Patent Publication Number: US-2023162158-A1

Title: Schedule creation assisting device and schedule creation assisting method

Description:
TECHNICAL FIELD 
     The present invention relates to a schedule creation assisting device and a schedule creation assisting method. 
     BACKGROUND ART 
     The concept of searching for a solution that maximizes or minimizes desired parameters under specified conditions, in other words, the concept of what is called a combinatorial optimization problem, can be applied to complex problems in the real world such as eliminating traffic congestion and reducing distribution costs in global supply chains. 
     However, in such problems, the number of solution candidates is tremendously large, making it difficult to solve the problem within a practical time unless the computer is one having a relatively high computing power, such as a supercomputer or a quantum computer. 
     For example, as a conventional technique related to quantum computers, a technique regarding a computer which enables a high-speed computation for an inverse problem or a combinatorial optimization problem requiring an exhaustive search has been proposed in which spins are used as variables in the computation, a problem intended to be solved is set using spin-spin interaction and a local field acting on each spin, all spins are caused to orient toward one direction by an external magnetic field at time t=0, the external magnetic field is gradually reduced such that the external magnetic field becomes zero at time t=τ, each spin is time-evolved on the assumption that the direction is determined to follow an effective magnetic field determined by all actions of spin-spin interaction and the external magnetic field of each site at time t, and in this process, the directions of the spins are not completely aligned to the effective magnetic fields but are caused to be quantum mechanically corrected directions so that the system can maintain an approximate ground state (see PTL 1). 
     CITATION LIST 
     Patent Literature 
     [PTL 1] WO2016/157333 
     SUMMARY OF INVENTION 
     Technical Problem 
     Unfortunately, there has not been proposed a configuration in which quantum computer techniques as described above are applied appropriately to the work of creating an overall schedule for a large number of workers who work in cooperation. 
     For example, the work of creating schedules of a call center requires creation of weekly or monthly shift schedules for hundreds of operators. In the current situation, an experienced person in charge creates schedules manually under predetermined rules (Example: Shift patterns such as early shifts and late shifts shall be combined and arranged in a fixed order and frequency for a specified period). 
     Such schedule creation can be made efficient to a certain extent by using functions in spreadsheet software on a common PC. However, in the case where the number of workers is larger than a certain level, or in the case where there are nonlinear constraint conditions a plurality of which affect one another, it is impossible to obtain a solution within a practical time. Hence, spreadsheet software can deal with only situations in a very small organization having only linear constraint conditions. 
     Creation of schedules for the case where a large number of workers work in corporation is greatly affected not only by basic factors such as rules for the number of working days for each worker and the number of necessary workers for each day but also various factors such as circumstances of each worker, workers&#39; vague requests, the work system, and various kinds of rules. In addition, those factors themselves vary depending on the number of workers, the organization that the workers belong to, and demand for the operation, and the factors interfere and affect one another in some cases. 
     In addition, there are cases where a sudden change occurs in those factors, such as a sudden increase/decrease in the demand for the operation and abrupt absence of workers. In such situations, even if an attempt was made to create a schedule in a conventional way by using a common PC, the amount of calculation would increase exponentially according to the number of factors, nonlinear constraint conditions, and the like as described above, and the calculation would take an enormous amount of time or lead to an overflow. Simply put, the schedule probably cannot be created at a desired timing. 
     Hence, an object of the present invention is to provide a technique for efficiently creating a schedule with nonlinear constraint conditions taken into account for a large number of workers who work in corporation. 
     Solution to Problem 
     A schedule creation assisting device of the present invention to solve the above object comprising: a storage unit that stores information on a total working time length in a specified period of each of workers who work in cooperation in a specified operation, a number of the workers necessary at each timing during the period, and a constraint condition regarding allocation of the workers to the operation; and a computation unit that computes an Ising model in which, regarding an objective function including, as terms, the total working time length in the period, the number of necessary workers, and a constraint condition function that is minimized when the constraint condition is satisfied, whether each of the workers is to attend at work is set as a spin, and a sensitivity between variables of the constraint condition function is set as an intensity of interaction between the spins, wherein the computation unit outputs, to a specified device, a schedule in which whether each of the workers is to attend at work at the each timing during the specified period is specified based on a result of the computation. 
     A schedule creation assisting method of the present invention comprising: by an information processing device including a storage unit that stores information on a total working time length in a specified period of each of workers who work in cooperation in a specified operation, a number of the workers necessary at each timing during the period, and a constraint condition regarding allocation of the workers to the operation, computing an Ising model in which, regarding an objective function including, as terms, the total working time length in the period, the number of necessary workers, and a constraint condition function that is minimized when the constraint condition is satisfied, whether each of the workers is to attend at work is set as a spin, and a sensitivity between variables of the constraint condition function is set as an intensity of interaction between the spins; and outputting, to a specified device, a schedule in which whether each of the workers is to attend at work at the each timing during the specified period is specified based on a result of the computation. 
     Advantageous Effects of Invention 
     The present invention makes it possible to efficiently create a schedule with nonlinear constraint conditions taken into account for a large number of workers who work in cooperation. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG.  1    is a network configuration diagram including a schedule creation assisting device of the present embodiment. 
         FIG.  2    is a diagram illustrating an example of a hardware configuration of the schedule creation assisting device in the present embodiment. 
         FIG.  3    is a diagram illustrating a timing chart example in the present embodiment. 
         FIG.  4    is a diagram illustrating a procedure example 1 in the present embodiment. 
         FIG.  5    is a diagram illustrating a configuration example of a basic information table in the present embodiment. 
         FIG.  6    is a diagram illustrating a configuration example of a constraint condition table in the present embodiment. 
         FIG.  7    is a diagram illustrating the configuration example of the constraint condition table in the present embodiment. 
         FIG.  8    is a flowchart showing a schedule creation assisting method in the present embodiment. 
         FIG.  9    is a diagram illustrating a screen example in the present embodiment. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     - - - Regarding Annealing Machine - - - 
     As described in the foregoing PTL 1, the applicant of the present application has developed quantum computing techniques and has been working to solve various problems, for example, in exhaustive search problems based on big data (including the concept of combinatorial optimization problems). 
     In general, expectation for quantum computers is high for such exhaustive search problems. A quantum computer uses basic elements called qubits which represent “0” and “1” simultaneously. Thus, the quantum computer is capable of calculating all the solution candidates simultaneously as initial values and has a possibility of achieving exhaustive search. However, the quantum computer needs to keep quantum coherence over the entire calculation time. 
     Under these circumstances, a method called adiabatic quantum computation has come to attract attention (Reference: E. Farhi, et al., “A quantum adiabatic evolution algorithm applied to random instances of an NP-complete problem,” Science 292, 472 (2001)). In this method, a problem is converted such that the ground state of a physical system is the solution, and the solution is sought for through finding the ground state. 
     The Hamiltonian of the physical system to which a problem is set is defined as H{circumflex over ( )}p. Here, at the start of computation, the Hamiltonian is not set to H{circumflex over ( )}p, but to another Hamiltonian H{circumflex over ( )}0 which is different from H{circumflex over ( )}p and the ground state of which is clear and easy to prepare. Next, the Hamiltonian is transformed from H{circumflex over ( )}0 to H{circumflex over ( )}p taking a sufficient time. Taking a sufficient time makes the system keep staying in the ground state, providing the ground state of the Hamiltonian H{circumflex over ( )}p. This is the principle of the adiabatic quantum computation. Defining τ as the calculation time, the Hamiltonian is expressed by Expression (1). 
     
