from the another computer. The network I/F  403  is, for example, a modem, a LAN adapter, or the like. 
     The recording medium I/F  404  controls reading and writing of data from and to the recording medium  405  under the control of the CPU  401 . The recording medium I/F  404  is, for example, a disk drive, an SSD, a USB port, or the like. The recording medium  405  is a nonvolatile memory that stores data written under the control of the recording medium I/F  404 . The recording medium  405  is, for example, a disk, a semiconductor memory, a USB memory, or the like. The recording medium  405  may be detachable from the order receiving side apparatus  202 . 
     In addition to the components described above, the order receiving side apparatus  202  may include, for example, a keyboard, a mouse, a display, a printer, a scanner, a microphone, a speaker, and the like. The order receiving side apparatus  202  may include a plurality of recording medium I/Fs  404  or a plurality of recording media  405 . The order receiving side apparatus  202  may not include the recording medium I/F  404  or the recording medium  405 . 
     Hardware Configuration Example of Ordering Side Apparatus  203   
     Next, a hardware configuration example of the ordering side apparatus  203  will be described with reference to  FIG.  5   . 
       FIG.  5    is a block diagram illustrating the hardware configuration example of the ordering side apparatus  203 . As illustrated in  FIG.  5   , the ordering side apparatus  203  includes a CPU  501 , a memory  502 , a network I/F  503 , a recording medium I/F  504 , and a recording medium  505 . The respective components are coupled to each other through a bus  500 . 
     The CPU  501  controls the entire ordering side apparatus  203 . The memory  502  includes, for example, a ROM, a RAM, a flash ROM, and the like. For example, the flash ROM or the ROM stores various programs, and the RAM is used as a work area of the CPU  501 . The programs stored in the memory  502  are loaded by the CPU  501  and cause the CPU  501  to execute coded processes. 
     The memory  502  stores an ordering side parameter. For example, the ordering side parameter corresponds to the second parameter described above. As the ordering side parameter, for example, ordering side confidential information is stored. For example, the ordering side confidential information corresponds to the second confidential information described above. For example, the ordering side confidential information includes demand information of a consumer for a product and an original profit obtained by an ordering side. As the ordering side parameter, for example, a profit ratio penalty and a commonization penalty are stored. 
     The network I/F  503  is coupled to the network  210  through a communication line and is coupled to another computer via the network  210 . The network I/F  503  controls an interface between the network  210  and internal components, and controls an input and an output of data to and from the another computer. The network I/F  503  is, for example, a modem, a LAN adapter, or the like. 
     The recording medium I/F  504  controls reading and writing of data from and to the recording medium  505  under the control of the CPU  501 . The recording medium I/F  504  is, for example, a disk drive, an SSD, a USB port, or the like. The recording medium  505  is a nonvolatile memory that stores the data written under the control of the recording medium I/F  504 . The recording medium  505  is, for example, a disk, a semiconductor memory, a USB memory, or the like. The recording medium  505  may be detachable from the ordering side apparatus  203 . 
     In addition to the components described above, the ordering side apparatus  203  may include, for example, a keyboard, a mouse, a display, a printer, a scanner, a microphone, a speaker, and the like. The ordering side apparatus  203  may include a plurality of recording medium I/Fs  504  or a plurality of recording media  505 . The ordering side apparatus  203  may not include the recording medium I/F  504  or the recording medium  505 . 
     Example of Functional Configuration of Information Processing System  200   
     Next, an example of a functional configuration of the information processing system  200  will be described with reference to  FIG.  6   . 
       FIG.  6    is a block diagram illustrating the example of the functional configuration of the information processing system  200 . As illustrated in  FIG.  6   , the management side apparatus  201  includes a first storage unit  600 , a first acquisition unit  601 , a first calculation unit  602 , and a first output unit  603 . 
     The first storage unit  600  is implemented by a storage region such as the memory  302  or the recording medium  305  illustrated in  FIG.  3   , for example. Hereinafter, a case where the first storage unit  600  is included in the management side apparatus  201  will be described, and the embodiment is not limited thereto. For example, in some cases, the first storage unit  600  may be included in an apparatus different from the management side apparatus  201  and contents stored in the first storage unit  600  may be referred to from the management side apparatus  201 , in some cases. 
     The first acquisition unit  601  to the first output unit  603  function as an example of a control unit. For example, the functions of the first acquisition unit  601  and the first output unit  603  are implemented by causing the CPU  301  to execute a program stored in a storage region such as the memory  302  or the recording medium  305  illustrated in  FIG.  3    or by using the network I/F  303 . A process result by each functional unit is stored in, for example, the storage region such as the memory  302  or the recording medium  305  illustrated in  FIG.  3   . 
     The first storage unit  600  stores various types of information to be referred to or updated in a process performed by each functional unit. For example, the first storage unit  600  stores a first order quantity from an order receiving side to an ordering side and a first profit amount distributed from the order receiving side to the ordering side. The order receiving side is, for example, a providing side that provides a product to the ordering side. The ordering side is, for example, a selling side that sells a product to a consumer. For example, the first order quantity and the first profit amount are calculated by the order receiving side. For example, the first order quantity and the first profit amount are acquired by the first acquisition unit  601 . For example, the first storage unit  600  stores a first ratio of a provisional profit obtained by the order receiving side to an original profit obtained by the order receiving side. For example, the first ratio is calculated by the order receiving side. For example, the first ratio is acquired by the first acquisition unit  601 . 
     For example, the first storage unit  600  stores a second order quantity from the order receiving side to the ordering side and a second profit amount distributed from the order receiving side to the ordering side. For example, the second order quantity and the second profit amount are calculated by the ordering side. For example, the second order quantity and the second profit amount are acquired by the first acquisition unit  601 . For example, the first storage unit  600  stores a second ratio of a provisional profit obtained by the ordering side to an original profit obtained by the ordering side. For example, the second ratio is calculated by the ordering side. For example, the second ratio is acquired by the first acquisition unit  601 . 
     For example, the first storage unit  600  stores a first penalty acting to reduce a difference between the first order quantity and the second order quantity and a difference between the first profit amount and the second profit amount. The first penalty is the commonization penalty described above. For example, the first penalty is calculated by the first calculation unit  602 . The first storage unit  600  stores a second penalty acting to reduce a difference between the first ratio and the second ratio. The second penalty is, for example, the profit ratio penalty described above. For example, the second penalty is calculated by the first calculation unit  602 . 
     The first acquisition unit  601  acquires various types of information to be used in a process performed by each functional unit. The first acquisition unit  601  stores the acquired various types of information in the first storage unit  600 , or outputs the acquired various types of information to each functional unit. The first acquisition unit  601  may output the various types of information stored in the first storage unit  600  to each functional unit. For example, the first acquisition unit  601  acquires various types of information based on an operation input by a management side user. For example, the first acquisition unit  601  may receive the various types of information from an apparatus different from the management side apparatus  201 . 
     For example, the first acquisition unit  601  acquires, from the order receiving side, the first order quantity and the first profit amount calculated by the order receiving side by using a first parameter. For example, the first parameter includes first confidential information owned by the order receiving side. For example, the first confidential information includes a cost of a product, and the original profit obtained by the order receiving side. For example, the first penalty may be included in the first parameter. For example, the second penalty may be included in the first parameter. 
     For example, the first acquisition unit  601  acquires the first order quantity and the first profit amount by receiving the first order quantity and the first profit amount from the order receiving side. For example, the first acquisition unit  601  may acquire the first order quantity and the first profit amount calculated by the order receiving side by using the first parameter further including the first penalty, by receiving the first order quantity and the first profit amount from the order receiving side. For example, the first acquisition unit  601  may acquire the first order quantity and the first profit amount calculated by the order receiving side by using the first parameter further including the first penalty and the second penalty, by receiving the first order quantity and the first profit amount from the order receiving side. 
     For example, the first acquisition unit  601  acquires, from the ordering side, the second order quantity and the second profit amount calculated by the ordering side by using a second parameter. For example, the second parameter includes second confidential information owned by the ordering side. For example, the second confidential information includes demand information of a consumer for a product and the original profit obtained by the ordering side. For example, the first penalty may be included in the second parameter. For example, the second penalty may be included in the second parameter. 
     For example, the first acquisition unit  601  acquires the second order quantity and the second profit amount by receiving the second order quantity and the second profit amount from the ordering side. For example, the first acquisition unit  601  may acquire the second order quantity and the second profit amount calculated by the ordering side by using the second parameter further including the first penalty by receiving the second order quantity and the second profit amount from the ordering side. For example, the first acquisition unit  601  may acquire the second order quantity and the second profit amount calculated by the ordering side by using the second parameter further including the first penalty and the second penalty by receiving the second order quantity and the second profit amount from the ordering side. 
     For example, the first acquisition unit  601  acquires, from the order receiving side, the first ratio calculated by the order receiving side by using the first parameter. For example, the first acquisition unit  601  acquires the first ratio by receiving the first ratio from the order receiving side. For example, the first acquisition unit  601  may acquire the first ratio calculated by the order receiving side by using the first parameter including the first penalty, by receiving the first ratio from the order receiving side. For example, the first acquisition unit  601  may acquire the first ratio calculated by the order receiving side by using the first parameter including the first penalty and the second penalty, by receiving the first ratio from the order receiving side. 
     For example, the first acquisition unit  601  acquires, from the ordering side, the second ratio calculated by the ordering side by using the second parameter. For example, the first acquisition unit  601  acquires the second ratio by receiving the second ratio from the ordering side. For example, the first acquisition unit  601  may acquire the second ratio calculated by the ordering side by using the second parameter including the first penalty, by receiving the second ratio from the ordering side. For example, the first acquisition unit  601  may acquire the second ratio calculated by the ordering side by using the second parameter including the first penalty and the second penalty, by receiving the second ratio from the ordering side. 
     The first acquisition unit  601  may accept a start trigger for starting a process of any functional unit. For example, the start trigger is generated when a predetermined operation input is performed by the management side user. The start trigger may be, for example, receipt of predetermined information from another computer. The start trigger may be, for example, an output of predetermined information by any functional unit. 
     For example, the first acquisition unit  601  accepts the acquisition of the first order quantity, the first profit amount, the second order quantity, and the second profit amount as a start trigger for starting a process of the first calculation unit  602 . For example, the first acquisition unit  601  accepts the acquisition of the first ratio and the second ratio as a start trigger for starting the process of the first calculation unit  602 . 
     For example, every time the first order quantity, the first profit amount, the second order quantity, and the second profit amount are acquired, the first calculation unit  602  calculates the first penalty based on the first order quantity, the first profit amount, the second order quantity, and the second profit amount which are acquired in the current time. For example, the first calculation unit  602  calculates a difference value obtained by subtracting a second matrix including the acquired second order quantity and second profit amount from a first matrix including the acquired first order quantity and first profit amount. The first calculation unit  602  calculates the first penalty by adding the calculated difference value and an integral value of the difference value. 
     A specific example of calculating the first penalty will be described later with reference to  FIGS.  8  to  13   , for example. For example, the first calculation unit  602  may update the first penalty stored in the first storage unit  600  with the first penalty calculated in the current time. Therefore, the management side apparatus  201  may obtain a guideline for reducing a difference between the first order quantity and the second order quantity and a difference between the first profit amount and the second profit amount. 
     For example, every time the first ratio and the second ratio are acquired, the first calculation unit  602  calculates the second penalty based on the first ratio and the second ratio which are acquired in the current time. For example, the first calculation unit  602  calculates the second penalty by adding a difference value obtained by subtracting the acquired second ratio from the acquired first ratio and an integral value of the difference value. 
     A specific example of calculating the second penalty will be described later with reference to  FIGS.  8  to  13   , for example. For example, the first calculation unit  602  may update the second penalty stored in the first storage unit  600  with the second penalty calculated in the current time. Therefore, the management side apparatus  201  may obtain a guideline for reducing a difference between the first ratio and the second ratio. 
     The first output unit  603  outputs a process result of at least any functional unit. The output is made in, for example, a form of display on a display, print output to a printer, transmission to an external apparatus through the network I/F  303 , or storage in a storage region such as the memory  302  or the recording medium  305 . Therefore, the first output unit  603  may notify the management side user of the process result of at least any functional unit, which may consequently improve the convenience of the management side apparatus  201 . 