       
         
           
             
               
                 
                   
                     
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     The solution is obtained by time evolution based on a Schrodinger equation of Expression (2). 
     
       
         
           
             
               
                 
                   
                     
                       
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     Adiabatic quantum computation is applicable to a problem that requires exhaustive search, and it is possible to reach a solution in a one-way process. However, if the calculation process needs to conform to the Schrodinger equation of Expression (2), quantum coherence needs to be kept as in the case of a quantum computer. 
     While the quantum computer repeats gate operations on 1 qubit or between 2 qubits, adiabatic quantum computation causes interaction over the entire qubit system at the same time, and thus, the concept of coherence is different. 
     For example, consider a gate operation on a certain qubit. In this case, if there is an interaction between the qubit and other qubits, it will cause decoherence. But for adiabatic quantum computation, all the qubits are interacted simultaneously, and thus decoherence as in this example will not occur. In consideration of this difference, adiabatic quantum computation is thought to be more robust in terms of decoherence than the quantum computer. 
     As has been described above, adiabatic quantum computation is effective for a difficult question that requires exhaustive search. Then, spins are used as variable for computation, and a problem to be solved is set as interactions between spins and local fields acting on respective spins. 
     At time t=0, all the spins are made to be oriented in one direction using an external magnetic field, and the external magnetic field is gradually reduced such that it becomes zero at time t=τ. 
     Each spin is time-evolved on the assumption that the direction of each spin is determined according to the effective magnetic field determined by all the actions at time t which are the external magnetic field at each site and interactions between spins. 
     In this process, the direction of the spin is not made to be perfectly aligned with the effective magnetic field but to be oriented in a direction corrected quantum-mechanically, so that the system can almost keep the ground state. 
     In addition, a term to keep each spin at the original direction during time evolution (a relaxation term) is added to the effective magnetic field to improve the convergence of the solution. 
     The schedule creation assisting device in the present embodiment on the assumption here is an annealing machine that performs the foregoing adiabatic quantum computation, but, of course, is not limited to this. The present invention can be applied to any device capable of solving combinatorial optimization problems following the schedule creation assisting method of the present invention as appropriate. 
     Specifically, the applicable devices include not only hardware for implementing the annealing method using an electronic circuit (a digital circuit or the like) but also hardware using a superconducting circuit or the like. The embodiment is also applicable to hardware implementing an Ising model by a method other than the annealing method. For example, it includes a laser network method (optical parametric oscillation) and a quantum neural network, too. Although part of the concept is different as described above, the present invention can also be realized by using a quantum gate method in which calculation using an Ising model is replaced with gates such as Hadamard gates, rotation gates, and controlled NOT gates. 
     - - - Network Configuration - - - 
     Hereinafter, an embodiment of the present invention will be described in detail using drawings.  FIG.  1    is a network configuration diagram including a schedule creation assisting device  100  of the present embodiment. 
     The schedule creation assisting device  100  illustrated in  FIG.  1    is a computer device that efficiently creates schedules in which nonlinear constraint conditions regarding a large number of workers who work in cooperation are taken into account, and specifically, on the assumption here, it is an annealing machine as an example. 
     Since an overview of the annealing machine has been already described based on PTL 1, details of the specific configuration, operations, and the like of the annealing machine will be omitted as appropriate (the same applies in the following). 
     The schedule creation assisting device  100  of the present embodiment is coupled to a user terminal  200  such that data can be communicated between them via an appropriate network  10  such as the Internet. 
     The user terminal  200  receives a schedule proposal from the schedule creation assisting device  100 . 
     The user of the user terminal  200  is specifically a business entity that has a large number of operators and performs call center operation with them, and on the assumption here, it is an organization such as a financial institution, an insurance company, or a major manufacturer. Examples of the user on the assumption also include a medical institution and a caregiving business entity that have a large number of nurses or caregiving staff members and carry out nursing work or caregiving work for patients or the like. 
     In any case, any business entity that allocates a necessary number, which is relatively large, of workers to days or time slots and carries out an operation as a whole can be the foregoing user. In other words, it can be said that the present invention can be applied to the operations of such business entities. 
     As a specific example that can be assumed, for example, in the case of creating a schedule for a call center of a bank, the reality is that a person in charge having specified experience manually inputs and creates monthly shift schedules for all the operators in a scale of several hundreds. In other words, such operation is manual work and tends to be dependent on individual skills. 
     For this reason, although it is possible to create schedules based on shifts according to fixed rules in a conventional way, it is difficult to create schedules for flexibly dealing with irregular shifts or external factors. 
     In addition, even if functions or the like in spreadsheet software are used, it is difficult to create schedules being free from realistic obstacles such as “holiday setting is limited only for Saturdays and Sundays” and “the number of workers that can be dealt with is up to 100”. 
     The obstacles result from mathematical difficulties and the absence (immature in a strict sense) of techniques for solving the mathematical difficulties. Although spreadsheet software is capable of solving a problem at high speed if the constraint conditions are linear, it has a characteristic that it takes an enormous amount of time to solve a problem with nonlinear constraint conditions. 
     Thus, in the case of creating a schedule in a conventional technique as above, as the number of nonlinear constraint conditions regarding elements, in other words, workers or the like increases, the amount of calculation increases exponentially and thus requires a long time to complete calculation. However, employing the schedule creation assisting device  100  using an annealing machine makes it possible to perform calculation, not being much dependent on the increase in the number of elements. 
     - - - Hardware Configuration - - - 
     The hardware configuration of the schedule creation assisting device  100  of the present embodiment is as described in  FIG.  2     
     Specifically, the schedule creation assisting device  100  includes a storage unit  101 , a memory  103 , a computation unit  104 , and a communication unit  105 . 
     Of these, the storage unit  101  includes an appropriate nonvolatile memory device such as a solid state drive (SSD) or a hard disk drive. 
     The memory  103  includes a volatile memory device such as RAM. 
     The computation unit  104  is a CPU that performs operation such as loading a program  102  stored in the storage unit  101  into the memory  103  and executing it to manage and control the device and that also performs various kinds of determination, computation, and control processing. 
     The communication unit  105  on the assumption here is a network interface card or the like that is coupled to the network  10  and performs processing for communication with the user terminal  200 . 
     Note that in the case where the schedule creation assisting device  100  is a stand-alone machine, it is preferable that the schedule creation assisting device  100  further includes an input device for receiving key input and voice input from the user and an output device such as a display for displaying processing data. 
     The storage unit  101  stores, in addition to the program  102  for implementing the functions necessary for the schedule creation assisting device of the present embodiment, at least a basic information table  125  and a constraint condition table  126 . Details of these tables will be described later. 
     The program  102 , in other words, the algorithm for implementing the operation as an annealing machine, holds information on an Ising model  1021  which is a problem to be solved. This Ising model  1021  is set in advance by the administrator or the like based on various kinds of information on the operation and workers the information on which needs to be provided and other information that affects those factors. 
     Note that the adiabatic quantum computation described in an overview of the annealing machine is also called another name, quantum annealing, in which the concept of classical annealing is extended into quantum mechanics. Specifically, it can be interpreted that adiabatic quantum computation can originally perform classical operation, and that quantum-mechanical effects were added to the adiabatic quantum computation to improve performance on high speed and the correct answer rate of a solution. In this respect, in the present invention, the computation unit itself is classical but parameters determined quantum-mechanically are introduced in the computation process to achieve a computation method and device that are classical but include quantum-mechanical effects. Here, of course, a configuration having a quantum computer as the computation unit may be employed. 
     Based on the above concept, the following example illustrates a classical algorithm to obtain the ground state as the solution and a device to achieve it while describing relationship with adiabatic quantum computation. 
     In the schedule creation assisting device  100  on the above premise, N variables sj z  (j=1, 2, . . . , N) take a value range of −1≤sj z ≤1, and a problem is set using the local fields gj and inter-variable interactions Jij (i, j=1, 2, . . . , N). 
     The computation unit  104 , dividing the time by m, performs computation discretely from t=t 0  (t 0 =0) to tm (tm=τ). To calculate the variable Sj z (tk) at each time tk, the value of the variable of Sj z (tk−1) (i=1, 2, . . . , N) at the previous time tk−1 and the coefficient of the relaxation term, 9pina or 9pinb, are used to calculate Bj z (tk)={ΣiJijSi z (tk−1)+gj+sgn(sj z (tk−1))·9pina}·tk/τ or Bj z (tk)={ΣiJiJSj z (tk−1)+gj+9pinb·Sj z (tk−1)}·tk/τ. The function f is determined such that the value range of the foregoing variable Sj z (tk) is −1≤sj z (tk)≤1, and Sj z (tk)=f(Bj z (tk),tk) is obtained. As the time step is advanced from t=t0 to t=tm, the foregoing variable Sj z  is made closer to −1 or 1. In the end, if sj z &lt;0, Sj zd  is set as Sj zd =−1, and if Sj z &gt;0, as Sj zd =1, and the solution is determined. 
     The coefficient gpinb is, for example, a value between 50% and 200% of the average value of |Jij|. As for the local field gj for the problem setting, the correction term δgj′ may be added to gj′ only for a certain site j′ to increase the magnitude of gj′ only for the site j′. The correction term δgj′ is, for example, a value between 10% and 100% of the average value of |Jij|. 
     Next, the basic principle of the annealing machine will be described by starting from a quantum-mechanical description and moving to a classical form. 
     The Ising spin Hamiltonian ground-state search problem given by Expression (3) includes a problem in a classification called NP-hardness and is known to be a useful problem (Reference: F. Barahona, “On the computational complexity of Isingspin glass models,” J. Phys. A: Math. Gen. 15, 3241 (1982)). 
     