     For example, the first output unit  603  notifies the order receiving side to calculate the first order quantity and the first profit amount by using the first parameter including the calculated first penalty. For example, the first output unit  603  transmits a notification including the calculated first penalty to the order receiving side. Therefore, the first output unit  603  may enable the order receiving side to adjust the first order quantity and the first profit amount so that the difference between the first order quantity and the second order quantity and the difference between the first profit amount and the second profit amount are reduced. 
     For example, the first output unit  603  may notify the order receiving side to calculate the first order quantity, the first profit amount, and the first ratio by using the first parameter including the calculated first penalty and the calculated second penalty. For example, the first output unit  603  transmits a notification including the calculated first penalty and second penalty to the order receiving side. Therefore, the first output unit  603  may enable the order receiving side to adjust the first order quantity and the first profit amount so that the difference between the first order quantity and the second order quantity and the difference between the first profit amount and the second profit amount are reduced. The first output unit  603  may enable the order receiving side to adjust the first ratio so that the difference between the first ratio and the second ratio is reduced. 
     For example, the first output unit  603  notifies the ordering side to calculate the second order quantity and the second profit amount by using the second parameter including the calculated first penalty. For example, the first output unit  603  transmits a notification including the calculated first penalty to the ordering side. Therefore, the first output unit  603  may enable the ordering side to adjust the second order quantity and the second profit amount so that the difference between the first order quantity and the second order quantity and the difference between the first profit amount and the second profit amount are reduced. 
     For example, the first output unit  603  may notify the ordering side to calculate the second order quantity, the second profit amount, and the second ratio by using the second parameter including the calculated first penalty and the calculated second penalty. For example, the first output unit  603  transmits a notification including the calculated first penalty and second penalty to the ordering side. Therefore, the first output unit  603  may enable the ordering side to adjust the second order quantity and the second profit amount so that the difference between the first order quantity and the second order quantity and the difference between the first profit amount and the second profit amount are reduced. The first output unit  603  may enable the ordering side to adjust the second ratio so that the difference between the first ratio and the second ratio is reduced. 
     The order receiving side apparatus  202  includes a second storage unit  610 , a second acquisition unit  611 , a second calculation unit  612 , and a second output unit  613 . 
     The second storage unit  610  is implemented by, for example, a storage region such as the memory  402  or the recording medium  405  illustrated in  FIG.  4   . Hereinafter, a case where the second storage unit  610  is included in the order receiving side apparatus  202  will be described, and the embodiment is not limited thereto. For example, the second storage unit  610  is included in an apparatus different from the order receiving side apparatus  202 , and contents stored in the second storage unit  610  may be referred to from the order receiving side apparatus  202 , in some cases. 
     The second acquisition unit  611  to the second output unit  613  function as an example of a control unit. For example, the functions of the second acquisition unit  611  to the second output unit  613  are implemented by causing the CPU  401  to execute a program stored in the storage region such as the memory  402  or the recording medium  405  illustrated in  FIG.  4    or by using the network I/F  403 . A process result by each functional unit is stored in, for example, the storage region such as the memory  402  or the recording medium  405  illustrated in  FIG.  4   . 
     The second storage unit  610  stores various types of information to be referred to or updated in a process performed by each functional unit. For example, the second storage unit  610  stores first confidential information. 
     For example, the second storage unit  610  stores a first order quantity and a first profit amount. For example, the first order quantity and the first profit amount are calculated by the second calculation unit  612 . For example, the second storage unit  610  stores a first ratio. For example, the first ratio is calculated by the second calculation unit  612 . 
     The second storage unit  610  stores a first penalty. For example, the first penalty is acquired by the second acquisition unit  611 . The second storage unit  610  stores a second penalty. For example, the second penalty is acquired by the second acquisition unit  611 . 
     The second acquisition unit  611  acquires various types of information to be used in a process performed by each functional unit. The second acquisition unit  611  stores the acquired various types of information in the second storage unit  610 , or outputs the acquired various types of information to each functional unit. The second acquisition unit  611  may output the various types of information stored in the second storage unit  610  to each functional unit. For example, the second acquisition unit  611  acquires various types of information based on an operation input by the order receiving side user. For example, the second acquisition unit  611  may receive the various types of information from an apparatus different from the order receiving side apparatus  202 . 
     For example, the second acquisition unit  611  acquires the first penalty from the management side apparatus  201 . For example, the second acquisition unit  611  acquires the first penalty by receiving a notification including the first penalty from the management side apparatus  201 . Therefore, the second acquisition unit  611  may obtain a guideline for reducing a difference between the first order quantity and the second order quantity and a difference between the first profit amount and the second profit amount. 
     For example, the second acquisition unit  611  acquires the second penalty from the management side apparatus  201 . For example, the second acquisition unit  611  acquires the second penalty by receiving a notification including the second penalty from the management side apparatus  201 . Therefore, the second acquisition unit  611  may obtain a guideline for reducing a difference between the first ratio and the second ratio. 
     The second acquisition unit  611  may accept a start trigger for starting a process of any functional unit. For example, the start trigger is generated when a predetermined operation input is performed by an order receiving side user. The start trigger may be, for example, receipt of predetermined information from another computer. The start trigger may be, for example, an output of predetermined information by any functional unit. For example, the second acquisition unit  611  accepts the acquisition of the first penalty as a start trigger for starting a process of the second calculation unit  612 . For example, the second acquisition unit  611  accepts the acquisition of the second penalty as a start trigger for starting the process of the second calculation unit  612 . 
     For example, the second calculation unit  612  calculates the first order quantity and the first profit amount by using a first parameter including at least the first confidential information. For example, the second calculation unit  612  may calculate the first order quantity and the first profit amount by using the first parameter further including the acquired first penalty. For example, the second calculation unit  612  may calculate the first order quantity and the first profit amount by using the first parameter further including the acquired first penalty and second penalty. 
     A specific example of calculating the first order quantity and the first profit amount will be described later with reference to  FIGS.  8  to  13   , for example. Therefore, the second calculation unit  612  may enable the management side apparatus  201  to calculate the first penalty for appropriately adjusting the first order quantity and the first profit amount, without making the first confidential information public. 
     For example, the second calculation unit  612  calculates the first ratio by using the first parameter including at least the first confidential information. For example, the second calculation unit  612  may calculate the first ratio by using the first parameter further including the acquired first penalty. For example, the second calculation unit  612  may calculate the first ratio by using the first parameter further including the acquired first penalty and second penalty. 
     A specific example of calculating the first ratio will be described later with reference to  FIGS.  8  to  13   , for example. Therefore, the second calculation unit  612  may enable the management side apparatus  201  to calculate the first penalty for appropriately adjusting the first ratio, without making the first confidential information public. 
     The second output unit  613  outputs a process result of at least any functional unit. The output is made in, for example, a form of display on a display, print output to a printer, transmission to an external apparatus through the network I/F  403 , or storage in a storage region such as the memory  402  or the recording medium  405 . Therefore, the second output unit  613  may notify the order receiving side user of the process result of at least any functional unit, which may consequently improve the convenience of the order receiving side apparatus  202 . 
     For example, the second output unit  613  transmits the calculated first order quantity and first profit amount to the management side apparatus  201 . For example, every time the first order quantity and the first profit amount are calculated, the second output unit  613  transmits the calculated first order quantity and first profit amount to the management side apparatus  201 . Therefore, the second output unit  613  may enable the management side apparatus  201  to calculate the first penalty. 
     For example, the second output unit  613  transmits the calculated first ratio to the management side apparatus  201 . For example, every time the first ratio is calculated, the second output unit  613  transmits the calculated first ratio to the management side apparatus  201 . Therefore, the second output unit  613  may enable the management side apparatus  201  to calculate the second penalty. 
     For example, the second output unit  613  may determine whether or not the first order quantity and the first profit amount converge. For example, in a case where the first penalty is a specific value indicating that the first order quantity and the second order quantity coincide with each other and the first profit amount and the second profit amount coincide with each other, the second output unit  613  determines that the convergence is made. For example, in a case where the first penalty is not the specific value, the second output unit  613  determines that the convergence is not made. 
     For example, in a case where the first order quantity and first profit amount calculated in the current time coincide with the first order quantity and first profit amount calculated in the previous time, the second output unit  613  may determine that the convergence is made. For example, in a case where the first order quantity and first profit amount calculated in the current time do not coincide with the first order quantity and first profit amount calculated in the previous time, the second output unit  613  may determine that the convergence is not made. 
     For example, in a case where it is determined that the convergence is made, the second output unit  613  outputs the first order quantity and the first profit amount so that the order receiving side user may refer to the first order quantity and the first profit amount. Therefore, the second output unit  613  enables the order receiving side user to refer to the first order quantity and the first profit amount for maximizing a profit of an entire supply chain. 
     The ordering side apparatus  203  includes a third storage unit  620 , a third acquisition unit  621 , a third calculation unit  622 , and a third output unit  623 . 
     The third storage unit  620  is implemented by, for example, a storage region such as the memory  502  or the recording medium  505  illustrated in  FIG.  5   . Hereinafter, a case where the third storage unit  620  is included in the ordering side apparatus  203  will be described, and the embodiment is not limited thereto. For example, the third storage unit  620  is included in an apparatus different from the ordering side apparatus  203 , and contents stored in the third storage unit  620  may be referred to from the ordering side apparatus  203 , in some cases. 
     The third acquisition unit  621  to the third output unit  623  function as an example of a control unit. For example, the functions of the third acquisition unit  621  to the third output unit  623  are implemented by causing the CPU  501  to execute a program stored in the storage region such as the memory  502  or the recording medium  505  illustrated in  FIG.  5    or by using the network I/F  503 . A process result by each functional unit is stored in the storage region such as the memory  502  or the recording medium  505  illustrated in  FIG.  5   , for example. 
     The third storage unit  620  stores various types of information to be referred to or updated in a process performed by each functional unit. For example, the third storage unit  620  stores second confidential information. 
     For example, the third storage unit  620  stores a second order quantity and a second profit amount. For example, the second order quantity and the second profit amount are calculated by the third calculation unit  622 . For example, the third storage unit  620  stores a second ratio. For example, the second ratio is calculated by the third calculation unit  622 . 
     The third storage unit  620  stores a first penalty. For example, the first penalty is acquired by the third acquisition unit  621 . The third storage unit  620  stores a second penalty. For example, the second penalty is acquired by the third acquisition unit  621 . 
     The third acquisition unit  621  acquires various types of information to be used in a process performed by each functional unit. The third acquisition unit  621  stores the acquired various types of information in the third storage unit  620 , or outputs the acquired various types of information to each functional unit. The third acquisition unit  621  may output the various types of information stored in the third storage unit  620  to each functional unit. For example, the third acquisition unit  621  acquires various types of information based on an operation input by an ordering side user. For example, the third acquisition unit  621  may receive the various types of information from an apparatus different from the ordering side apparatus  203 . 
     For example, the third acquisition unit  621  acquires the first penalty from the management side apparatus  201 . For example, the third acquisition unit  621  acquires the first penalty by receiving a notification including the first penalty from the management side apparatus  201 . Therefore, the third acquisition unit  621  may obtain a guideline for reducing a difference between the first order quantity and the second order quantity and a difference between the first profit amount and the second profit amount. 
     For example, the third acquisition unit  621  acquires the second penalty from the management side apparatus  201 . For example, the third acquisition unit  621  acquires the second penalty by receiving a notification including the second penalty from the management side apparatus  201 . Therefore, the third acquisition unit  621  may obtain a guideline for reducing a difference between the first ratio and the second ratio. 
     The third acquisition unit  621  may accept a start trigger for starting a process of any functional unit. For example, the start trigger is generated when a predetermined operation input is performed by the ordering side user. The start trigger may be, for example, receipt of predetermined information from another computer. The start trigger may be, for example, an output of predetermined information by any functional unit. For example, the third acquisition unit  621  accepts the acquisition of the first penalty as a start trigger for starting a process of the third calculation unit  622 . For example, the third acquisition unit  621  accepts the acquisition of the second penalty as a start trigger for starting the process of the third calculation unit  622 . 
     For example, the third calculation unit  622  calculates the second order quantity and the second profit amount by using a second parameter including at least the second confidential information. For example, the third calculation unit  622  may calculate the second order quantity and the second profit amount by using the second parameter further including the acquired first penalty. For example, the third calculation unit  622  may calculate the second order quantity and the second profit amount by using the second parameter further including the acquired first penalty and second penalty. 
     A specific example of calculating the second order quantity and the second profit amount will be described later with reference to  FIGS.  8  to  13   , for example. Therefore, the third calculation unit  622  may enable the management side apparatus  201  to calculate the first penalty for appropriately adjusting the second order quantity and the second profit amount, without making the second confidential information public. 
     For example, the third calculation unit  622  calculates the second ratio by using the second parameter including at least the second confidential information. For example, the third calculation unit  622  may calculate the second ratio by using the second parameter further including the acquired first penalty. For example, the third calculation unit  622  may calculate the second ratio by using a second parameter further including the acquired first penalty and second penalty. 
     A specific example of calculating the second ratio will be described later with reference to  FIGS.  8  to  13   , for example. Therefore, the third calculation unit  622  may enable the management side apparatus  201  to calculate the first penalty for appropriately adjusting the second ratio, without making the second confidential information public. 
     The third output unit  623  outputs a process result of at least any functional unit. The output is made in, for example, a form of display on a display, print output to a printer, transmission to an external apparatus through the network I/F  503 , or storage in a storage region such as the memory  502  or the recording medium  505 . Therefore, the third output unit  623  may notify the ordering side user of the process result in at least any functional unit, which may consequently improve the convenience of the ordering side apparatus  203 . 
     For example, the third output unit  623  transmits the calculated second order quantity and second profit amount to the management side apparatus  201 . For example, every time the second order quantity and the second profit amount are calculated, the third output unit  623  transmits the calculated second order quantity and second profit amount to the management side apparatus  201 . Therefore, the third output unit  623  may enable the management side apparatus  201  to calculate the first penalty. 
     For example, the third output unit  623  transmits the calculated second ratio to the management side apparatus  201 . For example, every time the second ratio is calculated, the third output unit  623  transmits the calculated second ratio to the management side apparatus  201 . Therefore, the third output unit  623  may enable the management side apparatus  201  to calculate the second penalty. 
     For example, the third output unit  623  may determine whether or not the second order quantity and the second profit amount converge. For example, the third output unit  623  determines that the convergence is made in a case where the first penalty is a specific value indicating that the second order quantity and the second order quantity coincide with each other and the second profit amount and the second profit amount coincide with each other. For example, in a case where the first penalty is not the specific value, the third output unit  623  determines that the convergence is not made. 
     For example, the third output unit  623  may determine that the convergence is made in a case where the second order quantity and the second profit amount calculated in the current time coincide with the second order quantity and the second profit amount calculated in the previous time. For example, in a case where the second order quantity and the second profit amount calculated in the current time do not coincide with the second order quantity and the second profit amount calculated in the previous time, the third output unit  623  may determine that the convergence is not made. 
     For example, in a case where it is determined that the convergence is made, the third output unit  623  outputs the second order quantity and the second profit amount so that the ordering side user may refer to the second order quantity and the second profit amount. Therefore, the third output unit  623  enables the ordering side user to refer to the second order quantity and the second profit amount for maximizing a profit of an entire supply chain. 
     Specific Example of Functional Configuration of Information Processing System  200   
     Next, a specific example of the functional configuration of the information processing system  200  will be described with reference to  FIG.  7   . 
       FIG.  7    is a block diagram illustrating the specific example of the functional configuration of the information processing system  200 . As illustrated in  FIG.  7   , the management side apparatus  201  includes a commonization calculation unit  701  and a profit ratio adjustment unit  702 . 
     For example, the commonization calculation unit  701  receives a provisional order amount and a provisional distribution amount of an order receiving side from an update calculation unit  711  of the order receiving side. For example, the commonization calculation unit  701  receives a provisional order amount of an ordering side and a provisional distribution amount of the ordering side from an update calculation unit  721  of the ordering side. For example, the commonization calculation unit  701  calculates a commonization penalty, based on the provisional order amount of the order receiving side, the provisional distribution amount of the order receiving side, the provisional order amount of the ordering side, and the provisional distribution amount of the ordering side. For example, the commonization calculation unit  701  transmits the calculated commonization penalty to the update calculation unit  711  and the update calculation unit  721 . For example, the commonization calculation unit  701  is implemented by computation units  901  to  903 , which will be described later in  FIG.  9    or computation units  1301  to  1303 , which will be described later in  FIG.  13   . 
     For example, the profit ratio adjustment unit  702  receives sharing information of the order receiving side from a sharing information calculation unit  714 . For example, the profit ratio adjustment unit  702  receives sharing information of the ordering side from a sharing information calculation unit  724 . For example, the profit ratio adjustment unit  702  calculates a profit ratio penalty, based on the acquired sharing information of the order receiving side and sharing information of the ordering side. For example, the profit ratio adjustment unit  702  transmits the calculated profit ratio penalty to the update calculation unit  711  and the update calculation unit  721 . For example, the profit ratio adjustment unit  702  is implemented by computation units  911  to  913 , which will be described later in  FIG.  9    or computation units  1311  to  1313 , which will be described later in  FIG.  13   . 
     As illustrated in  FIG.  7   , the order receiving side apparatus  202  includes order receiving side confidential information  710 . The order receiving side apparatus  202  includes the update calculation unit  711 , an achievement degree calculation unit  712 , an adjustment term calculation unit  713 , and the sharing information calculation unit  714 . 
     For example, the update calculation unit  711  reads the order receiving side confidential information  710 . For example, the update calculation unit  711  receives the commonization penalty from the commonization calculation unit  701 . For example, the update calculation unit  711  receives the profit ratio penalty from the profit ratio adjustment unit  702 . For example, the update calculation unit  711  receives a target profit penalty from the adjustment term calculation unit  713 . For example, the update calculation unit  711  calculates the provisional order amount of the order receiving side and the provisional distribution amount of the order receiving side, based on the order receiving side confidential information  710 , the commonization penalty, the profit ratio penalty, and the target profit penalty. For example, the update calculation unit  711  transmits the calculated provisional order amount of the order receiving side and the calculated provisional distribution amount of the order receiving side to the commonization calculation unit  701 , the achievement degree calculation unit  712 , and the sharing information calculation unit  714 . For example, the update calculation unit  711  is implemented by computation units  1011  to  1018 , which will be described later in  FIG.  10   . 
     For example, the achievement degree calculation unit  712  reads the order receiving side confidential information  710 . For example, the achievement degree calculation unit  712  receives the provisional order amount of the order receiving side and the provisional distribution amount of the order receiving side from the update calculation unit  711 . For example, the achievement degree calculation unit  712  calculates a target profit achievement degree, based on the order receiving side confidential information  710 , the provisional order amount of the order receiving side, and the provisional distribution amount of the order receiving side. For example, the achievement degree calculation unit  712  transmits the calculated target profit achievement degree to the adjustment term calculation unit  713 . For example, the achievement degree calculation unit  712  is implemented by a computation unit  1021 , which will be described later in  FIG.  10   . 
     For example, the adjustment term calculation unit  713  reads the order receiving side confidential information  710 . For example, the adjustment term calculation unit  713  receives the target profit achievement degree from the achievement degree calculation unit  712 . For example, the adjustment term calculation unit  713  calculates the target profit penalty, based on the order receiving side confidential information  710  and the target profit achievement degree. For example, the adjustment term calculation unit  713  transmits the calculated target profit penalty to the update calculation unit  711 . For example, the adjustment term calculation unit  713  is implemented by computation units  1031  and  1032 , which will be described later in  FIG.  10   . 
     For example, the sharing information calculation unit  714  reads the order receiving side confidential information  710 . For example, the sharing information calculation unit  714  receives the provisional order amount of the order receiving side and the provisional distribution amount of the order receiving side from the update calculation unit  711 . For example, the sharing information calculation unit  714  calculates the sharing information of the order receiving side, based on the order receiving side confidential information  710 , the provisional order amount of the order receiving side, and the provisional distribution amount of the order receiving side. For example, the sharing information calculation unit  714  transmits the calculated sharing information of the order receiving side to the profit ratio adjustment unit  702 . For example, the sharing information calculation unit  714  is implemented by a computation unit  1041 , which will be described later in  FIG.  10   . 
     As illustrated in  FIG.  7   , the ordering side apparatus  203  includes ordering side confidential information  720 . An ordering side apparatus  203  includes the update calculation unit  721 , an achievement degree calculation unit  722 , an adjustment term calculation unit  723 , and the sharing information calculation unit  724 . 
     For example, the update calculation unit  721  reads the ordering side confidential information  720 . For example, the update calculation unit  721  receives the commonization penalty from the commonization calculation unit  701 . For example, the update calculation unit  721  receives the profit ratio penalty from the profit ratio adjustment unit  702 . For example, the update calculation unit  721  receives the target profit penalty from the adjustment term calculation unit  723 . For example, the update calculation unit  721  calculates the provisional order amount of the ordering side and the provisional distribution amount of the ordering side, based on the ordering side confidential information  720 , the commonization penalty, the profit ratio penalty, and the target profit penalty. For example, the update calculation unit  721  transmits the calculated provisional order amount of the ordering side and the calculated provisional distribution amount of the ordering side to the commonization calculation unit  701 , the achievement degree calculation unit  722 , and the sharing information calculation unit  724 . For example, the update calculation unit  721  is implemented by computation units  1111  to  1118 , which will be described later in  FIG.  11   . 
     For example, the achievement degree calculation unit  722  reads the ordering side confidential information  720 . For example, the achievement degree calculation unit  722  receives the provisional order amount of the ordering side and the provisional distribution amount of the ordering side from the update calculation unit  721 . For example, the achievement degree calculation unit  722  calculates a target profit achievement degree, based on the ordering side confidential information  720 , the provisional order amount of the ordering side, and the provisional distribution amount of the ordering side. For example, the achievement degree calculation unit  722  transmits the calculated target profit achievement degree to the adjustment term calculation unit  723 . For example, the achievement degree calculation unit  722  is implemented by a computation unit  1121 , which will be described later in  FIG.  11   . 
     For example, the adjustment term calculation unit  723  reads the ordering side confidential information  720 . For example, the adjustment term calculation unit  723  receives the target profit achievement degree from the achievement degree calculation unit  722 . For example, the adjustment term calculation unit  723  calculates a target profit penalty, based on the ordering side confidential information  720  and the target profit achievement degree. For example, the adjustment term calculation unit  723  transmits the calculated target profit penalty to the update calculation unit  721 . For example, the adjustment term calculation unit  723  is implemented by computation units  1131  and  1132 , which will be described later in  FIG.  11   . 
     For example, the sharing information calculation unit  724  reads the ordering side confidential information  720 . For example, the sharing information calculation unit  724  receives the provisional order amount of the ordering side and the provisional distribution amount of the ordering side from the update calculation unit  721 . For example, the sharing information calculation unit  724  calculates sharing information of the ordering side, based on the ordering side confidential information  720 , the provisional order amount of the ordering side, and the provisional distribution amount of the ordering side. For example, the sharing information calculation unit  724  transmits the calculated sharing information of the ordering side to the profit ratio adjustment unit  702 . For example, the sharing information calculation unit  724  is implemented by a computation unit  1141 , which will be described later in  FIG.  11   . 
     First Operation Example of Information Processing System  200   
     A first operation example of the information processing system  200  will be described with reference to  FIGS.  8  to  11   . 