       
         
           
             
               
                 
                   
                     
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     Jij and gj are problem setting parameters, and σ{circumflex over ( )} z  is the z component of the Pauli spin matrix and takes an eigenvalue of ±1. The symbols i, j indicate the site of a spin. Ising spins are variables that can only take values of ±1. Since the eigenvalue of σ{circumflex over ( )} z  is ±1 in Expression (3), it expresses an Ising spin system. 
     The Ising spins of Expression (3) do not have to be literal spins, but they may be physically anything as long as the Hamiltonian is described by Expression (3). 
     For example, whether each worker is to attend at work can be associated with ±1, the high and low of a logic circuit can be associated with ±1, the vertical polarization waves and horizontal polarization waves of light can be associated with ±1, or the phases of 0 and τ can be associated with ±1. 
     In the method shown here as an example, as in adiabatic quantum computation, a system for computation is prepared in the ground state of the Hamiltonian given by Expression (4) at time t=0. 
     
       
         
           
             
               
                 
                   
                     
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     Here, γ is a constant of proportionality determined by the magnitude of the external field that are uniformly applied to all the sites j, and σ{circumflex over ( )}j x  is the x component of the Pauli spin matrix. If the system for computation is literal spins, the external field means a magnetic field. 
     Expression (4) means that a transverse magnetic field is applied, and the case where all the spins are oriented in the x direction (γ&gt;0) is the ground state. The Hamiltonian for problem setting is defined as an Ising spin system having only z components, but Expression (4) includes the x components of the spins. Hence, the spins during the computation process are not Ising but are vectors (Bloch vectors). At t=0, the system starts as the Hamiltonian in Expression (4). As time t progresses, the Hamiltonian is gradually changed. In the end, the system is changed to the Hamiltonian expressed by Expression (3) to obtain its ground state as the solution. 
         Ĥ=−B·{circumflex over (σ)}   [Expression 5]
 
     Here, σ{circumflex over ( )} expresses the three components of the Pauli spin matrix as a vector. The ground state is a state in which the spin is oriented in the magnetic field direction, and &lt;σ{circumflex over ( )}&gt; can be expressed as &lt;σ{circumflex over ( )}&gt;=B/|B|, where &lt;·&gt; means the quantum-mechanical expectation value. Since in the adiabatic process, the system always seeks to keep the ground state, the direction of the spin always follows the direction of the magnetic field. 
     The above discussion can be extended to a multi-spin system. At t=0, the Hamiltonian is given by Expression (4). This means that the magnetic field Bj x =γ is uniformly applied to all the spins. When t&gt;0, the x component of the magnetic field is gradually reduced, which is expressed as Bj x =γ(1−t/τ). Since the z components are affected by spin-spin interactions, the effective magnetic field is expressed by Expression (6). 
     
       
         
           
             
               
                 
                   
                     
                       
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     Since the direction of the spin can be defined by &lt;σ{circumflex over ( )} z &gt;/&lt;σ{circumflex over ( )} X &gt;, if the direction of the spin follows the effective magnetic field, the direction of the spin is determined by Expression (7). 
         {circumflex over (σ)} j   z   / {circumflex over (σ)} j   x     =     {circumflex over (B)}   j   z ( t ) /   {circumflex over (B)}   j   x ( t )   [Expression 7]
 
     Expression (7) is a quantum-mechanical description, but since it is expressed by expectation values, Expression (7) is a relational expression based on classical quantities. This point is different from Expressions (1) to (6). 
     Since a classical system does not have nonlocal correlation (quantum entanglement) that quantum mechanics has, the direction of the spin is perfectly determined by the local field at each site, and Expression (7) determines the behavior of the classical spin system. Since a quantum system has nonlocal correlation, Expression (7) is modified, which will be described later. Here, the classical system determined by Expression (7) will be described to mention the basic form of the invention. 
       FIG.  3    illustrates a timing chart ( 1 ) to obtain the ground state of a spin system. Since the illustration in  FIG.  3    is based on classical quantities, the spin at site j is expressed by sj not by σ{circumflex over ( )}j. With this, the effective magnetic field Bj in  FIG.  3    is a classical quantity. At t=0, the effective magnetic field Bj in the right direction is applied at all the sites, and all the spins Sj are initialized so that that the spins Sj are directed to the right. 
     As time t passes, a magnetic field in the z axis direction and spin-spin interactions are gradually applied to the spins. In the end, the spins are oriented in the +z direction or the −z direction, and the z component of the spin Sj becomes sj z =+1 or −1. Ideally, time t is continuous, but in the actual computation process, time can be discrete to improve the convenience. The following description is based on a case where time t is discrete. 
     Since the spins illustrated as an example here have not only z components but also x components, they are vector spins. Behavior as vectors can be understood also from  FIG.  3   . Y components have not appeared so far in the discussion. The reason is that since the direction of the external field is defined in the xz plane, the external field does not have a y component, and thus &lt;σ{circumflex over ( )} Y &gt;=0. 
     In the assumption here, each spin in the system for computation is a three-dimensional vector having a size of 1 (this is called a Bloch vector, the state of which can be described with a point on a spherical surface). However, in the case of the axes in the example in the figure, only two dimensions need to be considered (the state can be described with a point on a circle). 
     Here, since γ is constant, Bj x (t)&gt;0 (γ&gt;0) or Bj x (t)&lt;0 (γ&lt;0) holds. In this case, a two-dimensional spin vector can be described only with a semicircle. Hence, by specifying Sj z  with [−1, 1], one variable Sj z  determines a two-dimensional spin vector. Thus, in the example here, although a spin is a two-dimensional vector, it also can be expressed as one-dimensional continuous variable having a value range of [−1, 1]. 
     In the timing chart of  FIG.  3   , the effective magnetic field is calculated for each site at time t=tk, and using the calculated value, the direction of the spin at t=tk is calculated with Expression (8). 
         S   j   z ( t   k )/ S   j   x ( t   k )= B   j   z ( t   k )/ B   j   x ( t   k )  [Expression 8]
 
     Since Expression (8) is what Expression (7) was rewritten into so that the expression is based on classical quantities, it does not have the mark &lt;·&gt;. Next, the effective magnetic field at t=tk+1 is calculated by using the value of the spin at t=tk. The effective magnetic field at each time specifically written is Expressions (9) and (10). 
     
       
         
           
             
               
                 
                   
                     
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                     10 
                   
                   ] 
                 
               
             
           
         
       
     
     In the following, the spin and the effective magnetic field are calculated alternately according to the procedure schematically illustrated with the timing chart of  FIG.  3   . 
     In a classical system, the size of the spin vector is 1. In this case, each component of the spin vector is expressed as Sj z (tk)=sin θ and Sj x (tk)=cos θ, by using the parameter θ defined by tan θ=Bj z (tk)/Bj x (tk). 
     These can be rewritten as Sj z (tk)=sin(arctan(Bj z (tk)/Bj x (tk))) and Sj x (tk)=cos(arctan(Bj z (tk)/Bj x (tk))). 
     As is clear from Expression (9), the variable of Bj x (tk) is only tk, and τ and γ are constants. Thus, Sj z (tk)=sin(arctan(Bj z (tk)/Bj x (tk))) and Sjx(tk)=cos(arctan(Bj z (tk)/Bj x (tk))) can be expressed in generalized forms as Sj z (tk)=f1(Bj z (tk),tk) and Sj x (tk)=f2(Bj z (tk),tk), which are functions having Bj z (tk) and tk as variables. 
     Since the spin is described as a two-dimensional vector, the two components Sj z (tk) and sj x (tk) appear. However, if Bj z (tk) is determined based on Expression (10), Sj x (tK) is not necessary. 
     This corresponds to that the state of the spin can be described only by Sj z (tk) having a value range of [−1, 1]. Since the final solution Sj zd  needs to be Sj zd =−1 or 1, if Sj z (τ)&gt;0, it is determined that Sj zd =1, and if Sj z (τ)&lt;0, it is determined that Sj zd =−1. 
       FIG.  4    illustrates a flowchart in which the algorithm described above is organized. Here, tm=τ. Each of the steps s 1  to s 9  in the flowchart of  FIG.  4    corresponds to the process at a time in the timing chart of  FIG.  3    from time t=0 to t=τ. Specifically, the steps s 2 , s 4 , and s 6  in the flowchart correspond to the above Expressions (9) and (10) at t=t1, tk+1, and tm, respectively. The final solution is obtained by determining at step s 8  that Sj zd =−1 if sj z &lt;0 or that Sj zd =1 if Sj z &gt;0 (s 9 ). 
     The description up to this point has shown how the problem expressed by Expression (3) is solved. Next, a description is given of how a specific problem is expressed by Expression (3) including the local field gj and the inter-variable interaction Jij (i, j=1, 2, . . . , N), by showing a specific example. 
     A specific problem, in other words, an Ising model  1021  on the assumption here is an Ising model in which, for example, based on information on the total number of working days of each of the operators working for a call center operation in a specified month, the number of operators necessary for each day in the month, and constraint conditions regarding allocation of each operator to the call center operation, an objective function is set that includes, as terms, the total number of working days for the month, the number of operators necessary for each day in the month, and the constraint condition functions that are minimized when the above constraint conditions are satisfied, and regarding the objective function, whether each operator is to attend at work is defined as a spin, and the sensitivity between the variables of the constraint condition function is defined as the intensity of interaction between the spins. 
     In this case, the local field gj on the assumption here is set as the degree of influence on the objective function given by the values of the variables representing the total number of working days for the month, the number of operators necessary for each day in the month, and the constraint condition functions that are minimized when the constraint conditions are satisfied, as described above. 
     Through the discussion described above, the inter-variable interaction Jij (related to between the items of the above objective function) and the local field gj are specifically set. Searching for the ground state of the Ising model  1021  expressed by Expression (3) is performed, in other words, searching for the ground state that minimizes the objective function including the total number of working days for the month, the number of operators necessary for each day in the month, and the constraint condition functions that are minimized when the constraint conditions are satisfied is performed. Through the searching, the work shifts for each operator, in other words, the overall schedule for the month for the call center operation is determined. 
     Note that the calculation using an Ising model and the annealing method is used only for “minimizing the objective function”. Hence, if there are constraint conditions that need to be satisfied when the objective function is minimized, those conditions need to be added to the objective function in some way. 
     For example, think about a constraint condition expressed by Expression (11). 
     
       
         
           
             
               
                 
                   
                     
                       ∑ 
                       i 
                     
                     
                       x 
                       i 
                     
                   
                   = 
                   A 
                 
               
               
                 
                   [ 
                   
                     Expression 
                     ⁢ 
                         
                     11 
                   
                   ] 
                 
               
             
           
         
       
     
     This constraint condition can be converted into “a function that is minimized when the constraint condition is satisfied”, which is the following expression. 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           ∑ 
                           i 
                         
                         
                           x 
                           i 
                         
                       
                       - 
                       A 
                     
                     ] 
                   
                   2 
                 
               
               
                 
                   [ 
                   
                     Expression 
                     ⁢ 
                         
                     12 
                   
                   ] 
                 
               
             
           
         
       
     
     Since the square portion always has a positive value, this expression takes the minimum value only when the inside of the square is 0. Since the inside is 0 only when ΣXi−A=0, by finding a solution of the optimization problem that minimizes this function, the solution with which ΣXi=A is satisfied is automatically obtained. 
     For example, since in the foregoing annealing method, the items desired to be constraint conditions also need to be included in the objective function, the objective function and the constraint conditions are treated to the degree of the same importance. 
     For example, assume an optimization problem as below. 
     
       
         
           
             
               
                 
                   
                     
                       
                         min 
                         : 
                             
                         
                           
                             ∑ 
                             k 
                           
                           
                             
                               a 
                               k 
                             
                             ⁢ 
                             
                               x 
                               k 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         
                           subject 
                           ⁢ 
                               
                           to 
                           : 
                               
                           
                             
                               ∑ 
                               k 
                             
                             
                               
                                 b 
                                 k 
                               
                               ⁢ 
                               
                                 x 
                                 k 
                               
                             
                           
                         
                         = 
                         B 
                       
                     
                   
                   
                     
                       
                           
                         
                           
                             
                               ∑ 
                               k 
                             
                             
                               
                                 c 
                                 k 
                               
                               ⁢ 
                               
                                 x 
                                 k 
                               
                             
                           
                           = 
                           C 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Expression 
                     ⁢ 
                         
                     13 
                   
                   ] 
                 
               
             
           
         
       
     
     These can be changed into formularization for annealing as follows. 
     