       FIG.  8    to  FIG.  11    are explanatory diagrams illustrating the first operation example of the information processing system  200 . As illustrated in  FIG.  8   , the information processing system  200  is applied to a supply chain in which a retailer as an ordering side purchases a product from a manufacturer as an order receiving side, and the retailer as the ordering side sells the product to a consumer. 
     In the example illustrated in  FIG.  8   , there are the order receiving side apparatus  202  owned by the manufacturer, the ordering side apparatus  203  owned by the retailer, and the management side apparatus  201  belonging to neither the manufacturer nor the retailer. 
     The order receiving side apparatus  202  acquires confidential information of the manufacturing side, based on an operation input of a manufacturing side user. The confidential information of the manufacturing side includes a manufacturing cost of a product, a provisional profit of the manufacturing side, and the like. The order receiving side apparatus  202  stores a commonization penalty and a profit ratio penalty. The commonization penalty and the profit ratio penalty are initialized as predetermined values. For example, the predetermined value is 0. 
     Every time the commonization penalty is received from the management side apparatus  201 , the order receiving side apparatus  202  updates the stored commonization penalty with the received commonization penalty. Every time the profit ratio penalty is received from the management side apparatus  201 , the order receiving side apparatus  202  updates the stored profit ratio penalty with the received profit ratio penalty. 
     Based on the confidential information of the manufacturing side, the commonization penalty, and the profit ratio penalty, the order receiving side apparatus  202  calculates a provisional order amount of the manufacturing side, a provisional distribution amount of the manufacturing side, and sharing information of a profit ratio of the manufacturing side. The provisional order amount of the manufacturing side indicates an order amount of a product ordered from the retail side to the manufacturing side, which is provisionally determined by the manufacturing side. The provisional distribution amount of the manufacturing side indicates a profit amount to be distributed from the manufacturing side to the retail side, which is provisionally determined by the manufacturing side. The sharing information of the profit ratio of the manufacturing side indicates a profit ratio of the provisional profit of the manufacturing side to an original profit of the manufacturing side. 
     Until the provisional order amount of the manufacturing side, the provisional distribution amount of the manufacturing side, and the profit ratio of the manufacturing side converge, the order receiving side apparatus  202  may recalculate the provisional order amount of the manufacturing side, the provisional distribution amount of the manufacturing side, and the sharing information of the profit ratio of the manufacturing side every time the commonization penalty and the profit ratio penalty are updated. The order receiving side apparatus  202  transmits the calculated provisional order amount of the manufacturing side, the calculated provisional distribution amount of the manufacturing side, and the calculated sharing information of the profit ratio of the manufacturing side to the management side apparatus  201  via the network  210 . 
     The ordering side apparatus  203  acquires confidential information of the retail side, based on an operation input of a retail side user. The confidential information of the retail side includes demand information of the consumer for the product, a provisional profit of the retail side, and the like. For example, the demand information includes a probability distribution indicating the demand of the consumer. The ordering side apparatus  203  stores a commonization penalty and a profit ratio penalty. The commonization penalty and the profit ratio penalty are initialized as predetermined values. For example, the predetermined value is 0. 
     Every time the commonization penalty is received from the management side apparatus  201 , the ordering side apparatus  203  updates the stored commonization penalty with the received commonization penalty. Every time the profit ratio penalty is received from the management side apparatus  201 , the ordering side apparatus  203  updates the stored profit ratio penalty with the received profit ratio penalty. 
     Based on the confidential information of the retail side, the commonization penalty, and the profit ratio penalty, the ordering side apparatus  203  calculates a provisional order amount of the retail side, a provisional distribution amount of the retail side, and sharing information of a profit ratio of the retail side. The provisional order amount of the retail side indicates an order amount of a product ordered from the retail side to the manufacturing side, which is provisionally determined by the retail side. The provisional distribution amount of the retail side indicates a profit amount to be distributed from the manufacturing side to the retail side, which is provisionally determined by the retail side. The sharing information of the profit ratio of the retail side indicates a profit ratio of the provisional profit of the retail side to an original profit of the retail side. 
     Until the provisional order amount of the retail side, the provisional distribution amount of the retail side, and the profit ratio of the retail side converge, the ordering side apparatus  203  may recalculate the provisional order amount of the retail side, the provisional distribution amount of the retail side, and the sharing information of the profit ratio of the retail side every time the commonization penalty and the profit ratio penalty are updated. The ordering side apparatus  203  transmits the calculated provisional order amount of the retail side, the calculated provisional distribution amount of the retail side, and the calculated sharing information of the profit ratio of the retail side to the management side apparatus  201  via the network  210 . 
     The management side apparatus  201  receives the provisional order amount of the manufacturing side and the provisional distribution amount of the manufacturing side from the order receiving side apparatus  202  via the network  210 . The management side apparatus  201  receives the provisional order amount of the retail side and the provisional distribution amount of the retail side from the ordering side apparatus  203  via the network  210 . 
     Every time the provisional order amount of the manufacturing side, the provisional distribution amount of the manufacturing side, the provisional order amount of the retail side, and the provisional distribution amount of the retail side are received, the management side apparatus  201  calculates a commonization penalty. For example, the management side apparatus  201  calculates the commonization penalty, based on the provisional order amount of the manufacturing side, the provisional distribution amount of the manufacturing side, the provisional order amount of the retail side, and the provisional distribution amount of the retail side. 
     By transmitting the calculated commonization penalty to the order receiving side apparatus  202 , the management side apparatus  201  updates the commonization penalty stored in the order receiving side apparatus  202 . By transmitting the calculated commonization penalty to the ordering side apparatus  203 , the management side apparatus  201  updates the commonization penalty stored in the ordering side apparatus  203 . 
     The management side apparatus  201  receives the sharing information of the profit ratio of the manufacturing side from the order receiving side apparatus  202  via the network  210 . The sharing information of the profit ratio of the retail side is received from the ordering side apparatus  203  via the network  210 . 
     Every time the sharing information of the profit ratio of the manufacturing side and the sharing information of the profit ratio of the retail side are received, the management side apparatus  201  calculates a profit ratio penalty, based on the sharing information of the profit ratio of the manufacturing side and the sharing information of the profit ratio of the retail side. 
     By transmitting the calculated profit ratio penalty to the order receiving side apparatus  202 , the management side apparatus  201  updates the profit ratio penalty stored in the order receiving side apparatus  202 . By transmitting the calculated profit ratio penalty to the ordering side apparatus  203 , the management side apparatus  201  updates the profit ratio penalty stored in the ordering side apparatus  203 . Next, the description continues with reference to  FIG.  9   , and a specific example of computation by the management side apparatus  201  will be described. 
     As illustrated in  FIG.  9   , the order receiving side apparatus  202  has confidential information of the manufacturing side. For example, the confidential information of the manufacturing side includes a manufacturing cost c and an original profit t m  of the manufacturing side. The order receiving side apparatus  202  has the commonization penalty µ and the profit ratio penalty v. 
     Based on the confidential information of the manufacturing side, the commonization penalty µ, and the profit ratio penalty v, the order receiving side apparatus  202  calculates a provisional order amount q m  of the manufacturing side and a provisional distribution amount d m  of the manufacturing side. Based on the confidential information of the manufacturing side, the provisional order amount q m  of the manufacturing side, and the provisional distribution amount d m  of the manufacturing side, the order receiving side apparatus  202  calculates a profit ratio π m (q m , d m )/t m  of the provisional profit π m (q m , d m ) to the original profit t m  of the manufacturing side. 
     The order receiving side apparatus  202  transmits a matrix [q m  d m ] T  including the calculated provisional order amount q m  of the manufacturing side and the provisional distribution amount d m  of the manufacturing side to the management side apparatus  201 . The order receiving side apparatus  202  transmits the calculated profit ratio π m (q m , d m )/t m  of the manufacturing side to the management side apparatus  201 . A specific example of computation by the order receiving side apparatus  202  will be described later with reference to, for example,  FIG.  10   . 
     As illustrated in  FIG.  9   , the ordering side apparatus  203  has confidential information of the retail side. For example, the confidential information of the retail side includes a consumer demand function f (x)  and the original profit t r  of the retail side. The ordering side apparatus  203  has the commonization penalty µ and the profit ratio penalty v. 
     Based on the confidential information of the retail side, the commonization penalty µ, and the profit ratio penalty v, the ordering side apparatus  203  calculates a provisional order amount q r  of the retail side and a provisional distribution amount d r  of the retail side. The ordering side apparatus  203  calculates a profit ratio π r (q r , d r )/t r  of the provisional profit π r (q r , d r ) to the original profit t r  of the retail side, based on confidential information of the retail side, a provisional order amount q r  of the retail side, and the provisional distribution amount d r  of the retail side. 
     The ordering side apparatus  203  transmits a matrix [q r  d r ] T  including the calculated provisional order amount of the retail side q r  and the calculated provisional distribution amount of the retail side d r  to the management side apparatus  201 . The ordering side apparatus  203  transmits the calculated profit ratio π r (q r , d r )/t r  of the retail side to the management side apparatus  201 . A specific example of computation by the ordering side apparatus  203  will be described later with reference to, for example,  FIG.  11   . 
     As illustrated in  FIG.  9   , the management side apparatus  201  includes the computation units  901  to  903 . The management side apparatus  201  receives the matrix [q m  d m ] T  of the manufacturing side from the order receiving side apparatus  202 . A management side apparatus  201  receives the matrix [q r  d r ] T  of the retail side from the ordering side apparatus  203 . 
     The computation unit  901  calculates a difference obtained by subtracting the matrix [q r  d r ] T  of the retail side from the matrix [q m  d m ] T  of the manufacturing side, and transmits the difference to the computation units  902  and  903 . The computation unit  902  receives the difference, calculates an integral value of the received difference, and transmits the integral value to the computation unit  903 . By adding the difference and the integral value, the computation unit  903  calculates the commonization penalty µ. The management side apparatus  201  transmits the commonization penalty µ to the order receiving side apparatus  202  and the ordering side apparatus  203 . 
     As illustrated in  FIG.  9   , the management side apparatus  201  includes the computation units  911  to  913 . The management side apparatus  201  receives the profit ratio π m (q m , d m )/t m  of the manufacturing side from the order receiving side apparatus  202 . The management side apparatus  201  receives the profit ratio π r (q r , d r )/t r  of the retail side from the ordering side apparatus  203 . 
     The computation unit  911  calculates a difference obtained by subtracting the profit ratio π r (q r , d r )/t r  of the retail side from the profit ratio π m (q m , d m )/t m  of the manufacturing side, and transmits the difference to the computation units  912  and  913 . The computation unit  912  receives the difference, calculates an integral value of the received difference, and transmits the integral value to the computation unit  913 . By adding the difference and the integral value, the computation unit  913  calculates the profit ratio penalty v. The management side apparatus  201  transmits the profit ratio penalty v to the order receiving side apparatus  202  and the ordering side apparatus  203 . 
     Therefore, the management side apparatus  201  may cause the manufacturing side to adjust the provisional order amount q m  of the manufacturing side and may cause the retail side to adjust the provisional order amount q r  of the retail side so that the provisional order amount q m  of the manufacturing side and the provisional order amount q r  of the retail side coincide with each other. The management side apparatus  201  may cause the manufacturing side to adjust the provisional distribution amount d m  of the manufacturing side and cause the retail side to adjust the provisional distribution amount d r  of the retail side so that the provisional distribution amount d m  of the manufacturing side and the provisional distribution amount d r  of the retail side coincide with each other. The management side apparatus  201  may maximize a profit of the entire supply chain. 
     The management side apparatus  201  may cause the manufacturing side to adjust the provisional profit π m (q m , d m ) of the manufacturing side so that the profit ratio π m (q m , d m )/t m  of the manufacturing side and the profit ratio π r (q r , d r )/t r  of the retail side coincide with each other. The management side apparatus  201  may cause the retail side to adjust the provisional profit π r (q r , d r ) of the retail side so that the profit ratio π m (q m , d m )/t m  of the manufacturing side and the profit ratio π r (q r , d r )/t r  of the retail side coincide with each other. For maximizing the profit of the entire supply chain, the management side apparatus  201  may enable the manufacturing side and the retail side to fairly maximize the profits. Next, the description continues with reference to  FIG.  10   , and a specific example of computation of the order receiving side apparatus  202  will be described. 
     As illustrated in  FIG.  10   , the order receiving side apparatus  202  includes the computation units  1011  to  1018 , the computation unit  1021 , the computation units  1031  and  1032 , and the computation unit  1041 . The order receiving side apparatus  202  stores confidential information of the manufacturing side including the manufacturing cost c and the original profit t m  of the manufacturing side. The order receiving side apparatus  202  receives the commonization penalty µ from the management side apparatus  201 . The order receiving side apparatus  202  receives the profit ratio penalty v from the management side apparatus  201 . 
     The computation unit  1011  accepts the profit ratio penalty v as an input. The computation unit  1011  transmits a value obtained by multiplying the profit ratio penalty v, which is the input, by a value of the following equation (1) to the computation unit  1012 , as an output. 
     