       
         
           
             
               
                 
                   
                     min 
                     : 
                         
                     
                       
                         ∑ 
                         k 
                       
                       
                         
                           a 
                           k 
                         
                         ⁢ 
                         
                           x 
                           k 
                         
                       
                     
                   
                   + 
                   
                     
                       P 
                       [ 
                       
                         
                           
                             ∑ 
                             k 
                           
                           
                             
                               b 
                               k 
                             
                             ⁢ 
                             
                               x 
                               k 
                             
                           
                         
                         - 
                         B 
                       
                       ] 
                     
                     2 
                   
                   + 
                   
                     
                       Q 
                       [ 
                       
                         
                           
                             ∑ 
                             k 
                           
                           
                             
                               c 
                               k 
                             
                             ⁢ 
                             
                               x 
                               k 
                             
                           
                         
                         - 
                         C 
                       
                       ] 
                     
                     2 
                   
                 
               
               
                 
                   [ 
                   
                     Expression 
                     ⁢ 
                         
                     14 
                   
                   ] 
                 
               
             
           
         
       
     
     Here, P and Q are constants, which are factors that determine which item is preferentially minimized. For example, in the case of uniformly minimizing the three items (in other words, solving the problem without biasing the intensities of the constraint conditions), P and Q are set to be the same or similar values. In this way, the values are set to balance between the items. 
     However, if the problem setting is based on that “the constraint condition of the second item is strictly kept, but a great importance is not attached to the constraint condition of the third item”, the value of P which is the coefficient of the item of a great importance is set larger than the value of Q to obtain a desired solution. 
     As described above, the annealing method makes it possible to assign priority for the constraint conditions and make setting, for example, for a constraint condition of less importance like “it should be satisfied as much as possible”. 
     Note that various settings regarding the Ising model are made as appropriate according to each condition and information for creating a schedule in the present embodiment based on existing general concepts. 
     - - - Specific Examples of Spin (Variable) Setting - - - 
     &lt;Spins in Time Table&gt; 
     Consider a variable x_(i, j, k) that is 1 when a worker i carries out a work type k in a time slot j and that is 0 when the worker i does not (see  FIG.  5   ). Basically, each one of the variables x_(i, j, k) is assigned to a spin one by one in the CMOS annealing machine. 
     In the case of not taking the “work type” into account, this variable simply gives “whether a worker i is to work in a time slot j”. Specifically, in the following Table 1, the cells having 1 mean carrying out the work, and the cells having 0 mean not carrying out the work. 
     
       
         
           
               
               
               
               
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                   
                   
                   
                   
                   
                   
                 The Number 
               
               
                 Time 
                 Worker 1 
                 Worker 2 
                 Worker 3 
                   
                 Worker 30 
                 of Necessary 
               
               
                 Slot 
                 (i = 1) 
                 (i = 2) 
                 (i = 3) 
                 . . . 
                 (i = 30) 
                 Operators 
               
               
                   
               
             
            
               
                 9:00 to 
                 x 1, 1, k   
                 x 2, 1, k   
                 x 3, 1, k   
                 . . . 
                 x 30, 1, k   
                 10 
               
               
                 9:10 
               
               
                 (j = 1) 
               
               
                 9:10 to 
                 x 1, 2, k   
                 x 2, 2, k   
                 x 3, 2, k   
                 . . . 
                 x 30, 2, k   
                 12 
               
               
                 9:20 
               
               
                 (j = 2) 
               
               
                 9:20 to 
                 x 1, 3, k   
                 x 2, 3, k   
                 x 3, 3, k   
                 . . . 
                 x 30, 3, k   
                 10 
               
               
                 9:30 
               
               
                 (j = 3) 
               
               
                 9:30 to 
                 x 1, 4, k   
                 x 2, 4, k   
                 x 3, 4, k   
                 . . . 
                 x 30, 4, k   
                 10 
               
               
                 9:40 
               
               
                 (j = 4) 
               
               
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 
                   
                 
                 . . . 
                 . . . 
               
               
                 20:50 to 
                 x 1, 72, k   
                 x 2, 72, k   
                 x 3, 72, k   
                 . . . 
                 x 30, 72, k   
                  3 
               
               
                 21: 00 
               
               
                 (j = 72) 
               
               
                 The Number 
                 400 ± 50 
                 400 ± 50 
                 400 ± 50 
                 . . . 
                 400 ± 50 
               
               
                 of Working 
               
               
                 Shifts 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
             
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                 Value of x 1, 1, 1   
                 Value of x 1, 1, 2   
                 work type 
               
               
                   
                   
               
             
            
               
                   
                 0 
                 0 
                 Rest 
               
               
                   
                 1 
                 0 
                 Inbound Operation 
               
               
                   
                 0 
                 1 
                 Outbound Operation 
               
               
                   
                 1 
                 1 
                 (not applicable) 
               
               
                   
                   
                   
                 *That two variables 
               
               
                   
                   
                   
                 are both 1 is 
               
               
                   
                   
                   
                 prohibited by 
               
               
                   
                   
                   
                 constraint condition 
               
               
                   
                   
               
            
           
         
       
     
     In the case of taking the “work type” into account, in the above Table 2, the work type “inbound” is associated with k=1, and the work type “outbound” is associated with k=2. Thus, one cell on the timetable is expressed by the combination of the two variables. Specifically, if two variables (x_(i, j, 1) and x_(i, j, 2)) belonging to a cell are both 0, the cell means “rest”, if x_(i, j, 1) is 1, and x_(i, j, 2) is 0, the cell means “inbound”, and if x_(i, j, 1) is 0, and x_(i, j, 2) is 1, the cell means “outbound”. Here, since the case where x_(i, j, 1) and x_(i, j, 2) are both 1 means that “one person carries out two different kinds of work in one and the same time slot”, this case needs to be excluded as a constraint condition. 
     &lt;Spins in Shifts for Month&gt; 
     Here, consider a variable x_(i, j, k) that is 1 when a worker i carries out a work type k on a day j and that is 0 when the worker i does not. Here, L_i is the lower limit of the number of working days for the worker i, U_i is the upper limit, and N_j is the number of workers necessary for the day j. Basically, each one of the variables x_(i, j, k) is assigned to a spin one by one in the CMOS annealing machine (see Table 3). 
     
       
         
           
               
               
               
               
               
               
               
             
               
                 TABLE 3 
               
               
                   
               
               
                   
                   
                   
                   
                   
                   
                 The Number 
               
               
                   
                 Worker 1 
                 Worker 2 
                 Worker 3 
                   
                 Worker 30 
                 of Necessary 
               
               
                 Day 
                 (i = 1) 
                 (i = 2) 
                 (i = 3) 
                 . . . 
                 (i = 30) 
                 Operators 
               
               
                   
               
             
            
               
                 1st 
                 x 1, 1, k   
                 x 2, 1, k   
                 x 3, 1, k   
                 . . . 
                 x 30, 1, k   
                 N 1   
               
               
                 (j = 1) 
               
               
                 2nd 
                 x 1, 2, k   
                 x 2, 2, k   
                 x 3, 2, k   
                 . . . 
                 x 30, 2, k   
                 N 2   
               
               
                 (j = 2) 
               
               
                 3rd 
                 x 1, 3, k   
                 x 2, 3, k   
                 x 3, 3, k   
                 . . . 
                 x 30, 3, k   
                 N 3   
               
               
                 (j = 3) 
               
               
                 4th 
                 x 1, 4, k   
                 x 2, 4, k   
                 x 3, 4, k   
                 . . . 
                 x 30, 4, k   
                 N 4   
               
               
                 (j = 4) 
               
               
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 
                   
                 
                 . . . 
                 . . . 
               
               
                 31st 
                 x 1, 31, k   
                 x 2, 31, k   
                 x 3, 31, k   
                 . . . 
                 x 30, 31, k   
                     N 31   
               
               
                 (j = 31) 
               
               
                 The Number 
                 L 1  to 
                 L 2  to 
                 L 3  to 
                 . . . 
                 L 30  to 
               
               
                 of Working 
                 U 1   
                 U 2   
                 U 3   
                   
                 U 30   
               
               
                 Shifts 
               
               
                   
               
            
           
         
       
     
     In the case of not taking the “work type” into account, this variable simply gives “whether a worker i is to work on a day j”. Specifically, in Table 3, the cells having 1 mean attendance at work, and the cells having 0 mean holidays. 
     In the case of taking the “work type” into account, for example, it is conceivable that the “early shift” is associated with k=1, the “late shift” with k=2, and the “midnight shift” with k=3. In this case, there are three variables that correspond to the top leftmost cell of the table in  FIG.  7   , (x_1, 1, 1, x_1, 1, 2, and x_1, 1, 3). Since each of the three variables takes a value of 0 or 1, there are eight possible combinations as shown in the following Table 4. 
     
       
         
           
               
               
               
               
             
               
                 TABLE 4 
               
               
                   
               
               
                 Value of 
                 Value of 
                 Value of 
                   
               
               
                 x 1, 1, 1   
                 x 1, 1, 2   
                 x 1, 1, 3   
                 work type 
               
               
                   
               
             
            
               
                 0 
                 0 
                 0 
                 holiday 
               
               
                 1 
                 0 
                 0 
                 early shift 
               
               
                 0 
                 1 
                 0 
                 late shift 
               
               
                 0 
                 0 
                 1 
                 midnight shift 
               
               
                 1 
                 1 
                 0 
                 ×(prohibit by constraint 
               
               
                   
                   
                   
                 condition) 
               
               
                 1 
                 0 
                 1 
                 ×(prohibit by constraint 
               
               
                   
                   
                   
                 condition) 
               
               
                 0 
                 1 
                 1 
                 ×(prohibit by constraint 
               
               
                   
                   
                   
                 condition) 
               
               
                 1 
                 1 
                 1 
                 ×(prohibit by constraint 
               
               
                   
                   
                   
                 condition) 
               
               
                   
               
            
           
         
       
     
     In this case, a constraint condition that “of the three variables (x_1, 1, 1, x_1, 1, 2, and x_1, 1, 3), only one variable can take 1” needs to be added to prohibit the results in the bottom four lines in the above table. 
     - - - Example of Data Structure - - - 
     Next, a description will be given of various kinds of information used by the schedule creation assisting device  100  of the present embodiment.  FIG.  5    illustrates an example of a basic information table  125  in the present embodiment. 
     The basic information table  125  of the present embodiment stores information on the total number of working shifts for specified months for each of the operators that work in corporation in a call center operation and the number of operators necessary for each time slot on each day in the month. 
     This example is a combinatorial optimization problem in which the length of the time slot is 10 minutes, the number of necessary operators specified across each horizontal line needs to be satisfied in each time slot, and the number of working hours (the number of working shifts) for each operator needs to be kept. In this problem, the shorter the length of the divided time slot, the larger the number of cells necessary for calculation (the cells in this table=factors), and the higher the necessary calculation power. Since the number of cells is large, if constraints are applied, such as prohibited patterns, the minimum number of consecutive shifts (the guideline for the minimum number of consecutive working shifts), the maximum number of consecutive shifts (the guideline for the maximum number of consecutive working shifts), and the like, the number of constraint condition functions according to the constraint conditions is enormous. However, employing the CMOS annealing method makes it possible to determine preferred results, in other words, a preferred schedule within a realistic time. 
     Note that the example shown in the basic information table  125  of  FIG.  5    only has limited information for convenience of explanation, and thus it is assumed that the table stores information on other various events (the same applies in the following). 
       FIGS.  6  and  7    illustrate an example of a constraint condition table  126  in the present embodiment. The constraint condition table  126  of the present embodiment stores information on the constraint conditions regarding allocation of each operator to the foregoing call center operation. 
     The data structure of the table is a set of records including data such as the identification information (“#” in the figure) of each constraint condition, which is used as a key, the description of the constraint condition, an implementation example with an optimization solver, and an implementation example with an annealing machine (a constraint condition function). 
     The present embodiment not only shows implementation examples with an annealing machine, in other words, constraint condition functions, but to compare them with a conventional technique, the present embodiment also shows, side by side, examples of functions in which the constraint condition is implemented with an optimization solver. 
     - - - Example of Procedure - - - 
     Hereinafter, a description will be given of an actual procedure of the schedule creation assisting method in the present embodiment based on the figures. Various operations corresponding to the schedule creation assisting method described below are implemented by using a program that the schedule creation assisting device  100  loads into a memory or the like and executes. This program includes code for performing various operations described below. 
       FIG.  8    is a diagram illustrating an example of a procedure for the schedule creation assisting method in the present embodiment. In this case, the schedule creation assisting device  100  computes an Ising model  1021  which is set as a processing target in which regarding an objective function including, as terms, the total number of working shifts of each operator for a certain month, the number of necessary operators, and the constraint condition functions, whether each operator is to attend at work is defined as a spin, and the sensitivity between variables of the constraint condition function is set as the intensity of interaction between the spins. 
     The schedule creation assisting device  100  obtains conditions desired by each operator from the user terminal  200  and stores them in the constraint condition table  126  as constraint conditions (s 10 ). Alternatively, in this process, each operator may specify the constraint conditions that match desired constraint conditions out of the constraint condition table  126 , and the schedule creation assisting device  100  may receive the specification from each operator. 
     The schedule creation assisting device  100  converts the constraint conditions obtained at s 10  into constraint condition functions as already described (s 11 ). These constraint condition functions are functions that are minimized when the constraint conditions are satisfied. Note that in the case of receiving the specification of constraint conditions at s 10  as described above, the schedule creation assisting device  100  extracts constraint condition functions already defined for the constraint conditions from the constraint condition table  126 . 
     As an annealing machine, the schedule creation assisting device  100  sets, as a problem, an Ising model  1021  in which the foregoing three items (the total number of working shifts, the number of necessary operators, and the constraint condition functions) are set and calculates and determines the ground state that minimizes the objective function (s 12 ). Searching for the ground state in itself is the same as or similar to the process in conventional techniques. 
     Specifically, the constraint conditions regarding each operator and the rules on the basic information such as the total number of working shifts and the number of necessary operators are satisfied, transition toward the final state indicating whether each time slot is assigned (in theory based on sensitivities) progresses as time passes, and a state in which the results of assignment for each operator are settled is searched for as the ground state. 
     The schedule creation assisting device  100  transmits information indicating whether each time slot is assigned to each operator determined at s 12  (the screen  900  of  FIG.  9   ) to the user terminal  200  as a schedule (s 13 ) and ends the process. 
     The user terminal  200 , receiving provision of such information, displays a schedule screen  900  as illustrated in  FIG.  9    on an output device such as a display. 
     The operator of the user terminal  200  views the schedule screen  900 , recognizes the timetable, for example, for the next month, tomorrow, or one hour ahead, and checks and examines the call center operation appropriately. 
     Note that examples of schedule created according to the types of constraint conditions are shown as follows. Here, the result (Table 5) of creating a schedule on the premise that there is no such constraint condition regarding continuous work (Expression 15: Working shifts shall be continuous to the extent possible) and a schedule (Table 6) for the case where the constraint condition is solved are both shown for comparison. 
     