       
         
           
             
               ∇ 
               
                 
                   X 
                   m 
                 
               
             
             
               π 
               m 
             
             
               
                 
                   
                     
                       x 
                       m 
                     
                   
                 
               
               / 
               
                 
                   t 
                   m 
                 
               
             
           
         
       
     
     . 
     The computation unit  1012  accepts the commonization penalty µ and the output of the computation unit  1011  as inputs. The computation unit  1012  transmits a value obtained by making each value, which is the input, negative and adding up each value to the computation unit  1013  as an output. 
     The computation unit  1013  accepts the output of the computation unit  1012  and an output of the computation unit  1018  as inputs. The output of the computation unit  1018  will be described later. The computation unit  1013  transmits a value obtained by subtracting the output of the computation unit  1018 , which is the input, from the output of the computation unit  1012 , which is the input, to the computation unit  1014  as an output. 
     The computation unit  1014  accepts the output of the computation unit  1013  and an output of the computation unit  1016  as inputs. The output of the computation unit  1016  will be described later. The computation unit  1014  transmits a value obtained by subtracting the output of the computation unit  1016 , which is the input, from the output of the computation unit  1013 , which is the input, to the computation unit  1015  as an output. 
     The computation unit  1015  accepts the output of the computation unit  1014  as an input. The computation unit  1015  transmits a value obtained by integrating the output of the computation unit  1014 , which is the input, to the computation unit  1016 , the computation unit  1021 , and the computation unit  1041  as outputs. The order receiving side apparatus  202  transmits the output of the computation unit  1015  to the management side apparatus  201  as the matrix [q m  d m ] T  including the provisional order amount q m  of the manufacturing side and the provisional distribution amount d m  of the manufacturing side. 
     The computation unit  1016  accepts the output of the computation unit  1015  as an input. The computation unit  1016  transmits, as an output, a value obtained by substituting the output of the computation unit  1015 , which is the input, into (▪) in the following equation (2) to the computation unit  1014 .  
     
       
         
           
             − 
             
               ∇ 
               
                 
                   x 
                   m 
                 
               
             
             
               π 
               m 
             
             
               ⋅ 
             
           
         
       
     
     The computation unit  1021  accepts the output of the computation unit  1015  as an input. The computation unit  1021  transmits, as an output, a value obtained by substituting the output of the computation unit  1015 , which is the input, into (▪) of the following equation (3), to the computation unit  1031 .  
     
       
         
           
             
               t 
               m 
             
             − 
             
               π 
               m 
             
             . 
             
               ⋅ 
             
           
         
       
     
     The computation unit  1031  accepts the output of the computation unit  1021  as an input. The computation unit  1031  transmits, as an output, a value obtained by substituting the output of the computation unit  1021 , which is the input, into (▪) of the following equation (4), to the computation unit  1032 .  
     
       
         
           
             
               λ 
               m 
             
             ⋅ 
             
               ⋅ 
             
           
         
       
     
     The computation unit  1032  accepts the output of the computation unit  1031  as an input. The computation unit  1032  transmits a target profit penalty λ m  obtained by integrating and doubling the output of the computation unit  1031  to the computation unit  1017  as an output. 
     The computation unit  1017  accepts the output of the computation unit  1032  as an input. The computation unit  1017  transmits, as an output, a value obtained by substituting the output of the computation unit  1032 , which is the input, into (▪) of the following equation (5), to the computation unit  1018 .  
     
       
         
           
             
               ⋅ 
             
             ⋅ 
             
               ⋅ 
             
           
         
       
     
     The computation unit  1018  accepts the output of the computation unit  1017  as an input. The computation unit  1018  transmits a value obtained by multiplying a value of the following equation (6) by the output of the computation unit  1017 , which is the input, to the computation unit  1013  as an output.  
     
       
         
           
             
               ∇ 
               
                 
                   x 
                   m 
                 
               
             
             
               π 
               m 
             
             
               
                 
                   x 
                   m 
                 
               
             
           
         
       
     
     The computation unit  1041  accepts the output of the computation unit  1015  as an input. The computation unit  1041  outputs a value obtained by substituting the output of the computation unit  1015 , which is the input, into (▪) of the following equation (7). The order receiving side apparatus  202  transmits the output of the computation unit  1041  as the profit ratio ⊓ m (q m , d m )/t m  of the manufacturing side to the management side apparatus  201 .  
     
       
         
           
             
               
                 
                   π 
                   m 
                 
                 
                   ⋅ 
                 
               
               / 
               
                 
                   t 
                   m 
                 
               
             
           
         
       
     
     Therefore, the order receiving side apparatus  202  may adjust the provisional profit ⊓ m (q m , d m ) of the manufacturing side within a range in which the profit ratio ⊓ m (q m , d m )/t m  of the manufacturing side and the profit ratio ⊓ r (q r , d r )/t r  of the retail side coincide with each other. Since the order receiving side apparatus  202  does not have to make the confidential information of the manufacturing side public, security may be ensured, and the manufacturing side may be unlikely to suffer from disadvantages. Next, the description continues with reference to  FIG.  11   , and a specific example of computation of the ordering side apparatus  203  will be described. 
     As illustrated in  FIG.  11   , the ordering side apparatus  203  includes the computation units  1111  to  1118 , the computation unit  1121 , the computation units  1131  and  1132 , and the computation unit  1141 . The ordering side apparatus  203  stores confidential information of the retail side including the consumer demand function f( x ) and the original profit t r  of the retail side. The ordering side apparatus  203  receives the commonization penalty µ from the management side apparatus  201 . The ordering side apparatus  203  receives the profit ratio penalty v from the management side apparatus  201 . 
     The computation unit  1111  accepts the profit ratio penalty v as an input. The computation unit  1111  transmits a value obtained by multiplying the profit ratio penalty v, which is the input, by a value of the following equation (8) to the computation unit  1112 , as an output.  
     
       
         
           
             
               
                 
                   ∇ 
                   
                     
                       x 
                       r 
                     
                   
                 
                 
                   π 
                   r 
                 
                 
                   
                     
                       x 
                       r 
                     
                   
                 
               
               / 
               
                 
                   t 
                   r 
                 
               
             
           
         
       
     
     The computation unit  1112  accepts the commonization penalty µ and the output of the computation unit  1111  as inputs. The computation unit  1112  transmits a value obtained by adding up each value which is the input to the computation unit  1113  as an output. 
     The computation unit  1113  accepts the output of the computation unit  1112  and an output of the computation unit  1118  as inputs. The output of the computation unit  1118  will be described later. The computation unit  1113  transmits a value obtained by subtracting the output of the computation unit  1118 , which is the input, from the output of the computation unit  1112 , which is the input, to the computation unit  1114  as an output. 
     The computation unit  1114  accepts the output of the computation unit  1113  and an output of the computation unit  1116  as inputs. The output of the computation unit  1116  will be described later. The computation unit  1114  transmits a value obtained by subtracting the output of the computation unit  1116 , which is the input, from the output of the computation unit  1113 , which is the input, to the computation unit  1115  as an output. 
     The computation unit  1115  accepts the output of the computation unit  1114  as an input. The computation unit  1115  transmits a value obtained by integrating the output of the computation unit  1114 , which is the input, to the computation unit  1161 , the computation unit  1121 , and the computation unit  1141  as outputs. The ordering side apparatus  203  transmits the output of the computation unit  1115  to the management side apparatus  201  as the matrix [q r  d r ] T  including the provisional order amount q r  of the retail side and the provisional distribution amount d r  of the retail side. 
     The computation unit  1116  accepts the output of the computation unit  1115  as an input. The computation unit  1116  transmits, as an output, a value obtained by substituting the output of the computation unit  1115 , which is the input, into (▪) in the following equation (9) to the computation unit  1114 .  
     
       
         
           
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               ∇ 
               
                 
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               π 
               r 
             
             
               ⋅ 
             
           
         
       
     
     The computation unit  1121  accepts the output of the computation unit  1115  as an input. The computation unit  1121  transmits, as an output, a value obtained by substituting the output of the computation unit  1115 , which is the input, into (▪) of the following equation (10), to the computation unit  1131 .  
     
       
         
           
             
               t 
               r 
             
             − 
             
               π 
               r 
             
             ⋅ 
             
               ⋅ 
             
           
         
       
     
     The computation unit  1131  accepts the output of the computation unit  1121  as an input. The computation unit  1131  transmits, as an output, a value obtained by substituting the output of the computation unit  1121 , which is the input, into (▪) of the following equation (11), to the computation unit  1132 .  
     
       
         
           
             
               λ 
               r 
             
             ⋅ 
             
               ⋅ 
             
           
         
       
     
     The computation unit  1132  accepts the output of the computation unit  1131  as an input. The computation unit  1132  transmits a target profit penalty λ r  obtained by integrating and doubling the output of the computation unit  1131  to the computation unit  1117  as an output. 
     The computation unit  1117  accepts the output of the computation unit  1132  as an input. The computation unit  1117  transmits, as an output, a value obtained by substituting the output of the computation unit  1132 , which is the input, into (▪) of the following equation (12), to the computation unit  1118 .  
     
       
         
           
             
               ⋅ 
             
             ⋅ 
             
               ⋅ 
             
           
         
       
     
     The computation unit  1118  accepts the output of the computation unit  1117  as an input. The computation unit  1118  transmits a value obtained by multiplying a value of the following equation (13) by the output of the computation unit  1117 , which is the input, to the computation unit  1113  as an output.  
     
       
         
           
             
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               π 
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                   x 
                   r 
                 
               
             
           
         
       
     
     The computation unit  1141  accepts the output of the computation unit  1115  as an input. The computation unit  1141  outputs a value obtained by substituting the output of the computation unit  1115 , which is the input, into (▪) of the following equation (14). The ordering side apparatus  203  transmits the output of the computation unit  1141  as the profit ratio ⊓ r (q r , d r )/t r  of the retail side to the management side apparatus  201 .  
     