       
         
           
             [ 
             
               Expression 
               ⁢ 
                   
               15 
             
             ] 
           
         
       
       
         
           
             
               
                 
                   min 
                   - 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       4 
                     
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           2 
                         
                         15 
                       
                       
                         
                           x 
                           
                             i 
                             , 
                             
                               j 
                               - 
                               1 
                             
                           
                         
                         ⁢ 
                         
                           x 
                           
                             i 
                             , 
                             j 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Expression 
                   ⁢ 
                       
                   15 
                 
               
             
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 5 
               
             
            
               
                   
               
               
                 In the case where there are no constraint conditions 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                 The 
               
               
                   
                   
                   
                   
                   
                 Number of 
               
               
                 Time 
                 Operator 
                 Operator 
                 Operator 
                 Operator 
                 Necessary 
               
               
                 Slot 
                 1 
                 2 
                 3 
                 4 
                 Operators 
               
               
                   
               
               
                 9:00 to 
                 work 
                 rest 
                 rest 
                 work 
                 2 
               
               
                 9:10 
                   
                   
                   
                   
                   
               
               
                 9:10 to 
                 rest 
                 work 
                 rest 
                 work 
                 2 
               
               
                 9:20 
                   
                   
                   
                   
                   
               
               
                 9:20 to 
                 work 
                 rest 
                 work 
                 rest 
                 2 
               
               
                 9:30 
                   
                   
                   
                   
                   
               
               
                 9:30 to 
                 rest 
                 work 
                 rest 
                 work 
                 2 
               
               
                 9:40 
                   
                   
                   
                   
                   
               
               
                 9:40 to 
                 work 
                 rest 
                 work 
                 rest 
                 2 
               
               
                 9:50 
                   
                   
                   
                   
                   
               
               
                 9:50 to 
                 rest 
                 work 
                 work 
                 work 
                 3 
               
               
                 10:00 
                   
                   
                   
                   
                   
               
               
                 10:00 to 
                 work 
                 work 
                 work 
                 work 
                 4 
               
               
                 10:10 
                   
                   
                   
                   
                   
               
               
                 10:10 to 
                 work 
                 work 
                 work 
                 work 
                 4 
               
               
                 10:20 
                   
                   
                   
                   
                   
               
               
                 10:20 to 
                 work 
                 work 
                 work 
                 rest 
                 3 
               
               
                 10:30 
                   
                   
                   
                   
                   
               
               
                 10:30 to 
                 work 
                 rest 
                 work 
                 work 
                 3 
               
               
                 10:40 
                   
                   
                   
                   
                   
               
               
                 10:40 to 
                 rest 
                 work 
                 work 
                 rest 
                 2 
               
               
                 10:50 
                   
                   
                   
                   
                   
               
               
                 10:50 to 
                 work 
                 rest 
                 rest 
                 work 
                 2 
               
               
                 11:00 
                   
                   
                   
                   
                   
               
               
                 11:00 to 
                 rest 
                 work 
                 work 
                 rest 
                 2 
               
               
                 11:10 
                   
                   
                   
                   
                   
               
               
                 11:10 to 
                 work 
                 work 
                 rest 
                 work 
                 3 
               
               
                 11:20 
                   
                   
                   
                   
                   
               
               
                 11:20 to 
                 work 
                 work 
                 work 
                 work 
                 4 
               
               
                 11:30 
                   
                   
                   
                   
                   
               
               
                 The 
                 10 
                 10 
                 10 
                 10 
                   
               
               
                 Number 
                   
                   
                   
                   
                   
               
               
                 of 
                   
                   
                   
                   
                   
               
               
                 Working 
                   
                   
                   
                   
                   
               
               
                 Shifts 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 6 
               
             
            
               
                   
               
               
                 In the case where there are constraint conditions 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                 The 
               
               
                   
                   
                   
                   
                   
                 Number of 
               
               
                 Time 
                 Operator 
                 Operator 
                 Operator 
                 Operator 
                 Necessary 
               
               
                 Slot 
                 1 
                 2 
                 3 
                 4 
                 Operators 
               
               
                   
               
               
                 9:00 to 
                 work 
                 rest 
                 rest 
                 work 
                 2 
               
               
                 9:10 
                   
                   
                   
                   
                   
               
               
                 9:10 to 
                 work 
                 rest 
                 rest 
                 work 
                 2 
               
               
                 9:20 
                   
                   
                   
                   
                   
               
               
                 9:20 to 
                 work 
                 rest 
                 work 
                 rest 
                 2 
               
               
                 9:30 
                   
                   
                   
                   
                   
               
               
                 9:30 to 
                 rest 
                 work 
                 work 
                 rest 
                 2 
               
               
                 9:40 
                   
                   
                   
                   
                   
               
               
                 9:40 to 
                 rest 
                 work 
                 work 
                 rest 
                 2 
               
               
                 9:50 
                   
                   
                   
                   
                   
               
               
                 9:50 to 
                 rest 
                 work 
                 work 
                 work 
                 3 
               
               
                 10:00 
                   
                   
                   
                   
                   
               
               
                 10:00 to 
                 work 
                 work 
                 work 
                 work 
                 4 
               
               
                 10:10 
                   
                   
                   
                   
                   
               
               
                 10:10 to 
                 work 
                 work 
                 work 
                 work 
                 4 
               
               
                 10:20 
                   
                   
                   
                   
                   
               
               
                 10:20 to 
                 work 
                 work 
                 work 
                 rest 
                 3 
               
               
                 10:30 
                   
                   
                   
                   
                   
               
               
                 10:30 to 
                 work 
                 work 
                 work 
                 rest 
                 3 
               
               
                 10:40 
                   
                   
                   
                   
                   
               
               
                 10:40 to 
                 rest 
                 work 
                 rest 
                 work 
                 2 
               
               
                 10:50 
                   
                   
                   
                   
                   
               
               
                 10:50 to 
                 rest 
                 work 
                 rest 
                 work 
                 2 
               
               
                 11:00 
                   
                   
                   
                   
                   
               
               
                 11:00 to 
                 work 
                 rest 
                 rest 
                 work 
                 2 
               
               
                 11:10 
                   
                   
                   
                   
                   
               
               
                 11:10 to 
                 work 
                 rest 
                 work 
                 work 
                 3 
               
               
                 11:20 
                   
                   
                   
                   
                   
               
               
                 11:20 to 
                 work 
                 work 
                 work 
                 work 
                 4 
               
               
                 11:30 
                   
                   
                   
                   
                   
               
               
                 The 
                 10 
                 10 
                 10 
                 10 
                   
               
               
                 Number 
                   
                   
                   
                   
                   
               
               
                 of 
                   
                   
                   
                   
                   
               
               
                 Working 
                   
                   
                   
                   
                   
               
               
                 Shifts 
               
               
                   
               
            
           
         
       
     
     As shown above, in the case where there is no constraint, working shifts are fragmentary, and there are many portions where “work→rest→work→rest” are repeated at intervals of 10 minutes. Thus, the timetable is not realistic. 
     In contrast, in the case where the constraint was considered, the working shifts are basically continuous, and the same type of work can be carried out for a certain length of time. Thus, the timetable is realistic. 
     Next, the result (Table 7) of creating a schedule on the premise that there is no constraint condition regarding discontinuous work (Expression 16: Too many holidays shall not be continued in a row) and a schedule (Table 8) for the case where the constraint condition is solved are shown. Note that here is shown an example of results of the constraint condition regarding discontinuous work in work shifts of a month. An example of an expression of the constraint condition considered this time is shown below. This time, the “work type” is not mentioned, and thus, the variable x_(i,j) in which the subscript (k) related to the work type is omitted is considered. Here, the symbol A is an adjusted integer. 
     