       
         
           
             
               
                 
                   π 
                   r 
                 
                 
                   ⋅ 
                 
               
               / 
               
                 
                   t 
                   r 
                 
               
             
           
         
       
     
     Therefore, the ordering side apparatus  203  may adjust the provisional profit ⊓ r (q r , d r ) of the retail side within a range in which the profit ratio ⊓ m (q m , d m )/t m  of the manufacturing side and the profit ratio ⊓ r (q r , d r )/t r  of the retail side coincide with each other. Since the ordering side apparatus  203  does not have to make the confidential information of the retail side public, security may be ensured, and the retail side may be unlikely to suffer from disadvantages. In this manner, the information processing system  200  may maximize the profit of the entire supply chain even when the retail side and the manufacturing side do not make the confidential information public. 
     Second Operation Example of Information Processing System 200 
     Next, a second operation example of the information processing system  200  will be described with reference to  FIGS.  12  and  13   . The first operation example is an operation example corresponding to a case where the information processing system  200  includes one management side apparatus  201 . By contrast, the second operation example is an operation example corresponding to a case where the information processing system  200  includes two management side apparatuses  201 . 
       FIG.  12    and  FIG.  13    are explanatory diagrams illustrating the second operation example of the information processing system  200 . As illustrated in  FIG.  12   , the information processing system  200  is applied to a supply chain in which a retailer as an ordering side purchases a product from a manufacturer as an order receiving side, and the retailer as the ordering side sells the product to a consumer. 
     In the example illustrated in  FIG.  12   , there are the order receiving side apparatus  202  owned by the manufacturer, the ordering side apparatus  203  owned by the retailer, and the two management side apparatuses  201  belonging to neither the manufacturer nor the retailer. For example, it is preferable that the two management side apparatuses  201  may not access each other. For example, it is preferable that the two management side apparatuses  201  belong to business entities different from each other. In the following description and drawings, the two management side apparatuses  201  are referred to as a “management side apparatus  201 - 1 ” and a “management side apparatus  201 - 2 ” so as to be distinguished from each other, in some cases. 
     The order receiving side apparatus  202  acquires confidential information of the manufacturing side, based on an operation input of a manufacturing side user. The confidential information of the manufacturing side includes a manufacturing cost of a product, a provisional profit of the manufacturing side, and the like. The order receiving side apparatus  202  stores a commonization penalty and a profit ratio penalty. The commonization penalty and the profit ratio penalty are initialized as predetermined values. For example, the predetermined value is 0. 
     Every time the commonization penalty is received from the management side apparatus  201 - 1 , the order receiving side apparatus  202  updates the stored commonization penalty with the received commonization penalty. Every time the profit ratio penalty is received from the management side apparatus  201 - 2 , the order receiving side apparatus  202  updates the stored profit ratio penalty with the received profit ratio penalty. 
     Based on the confidential information of the manufacturing side, the commonization penalty, and the profit ratio penalty, the order receiving side apparatus  202  calculates a provisional order amount of the manufacturing side, a provisional distribution amount of the manufacturing side, and sharing information of a profit ratio of the manufacturing side. The provisional order amount of the manufacturing side indicates an order amount of a product ordered from the retail side to the manufacturing side, which is provisionally determined by the manufacturing side. The provisional distribution amount of the manufacturing side indicates a profit amount to be distributed from the manufacturing side to the retail side, which is provisionally determined by the manufacturing side. The sharing information of the profit ratio of the manufacturing side indicates a profit ratio of the provisional profit of the manufacturing side to an original profit of the manufacturing side. 
     Until the provisional order amount of the manufacturing side, the provisional distribution amount of the manufacturing side, and the profit ratio of the manufacturing side converge, the order receiving side apparatus  202  may recalculate the provisional order amount of the manufacturing side, the provisional distribution amount of the manufacturing side, and the sharing information of the profit ratio of the manufacturing side every time the commonization penalty and the profit ratio penalty are updated. The order receiving side apparatus  202  transmits the calculated provisional order amount of the manufacturing side and the calculated provisional distribution amount of the manufacturing side to the management side apparatus  201 - 1  via the network  210 . The order receiving side apparatus  202  transmits the calculated sharing information of the profit ratio of the manufacturing side to the management side apparatus  201 - 2  via the network  210 . 
     The ordering side apparatus  203  acquires confidential information of the retail side, based on an operation input of a retail side user. The confidential information of the retail side includes demand information of the consumer for the product, a provisional profit of the retail side, and the like. For example, the demand information includes a probability distribution indicating the demand of the consumer. The ordering side apparatus  203  stores a commonization penalty and a profit ratio penalty. The commonization penalty and the profit ratio penalty are initialized as predetermined values. For example, the predetermined value is 0. 
     Every time the commonization penalty is received from the management side apparatus  201 , the ordering side apparatus  203  updates the stored commonization penalty with the received commonization penalty. Every time the profit ratio penalty is received from the management side apparatus  201 , the ordering side apparatus  203  updates the stored profit ratio penalty with the received profit ratio penalty. 
     Based on the confidential information of the retail side, the commonization penalty, and the profit ratio penalty, the ordering side apparatus  203  calculates a provisional order amount of the retail side, a provisional distribution amount of the retail side, and sharing information of a profit ratio of the retail side. The provisional order amount of the retail side indicates an order amount of a product ordered from the retail side to the manufacturing side, which is provisionally determined by the retail side. The provisional distribution amount of the retail side indicates a profit amount to be distributed from the manufacturing side to the retail side, which is provisionally determined by the retail side. The sharing information of the profit ratio of the retail side indicates a profit ratio of the provisional profit of the retail side to an original profit of the retail side. 
     Until the provisional order amount of the retail side, the provisional distribution amount of the retail side, and the profit ratio of the retail side converge, the ordering side apparatus  203  may recalculate the provisional order amount of the retail side, the provisional distribution amount of the retail side, and the sharing information of the profit ratio of the retail side every time the commonization penalty and the profit ratio penalty are updated. The ordering side apparatus  203  transmits the calculated provisional order amount of the retail side and the calculated provisional distribution amount of the retail side to the management side apparatus  201 - 1  via the network  210 . The ordering side apparatus  203  transmits the calculated sharing information of the profit ratio of the retail side to the management side apparatus  201 - 2  via the network  210 . 
     Until the provisional order amount of the retail side, the provisional distribution amount of the retail side, and the profit ratio of the retail side converge, the ordering side apparatus  203  may recalculate the provisional order amount of the retail side, the provisional distribution amount of the retail side, and the sharing information of the profit ratio of the retail side every time the commonization penalty and the profit ratio penalty are updated. The ordering side apparatus  203  transmits the calculated provisional order amount of the retail side, the calculated provisional distribution amount of the retail side, and the calculated sharing information of the profit ratio of the retail side to the management side apparatus  201  via the network  210 . 
     The management side apparatus  201 - 1  receives the provisional order amount of the manufacturing side and the provisional distribution amount of the manufacturing side from the order receiving side apparatus  202  via the network  210 . The management side apparatus  201 - 1  receives the provisional order amount of the retail side and the provisional distribution amount of the retail side from the ordering side apparatus  203  via the network  210 . 
     Every time the provisional order amount of the manufacturing side, the provisional distribution amount of the manufacturing side, the provisional order amount of the retail side, and the provisional distribution amount of the retail side are received, the management side apparatus  201 - 1  calculates a commonization penalty. For example, the management side apparatus  201 - 1  calculates the commonization penalty, based on the provisional order amount of the manufacturing side, the provisional distribution amount of the manufacturing side, the provisional order amount of the retail side, and the provisional distribution amount of the retail side. 
     By transmitting the calculated commonization penalty to the order receiving side apparatus  202 , the management side apparatus  201 - 1  updates the commonization penalty stored in the order receiving side apparatus  202 . By transmitting the calculated commonization penalty to the ordering side apparatus  203 , the management side apparatus  201 - 1  updates the commonization penalty stored in the ordering side apparatus  203 . 
     The management side apparatus  201 - 2  receives the sharing information of the profit ratio of the manufacturing side from the order receiving side apparatus  202  via the network  210 . The sharing information of the profit ratio of the retail side is received from the ordering side apparatus  203  via the network  210 . 
     Every time the sharing information of the profit ratio of the manufacturing side and the sharing information of the profit ratio of the retail side are received, the management side apparatus  201 - 2  calculates a profit ratio penalty, based on the sharing information of the profit ratio of the manufacturing side and the sharing information of the profit ratio of the retail side. 
     By transmitting the calculated profit ratio penalty to the order receiving side apparatus  202 , the management side apparatus  201 - 2  updates the profit ratio penalty stored in the order receiving side apparatus  202 . By transmitting the calculated profit ratio penalty to the ordering side apparatus  203 , the management side apparatus  201 - 2  updates the profit ratio penalty stored in the ordering side apparatus  203 . Next, the description continues with reference to  FIG.  13   , and a specific example of computation by the management side apparatus  201 - 1  and the management side apparatus  201 - 2  will be described. 
     As illustrated in  FIG.  13   , the order receiving side apparatus  202  has confidential information of a manufacturing side. For example, the confidential information of the manufacturing side includes a manufacturing cost c and an original profit t m  of the manufacturing side. The order receiving side apparatus  202  has the commonization penalty µ and the profit ratio penalty v. 
     Based on the confidential information of the manufacturing side, the commonization penalty µ, and the profit ratio penalty v, the order receiving side apparatus  202  calculates a provisional order amount q m  of the manufacturing side and a provisional distribution amount d m  of the manufacturing side. Based on the confidential information of the manufacturing side, the provisional order amount q m  of the manufacturing side, and the provisional distribution amount d m  of the manufacturing side, the order receiving side apparatus  202  calculates a profit ratio ⊓ m (q m , d m )/t m  of the provisional profit ⊓ m (q m , d m ) to the original profit t m  of the manufacturing side. 
     The order receiving side apparatus  202  transmits a matrix [q m  d m ] T  including the calculated provisional order amount q m  of the manufacturing side and the provisional distribution amount d m  of the manufacturing side to the management side apparatus  201 - 1 . The order receiving side apparatus  202  transmits the calculated profit ratio ⊓ m (q m , d m )/t m  of the manufacturing side to the management side apparatus  201 - 2 . The specific example of computation by the order receiving side apparatus  202  has the same manner as the example in  FIG.  10   , for example. 
     As illustrated in  FIG.  13   , the ordering side apparatus  203  has confidential information of a retail side. For example, the confidential information of the retail side includes a consumer demand function f (x)  and the original profit t r  of the retail side. The ordering side apparatus  203  has the commonization penalty µ and the profit ratio penalty v. 
     Based on the confidential information of the retail side, the commonization penalty µ, and the profit ratio penalty v, the ordering side apparatus  203  calculates a provisional order amount q r  of the retail side and a provisional distribution amount d r  of the retail side. The ordering side apparatus  203  calculates a profit ratio ⊓ r (q r , d r )/t r  of the provisional profit ⊓ r (q r , d r ) to the original profit t r  of the retail side, based on confidential information of the retail side, a provisional order amount q r  of the retail side, and the provisional distribution amount d r  of the retail side. 
     The ordering side apparatus  203  transmits a matrix [q r  d r ] T  including the calculated provisional order amount of the retail side q r  and the calculated provisional distribution amount of the retail side d r  to the management side apparatus  201 - 1 . The ordering side apparatus  203  transmits the calculated profit ratio ⊓ r (q r , d r )/t r  of the retail side to the management side apparatus  201 - 2 . The specific example of computation by the ordering side apparatus  203  has the same manner as the example in  FIG.  11   , for example. 
     As illustrated in  FIG.  13   , the management side apparatus  201 - 1  includes the computation units  1301  to  1303 . The management side apparatus  201 - 1  receives the matrix [q m  d m ] T  of the manufacturing side from the order receiving side apparatus  202 . A management side apparatus  201 - 1  receives the matrix [q r  d r ] T  of the retail side from the ordering side apparatus  203 . 
     The computation unit  1301  calculates a difference obtained by subtracting the matrix [q r  d r ] T  of the retail side from the matrix [q m  d m ] T  of the manufacturing side, and transmits the difference to the computation units  1302  and  1303 . The computation unit  1302  receives the difference, calculates an integral value of the received difference, and transmits the integral value to the computation unit  1303 . By adding the difference and the integral value, the computation unit  1303  calculates the commonization penalty µ. The management side apparatus  201 - 1  transmits the commonization penalty µ to the order receiving side apparatus  202  and the ordering side apparatus  203 . 
     As illustrated in  FIG.  13   , the management side apparatus  201 - 2  includes the computation units  1311  to  1313 . The management side apparatus  201 - 2  receives the profit ratio ⊓ m (q m , d m )/t m  of the manufacturing side from the order receiving side apparatus  202 . The management side apparatus  201 - 2  receives the profit ratio ⊓ r (q r , d r )/t r  of the retail side from the ordering side apparatus  203 . 
     The computation unit  1311  calculates a difference obtained by subtracting the profit ratio ⊓ r (q r , d r )/t r  of the retail side from the profit ratio ⊓ m (q m , d m )/t m  of the manufacturing side, and transmits the difference to the computation units  1312  and  1313 . The computation unit  1312  receives the difference, calculates an integral value of the received difference, and transmits the integral value to the computation unit  1313 . By adding the difference and the integral value, the computation unit  1313  calculates the profit ratio penalty v. The management side apparatus  201 - 2  transmits the profit ratio penalty v to the order receiving side apparatus  202  and the ordering side apparatus  203 . 
     Therefore, the management side apparatus  201 - 1  may cause the manufacturing side to adjust the provisional order amount q m  of the manufacturing side and may cause the retail side to adjust the provisional order amount q r  of the retail side so that the provisional order amount q m  of the manufacturing side and the provisional order amount q r  of the retail side coincide with each other. The management side apparatus  201 - 1  may cause the manufacturing side to adjust the provisional distribution amount d m  of the manufacturing side and cause the retail side to adjust the provisional distribution amount d r  of the retail side so that the provisional distribution amount d m  of the manufacturing side and the provisional distribution amount d r  of the retail side coincide with each other. The management side apparatus  201 - 1  may maximize a profit of the entire supply chain. 
     The management side apparatus  201 - 2  may cause the manufacturing side to adjust the provisional profit ⊓ m (q m , d m ) of the manufacturing side so that the profit ratio ⊓ m (q m , d m )/t m  of the manufacturing side and the profit ratio ⊓ r (q r , d r )/t r  of the retail side coincide with each other. The management side apparatus  201 - 2  may cause the retail side to adjust the provisional profit ⊓ r (q r , d r ) of the retail side so that the profit ratio ⊓ m (q m , d m )/t m  of the manufacturing side and the profit ratio ⊓ r (q r , d r )/t r  of the retail side coincide with each other. For maximizing the profit of the entire supply chain, the management side apparatus  201 - 2  may enable the manufacturing side and the retail side to fairly maximize the profits. 
     In this manner, the information processing system  200  may maximize the profit of the entire supply chain even when the retail side and the manufacturing side do not make the confidential information public. 
     The information processing system  200  may distribute the provisional order amount q m  of the manufacturing side, the provisional distribution amount d m  of the manufacturing side, and the profit ratio ⊓ m (q m , d m )/t m  of the manufacturing side to the management side apparatus  201 - 1  and the management side apparatus  201 - 2  not to be collected in one computer. For this reason, the information processing system  200  may reduce the existence of a computer capable of estimating the confidential information of the manufacturing side, based on a history of the provisional order amount q m  of the manufacturing side, the provisional distribution amount d m  of the manufacturing side, and the profit ratio ⊓ m (q m , d m )/t m  of the manufacturing side. For this reason, the information processing system  200  may suppress leakage of the confidential information of the manufacturing side. 
     The information processing system  200  may distribute the provisional order amount q r  of the retail side, the provisional distribution amount d r  of the retail side, and the profit ratio ⊓ r (q r , d r )/t r  of the retail side to the management side apparatus  201 - 1  and the management side apparatus  201 - 2  not to be collected in one computer. For this reason, the information processing system  200  may reduce the existence of a computer capable of estimating the confidential information of the retail side, based on a history of the provisional order amount q r  of the retail side, the provisional distribution amount d r  of the retail side, and the profit ratio ⊓ r (q r , d r )/t r  of the retail side. For this reason, the information processing system  200  may suppress leakage of the confidential information of the retail side. 
     Example of Effect by Information Processing System 200 
     Next, an example of effects of the information processing system  200  will be described with reference to  FIG.  14   . 
       FIG.  14    is an explanatory diagram illustrating the example of the effects obtained by the information processing system  200 . As illustrated in  FIG.  14   , the information processing system  200  may solve an optimization problem  1400  for maximizing a profit of an entire supply chain. For example, the optimization problem  1400  includes an evaluation function represented by the following equation (15). 
     
       
         
           
             
               
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                               d 
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     An evaluation function indicates that a provisional profit ⊓ m   b (q m , d m ) of a manufacturing side and a provisional profit ⊓ r   b (q r , d r ) of a retail side are maximized. An evaluation function indicates that a difference between a provisional order amount q m  of the manufacturing side and a provisional order amount q r  of the retail side and a difference between a provisional distribution amount d m  of the manufacturing side and a provisional distribution amount d r  of the retail side are minimized. 
     For example, the optimization problem  1400  includes a constraint condition “(original profit of manufacturing side) ≤ ⊓ m   b (q m , d m )” and a constraint condition “(original profit of retail side) ≤ ⊓ r   b (q r , d r )”. For example, the optimization problem  1400  includes a constraint condition “⊓ m   b (q m , d m ): ⊓ r   b (q r , d r ) = original profit of manufacturing side: original profit of retail side”. For example, the optimization problem  1400  includes a constraint condition “difference between provisional order amount q m  of manufacturing side and provisional order amount q r  of retail side = 0” and a constraint condition “difference between provisional distribution amount d m  of manufacturing side and provisional distribution amount d r  of retail side = 0”. 
     By introducing the provisional distribution amount d m  on the manufacturing side and the provisional distribution amount d r  of the retail side, the optimization problem  1400  is reduced to a distributable convex optimization problem, and the evaluation function is a convex function with respect to decision variables. For this reason, in the information processing system  200 , the management side apparatus  201 , the order receiving side apparatus  202 , and the ordering side apparatus  203  may solve the optimization problem  1400  by performing a distributed process on the optimization problem  1400 . 
     The decision variables are the provisional order amount q m  of the manufacturing side, the provisional distribution amount d m  of the manufacturing side, the provisional order amount q r  of the retail side, and the provisional distribution amount d r  of the retail side. With the distributable convex optimization problem, the evaluation function and the constraint condition do not have to be shared between computers that perform the distributed process on the optimization problem  1400 . For this reason, the information processing system  200  may solve the optimization problem  1400  even when confidential information of the manufacturing side and confidential information of the retail side are not made public. 
     According to the constraint condition, the information processing system  200  may make the provisional profit ⊓ m   b (q m , d m ) of the manufacturing side larger than the original profit. According to the constraint condition, the information processing system  200  may make the provisional profit ⊓ r   b (q r , d r ) on the retail side larger than the original profit. The information processing system  200  may maintain a fixed profit ratio between the provisional profit ⊓ m   b (q m , d m ) of the manufacturing side and the provisional profit ⊓ r   b (q r , d r ) of the retail side. 
     In this manner, with the information processing system  200 , both the manufacturing side and the retail side may not suffer from disadvantages. For example, it is conceivable to adopt values at a time of double marginalization as the original profit of the manufacturing side and the original profit of the retail side. By contrast, in the information processing system  200 , both the manufacturing side and the retail side may not suffer from the disadvantage, as compared with a case of the double marginalization serving as a base. 
     For example, as illustrated in a graph  1401 , the information processing system  200  may optimize the provisional order amount of the retail side q r  and the provisional distribution amount of the retail side d r , and make the provisional order amount of the retail side q r  and the provisional distribution amount of the retail side d r  converge. A thin line in the graph  1401  indicates the provisional order amount q r  of the retail side. A thick line in the graph  1401  indicates the provisional distribution amount d r  of the retail side. For example, in the same manner, the information processing system  200  may make the provisional order amount q m  of the manufacturing side and the provisional distribution amount d m  of the manufacturing side converge. 
     As illustrated in the graph  1401 , the information processing system  200  may make the convergence of q m  = q r  = 97.4 and d m  = d r  =695. In this case, the provisional profit ⊓ m   b (97.4, 695) of the manufacturing side is  2230 , and the provisional profit ⊓ r   b (97.4, 695) of the retail side is 2050. By contrast, in an initial state, the original profit of the manufacturing side is  1980  and the original profit of the retail side is 1820. In this manner, the information processing system  200  may maximize the profit of the entire supply chain while maintaining a fixed profit ratio between the provisional profit ⊓ m   b (q m , d m ) of the manufacturing side and the provisional profit ⊓ r   b (q r , d r ) of the retail side. 
     Order Receiving Side Calculation Process Procedure 
     Next, an example of an order receiving side calculation process procedure executed by the order receiving side apparatus  202  will be described with reference to  FIG.  15   . An order receiving side calculation process is implemented by, for example, the CPU  401 , a storage region such as the memory  402  or the recording medium  405 , and the network I/F  403  illustrated in  FIG.  4   . 
       FIG.  15    is a flowchart illustrating the example of the order receiving side calculation process procedure. As illustrated in  FIG.  15   , the order receiving side apparatus  202  initializes a provisional profit, a provisional order amount, a provisional distribution amount, a profit ratio penalty, and a commonization penalty (step S 1501 ). 
     Next, the order receiving side apparatus  202  acquires order receiving side confidential information including a manufacturing cost of a product, an original profit of an order receiving side, and the like (step S 1502 ). Based on the order receiving side confidential information, the order receiving side apparatus  202  transmits order receiving side sharing information including a ratio of the provisional profit to the original profit of the order receiving side to the management side apparatus  201  (step S 1503 ). 
     Next, the order receiving side apparatus  202  transmits the provisional order amount and the provisional distribution amount to the management side apparatus  201  (step S 1504 ). The order receiving side apparatus  202  calculates a target profit achievement degree based on the provisional order amount and the provisional distribution amount, and calculates a target profit penalty based on the calculated target profit achievement degree (step S 1505 ). 
     After that, the order receiving side apparatus  202  receives the profit ratio penalty and the commonization penalty from the management side apparatus  201  (step S 1506 ). By using the order receiving side confidential information, the profit ratio penalty, the commonization penalty, and the target profit penalty as parameters, the order receiving side apparatus  202  updates the provisional order amount and the provisional distribution amount (step S 1507 ). 
     Next, the order receiving side apparatus  202  determines whether or not the provisional order amount and the provisional distribution amount converge (step S 1508 ). In a case where the convergence is not made (No in step S 1508 ), the order receiving side apparatus  202  returns to the process in step S 1503 . By contrast, in a case where the convergence is made (Yes in step S 1508 ), the order receiving side apparatus  202  proceeds to the process in step S 1509 . 
     At step S 1509 , the order receiving side apparatus  202  outputs the provisional order amount and the provisional distribution amount, as a determined order amount and a determined distribution amount (step S 1509 ). The order receiving side apparatus  202  ends the order receiving side calculation process. Therefore, the order receiving side apparatus  202  may calculate the determined order amount and the determined distribution amount for maximizing a profit of an entire supply chain, and an order receiving side user may recognize the determined order amount and the determined distribution amount. 
     Ordering Side Calculation Process Procedure 
     Next, an example of an ordering side calculation process procedure executed by the ordering side apparatus  203  will be described with reference to  FIG.  16   . An ordering side calculation process is implemented by, for example, the CPU  501 , a storage region such as the memory  502  or the recording medium  505 , and the network I/F  503  illustrated in  FIG.  5   . 
       FIG.  16    is a flowchart illustrating the example of the ordering side calculation process procedure. As illustrated in  FIG.  16   , the ordering side apparatus  203  initializes a provisional profit, a provisional order amount, a provisional distribution amount, a profit ratio penalty, and a commonization penalty (step S 1601 ). 
     Next, the ordering side apparatus  203  acquires ordering side confidential information including demand information of a consumer, an original profit of an ordering side, and the like (step S 1602 ). Based on the ordering side confidential information, the ordering side apparatus  203  transmits ordering side sharing information including a ratio of the provisional profit to the original profit of the ordering side to the management side apparatus  201  (step S 1603 ). 
     Next, the ordering side apparatus  203  transmits the provisional order amount and the provisional distribution amount to the management side apparatus  201  (step S 1604 ). The ordering side apparatus  203  calculates a target profit achievement degree based on the provisional order amount and the provisional distribution amount, and calculates a target profit penalty based on the calculated target profit achievement degree (step S 1605 ). 
     Next, the ordering side apparatus  203  receives the profit ratio penalty and the commonization penalty from the management side apparatus  201  (step S 1606 ). By using the ordering side confidential information, the profit ratio penalty, the commonization penalty, and the target profit penalty as parameters, the ordering side apparatus  203  updates the provisional order amount and the provisional distribution amount (step S 1607 ). 
     Next, the ordering side apparatus  203  determines whether or not the provisional order amount and the provisional distribution amount converge (step S 1608 ). In a case where the convergence is not made (No in step S 1608 ), the ordering side apparatus  203  returns to the process in step S 1603 . By contrast, in a case where the convergence is made (Yes in step S 1608 ), the ordering side apparatus  203  proceeds to the process in step S 1609 . 
     At step S 1609 , the ordering side apparatus  203  outputs the provisional order amount and the provisional distribution amount as a determined order amount and a determined distribution amount (step S 1609 ). The ordering side apparatus  203  ends the ordering side calculation process. Therefore, the ordering side apparatus  203  may calculate the determined order amount and the determined distribution amount for maximizing a profit of an entire supply chain, and an ordering side user may recognize the determined order amount and the determined distribution amount. 
     First Penalty Calculation Process Procedure 
     Next, an example of a first penalty calculation process procedure executed by the management side apparatus  201  will be described with reference to  FIG.  17   . A first penalty calculation process is implemented by, for example, the CPU  301 , a storage region such as the memory  302  or the recording medium  305 , and the network I/F  303  illustrated in  FIG.  3   . 
       FIG.  17    is a flowchart illustrating the example of the first penalty calculation process procedure. As illustrated in  FIG.  17   , the management side apparatus  201  initializes a profit ratio penalty (step S 1701 ). 
     Next, the management side apparatus  201  acquires order receiving side sharing information and ordering side sharing information (step S 1702 ). Based on the acquired order receiving side sharing information and ordering side sharing information, the management side apparatus  201  updates the profit ratio penalty (step S 1703 ). 
     Next, the management side apparatus  201  transmits the updated profit ratio penalty to the order receiving side apparatus  202  and the ordering side apparatus  203  (step S 1704 ). The management side apparatus  201  returns to the process in step S 1702 . Therefore, the management side apparatus  201  may control the order receiving side apparatus  202  and the ordering side apparatus  203  so that a provisional profit of an order receiving side and a provisional profit of an ordering side coincide with each other. 
     Second Penalty Calculation Process Procedure 
     Next, an example of a second penalty calculation process procedure executed by the management side apparatus  201  will be described with reference to  FIG.  18   . A second penalty calculation process is implemented by, for example, the CPU  301 , a storage region such as the memory  302  or the recording medium  305 , and the network I/F  303  illustrated in  FIG.  3   . 
       FIG.  18    is a flowchart illustrating the example of the second penalty calculation process procedure. As illustrated in  FIG.  18   , the management side apparatus  201  initializes a commonization penalty (step S 1801 ). 
     After that, the management side apparatus  201  acquires a provisional order amount of an order receiving side, a provisional distribution amount of the order receiving side, a provisional order amount of an ordering side, and a provisional distribution amount of the ordering side (step S 1802 ). Based on the acquired provisional order amount of the order receiving side, provisional distribution amount of the order receiving side, provisional order amount of the ordering side, and provisional distribution amount of the ordering side, the management side apparatus  201  updates the commonization penalty (step S 1803 ). 
     Next, the management side apparatus  201  transmits the updated commonization penalty to the order receiving side apparatus  202  and the ordering side apparatus  203  (step S 1804 ). The management side apparatus  201  returns to the process in step S 1802 . Therefore, the management side apparatus  201  may control the order receiving side apparatus  202  and the ordering side apparatus  203  so that the provisional order amount of the order receiving side and the provisional order amount of the ordering side coincide with each other and the provisional distribution amount of the order receiving side and the provisional distribution amount of the ordering side coincide with each other. 
     The management side apparatus  201  may change and execute the order of the processes of some steps illustrated in each flowchart in  FIGS.  15  to  18   . For example, the order of the processes in steps S 1503  and S 1504  may be changed. For example, the order of the processes in steps S 1603  and S 1604  may be changed. The management side apparatus  201  may omit the process in some steps in each flowchart in  FIGS.  15  to  18   . 
     As described above, with the management side apparatus  201 , it is possible to acquire, from the order receiving side, the first order quantity and the first profit amount calculated by the order receiving side by using the first parameter including the first confidential information owned by the order receiving side. With the management side apparatus  201 , it is possible to acquire, from the ordering side, the second order quantity and the second profit amount calculated by the ordering side by using the second parameter including the second confidential information owned by the ordering side. With the management side apparatus  201 , it is possible to calculate, based on the acquired first order quantity, first profit amount, second order quantity, and second profit amount, the first penalty acting to reduce the difference between the first order quantity and the second order quantity and the difference between the first profit amount and the second profit amount. With the management side apparatus  201 , it is possible to notify the order receiving side to calculate the first order quantity and the first profit amount by using the first parameter including the calculated first penalty. With the management side apparatus  201 , it is possible to notify the ordering side to calculate the second order quantity and the second profit amount by using the second parameter including the calculated first penalty. Therefore, the management side apparatus  201  may maximize the profit of the entire supply chain. 
     With the management side apparatus  201 , it is possible to acquire, from the order receiving side, the first order quantity and the first profit amount calculated by the order receiving side by using the first parameter including the first penalty. With the management side apparatus  201 , it is possible to acquire, from the ordering side, the second order quantity and the second profit amount calculated by the ordering side by using the second parameter including the first penalty. With the management side apparatus  201 , it is possible to update the first penalty based on the first order quantity, the first profit amount, the second order quantity, and the second profit amount which are acquired in the current time. With the management side apparatus  201 , it is possible to notify the order receiving side to calculate the first order quantity and the first profit amount by using the first parameter including the updated first penalty. With the management side apparatus  201 , it is possible to notify the ordering side to calculate the second order quantity and the second profit amount by using the second parameter including the updated first penalty. Therefore, the management side apparatus  201  may repeatedly maximize the profit of the entire supply chain. 
     With the management side apparatus  201 , it is possible to acquire, from the order receiving side, the first ratio of the provisional profit obtained by the order receiving side to the original profit obtained by the order receiving side, which is calculated by the order receiving side by using the first parameter. With the management side apparatus  201 , it is possible to acquire, from the ordering side, the second ratio of the provisional profit obtained by the ordering side to the original profit obtained by the ordering side, which is calculated by the ordering side by using the second parameter. With the management side apparatus  201 , it is possible to calculate the second penalty acting to reduce the difference between the first ratio and the second ratio based on the acquired first ratio and second ratio. With the management side apparatus  201 , it is possible to notify the order receiving side to calculate the first order quantity, the first profit amount, and the first ratio by using the first parameter including the first penalty and the calculated second penalty. With the management side apparatus  201 , it is possible to notify the ordering side to calculate the second order quantity, the second profit amount, and the second ratio by using the second parameter including the first penalty and the calculated second penalty. Therefore, the management side apparatus  201  may maintain the profit ratio between the provisional profit obtained by the order receiving side and the provisional profit obtained by the ordering side. 
     With the management side apparatus  201 , it is possible to acquire, from the order receiving side, the first ratio calculated by the order receiving side by using the first parameter including the first penalty and the second penalty. With the management side apparatus  201 , it is possible to acquire, from the ordering side, the second ratio calculated by the ordering side by using the second parameter including the first penalty and the second penalty. With the management side apparatus  201 , it is possible to update the second penalty acting to reduce the difference between the first ratio and the second ratio, based on the first ratio and the second ratio which are acquired in the current time. With the management side apparatus  201 , it is possible to notify the order receiving side to calculate the first order quantity, the first profit amount, and the first ratio by using the first parameter including the first penalty and the updated second penalty. With the management side apparatus  201 , it is possible to notify the ordering side to calculate the second order quantity, the second profit amount, and the second ratio by using the second parameter including the first penalty and the updated second penalty. Therefore, the management side apparatus  201  may maintain the profit ratio between the provisional profit obtained by the order receiving side and the provisional profit obtained by the ordering side. 
     The management side apparatus  201  may be applied to a case where the order receiving side is a providing side that provides a product to the ordering side, and the ordering side is a selling side that sells the product to a consumer. The management side apparatus  201  may be applied to a case where the first confidential information includes the cost of the product and the original profit obtained by the order receiving side, and the second confidential information includes the demand information of the product and the original profit obtained by the ordering side. Therefore, the management side apparatus  201  may maximize the profit of the entire supply chain including the providing side that provides the product to the ordering side and the selling side that sells the product to the consumer. 
     With the management side apparatus  201 , it is possible to add the difference value obtained by subtracting the second matrix including the acquired second order quantity and second profit amount from the first matrix including the acquired first order quantity and first profit amount, and the integral value of the difference value. Therefore, the management side apparatus  201  may calculate the first penalty with high accuracy. 
     With the management side apparatus  201 , it is possible to add the difference value obtained by subtracting the acquired second ratio from the acquired first ratio and the integral value of the difference value. Therefore, the management side apparatus  201  may calculate the second penalty with high accuracy. 
     With the order receiving side apparatus  202 , it is possible to calculate the first order quantity from the order receiving side to the ordering side and the first profit amount distributed from the order receiving side to the ordering side by using the first parameter including the first confidential information of the order receiving side. With the order receiving side apparatus  202 , it is possible to transmit the calculated first order quantity and first profit amount to the management side apparatus  201 . With the order receiving side apparatus  202 , it is possible to receive, from the management side apparatus  201 , the first penalty acting to reduce the difference between the first order quantity and the second order quantity and the difference between the first profit amount and the second profit amount. With the order receiving side apparatus  202 , it is possible to calculate the first order quantity and the first profit amount by using the first parameter including the received first penalty. Therefore, the order receiving side apparatus  202  may optimize the first order quantity and the first profit amount. 
     With the order receiving side apparatus  202 , it is possible to output the calculated first order quantity and first profit amount in a case where the first penalty indicates that the first order quantity and the second order quantity coincide with each other and the first profit amount and the second profit amount coincide with each other. Therefore, the order receiving side apparatus  202  may detect that the first order quantity and the first profit amount converge, and may enable the order receiving side user to refer to the appropriate first order quantity and first profit amount. 
     With the ordering side apparatus  203 , it is possible to calculate the first order quantity from the order receiving side to the ordering side and the first profit amount distributed from the order receiving side to the ordering side by using the first parameter including the first confidential information of the ordering side. With the ordering side apparatus  203 , it is possible to transmit the calculated first order quantity and first profit amount to the management side apparatus  201 . With the ordering side apparatus  203 , it is possible to receive, from the management side apparatus  201 , the first penalty acting to reduce the difference between the first order quantity and the second order quantity and the difference between the first profit amount and the second profit amount. With the ordering side apparatus  203 , it is possible to calculate the first order quantity and the first profit amount by using the first parameter including the received first penalty. Therefore, the ordering side apparatus  203  may optimize the first order quantity and the first profit amount. 
     With the ordering side apparatus  203 , it is possible to output the calculated first order quantity and first profit amount in a case where the first penalty indicates that the first order quantity and the second order quantity coincide with each other and the first profit amount and the second profit amount coincide with each other. Therefore, the ordering side apparatus  203  may detect that the first order quantity and the first profit amount converge, and may enable the ordering side user to refer to the appropriate first order quantity and first profit amount. 
     The information processing method described in the present embodiment may be implemented by executing a program prepared in advance by a computer, such as a PC or a workstation. The information processing program described in the present embodiment is recorded on a computer-readable recording medium. The information processing program is read from the recording medium by the computer and is executed by the computer. The recording medium is a hard disk, a flexible disk, a compact disc (CD)-ROM, a magneto-optical (MO) disc, a Digital Versatile Disc (DVD), or the like. The information processing program described in the present embodiment may be distributed via a network, such as the Internet. 
     All examples and conditional language provided herein are intended for the pedagogical purposes of aiding the reader in understanding the invention and the concepts contributed by the inventor to further the art, and are not to be construed as limitations to such specifically recited examples and conditions, nor does the organization of such examples in the specification relate to a showing of the superiority and inferiority of the invention. Although one or more embodiments of the present invention have been described in detail, it should be understood that the various changes, substitutions, and alterations could be made hereto without departing from the spirit and scope of the invention.