       
         
           
             	 
             
               [ 
               
                 Expression 
                 ⁢ 
                     
                 16 
               
               ] 
             
           
         
       
       
         
           
             
               
                 
                   min 
                   - 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       4 
                     
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           2 
                         
                         14 
                       
                       
                         
                           ( 
                           
                             1 
                             - 
                             
                               x 
                               
                                 i 
                                 , 
                                 
                                   j 
                                   - 
                                   1 
                                 
                               
                             
                           
                           ) 
                         
                         ⁢ 
                         
                           ( 
                           
                             1 
                             - 
                             
                               x 
                               
                                 i 
                                 , 
                                 j 
                               
                             
                           
                           ) 
                         
                       
                     
                   
                   + 
                   
                     A 
                     ⁢ 
                     
                       
                         ∑ 
                         
                           i 
                           = 
                           1 
                         
                         4 
                       
                       
                         
                           ∑ 
                           
                             j 
                             = 
                             3 
                           
                           14 
                         
                         
                           
                             ∏ 
                             
                               l 
                               = 
                               
                                 j 
                                 - 
                                 2 
                               
                             
                             j 
                           
                           
                             ( 
                             
                               1 
                               - 
                               
                                 x 
                                 
                                   i 
                                   , 
                                   j 
                                 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Expression 
                   ⁢ 
                       
                   16 
                 
               
             
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 7 
               
             
            
               
                   
               
               
                 In the case where there are no constraint conditions 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                 The 
               
               
                   
                   
                   
                   
                   
                 Number of 
               
               
                   
                 Operator 
                 Operator 
                 Operator 
                 Operator 
                 Necessary 
               
               
                 Day 
                 1 
                 2 
                 3 
                 4 
                 Operators 
               
               
                   
               
               
                  1st 
                 work 
                 holiday 
                 work 
                 work 
                 3 
               
               
                  2nd 
                 work 
                 holiday 
                 work 
                 work 
                 3 
               
               
                  3rd 
                 work 
                 holiday 
                 work 
                 work 
                 3 
               
               
                  4th 
                 work 
                 holiday 
                 work 
                 holiday 
                 2 
               
               
                  5th 
                 work 
                 work 
                 work 
                 holiday 
                 3 
               
               
                  6th 
                 work 
                 work 
                 work 
                 holiday 
                 3 
               
               
                  7th 
                 work 
                 work 
                 work 
                 holiday 
                 3 
               
               
                  8th 
                 work 
                 work 
                 holiday 
                 work 
                 3 
               
               
                  9th 
                 work 
                 work 
                 holiday 
                 work 
                 3 
               
               
                 10th 
                 work 
                 work 
                 holiday 
                 work 
                 3 
               
               
                 11th 
                 holiday 
                 work 
                 holiday 
                 work 
                 2 
               
               
                 12th 
                 holiday 
                 work 
                 work 
                 work 
                 3 
               
               
                 13th 
                 holiday 
                 work 
                 work 
                 work 
                 3 
               
               
                 14th 
                 holiday 
                 work 
                 work 
                 work 
                 3 
               
               
                 The 
                 10 
                 10 
                 10 
                 10 
                   
               
               
                 Number 
                   
                   
                   
                   
                   
               
               
                 of 
                   
                   
                   
                   
                   
               
               
                 Working 
                   
                   
                   
                   
                   
               
               
                 Shifts 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 8 
               
             
            
               
                   
               
               
                 In the case where there are constraint conditions 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                 The 
               
               
                   
                   
                   
                   
                   
                 Number of 
               
               
                   
                 Operator 
                 Operator 
                 Operator 
                 Operator 
                 Necessary 
               
               
                 Day 
                 1 
                 2 
                 3 
                 4 
                 Operators 
               
               
                   
               
               
                  1st 
                 holiday 
                 work 
                 work 
                 work 
                 3 
               
               
                  2nd 
                 holiday 
                 work 
                 work 
                 work 
                 3 
               
               
                  3rd 
                 work 
                 work 
                 holiday 
                 work 
                 3 
               
               
                  4th 
                 work 
                 work 
                 holiday 
                 holiday 
                 2 
               
               
                  5th 
                 work 
                 work 
                 work 
                 holiday 
                 3 
               
               
                  6th 
                 work 
                 holiday 
                 work 
                 work 
                 3 
               
               
                  7th 
                 work 
                 holiday 
                 work 
                 work 
                 3 
               
               
                  8th 
                 holiday 
                 work 
                 work 
                 work 
                 3 
               
               
                  9th 
                 holiday 
                 work 
                 work 
                 work 
                 3 
               
               
                 10th 
                 work 
                 work 
                 holiday 
                 work 
                 3 
               
               
                 11th 
                 work 
                 work 
                 holiday 
                 holiday 
                 2 
               
               
                 12th 
                 work 
                 holiday 
                 work 
                 work 
                 3 
               
               
                 13th 
                 work 
                 holiday 
                 work 
                 work 
                 3 
               
               
                 14th 
                 work 
                 work 
                 work 
                 holiday 
                 3 
               
               
                 The 
                 10 
                 10 
                 10 
                 10 
                   
               
               
                 Number of 
                   
                   
                   
                   
                   
               
               
                 Working 
                   
                   
                   
                   
                   
               
               
                 Shifts 
               
               
                   
               
            
           
         
       
     
     As shown above, in the case where there is no constraint, work days or holidays continue more than necessary, and the work shifts include “10 consecutive work days” and “4 consecutive holidays”, the work shifts of the month is unrealistic also in terms of laws, office rules, and burdens on each operator. In contrast, in the case where the constraint was considered, consecutive work days and consecutive holidays are randomly arranged to an appropriate degree. Thus, the work shifts of the month are realistic. 
     Next, the result (Table 9) of creating a schedule on the premise that there is no constraint condition regarding prohibited patterns (Expression 17: An early shift on the next day of a late shift shall be prohibited) and a schedule (Table 10) for the case where the constraint condition is solved are shown. Here is shown an example of results of the constraint condition regarding a prohibited pattern in work shifts of a month. An example of an expression of the constraint condition considered this time is shown below. Since this time, of the “work types”, only the early shift (k=1) and the late shift (k=2) are mentioned, the number of the subscript (k) concerning the work type considered here is up to 2. 
     
       
         
           
             [ 
             
               Expression 
               ⁢ 
                   
               17 
             
             ] 
           
         
       
       
         
           
             
               
                 
                   min 
                   ⁢ 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       4 
                     
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           2 
                         
                         14 
                       
                       
                         
                           x 
                           
                             i 
                             , 
                             
                               j 
                               - 
                               1 
                             
                             , 
                             2 
                           
                         
                         ⁢ 
                         
                           x 
                           
                             i 
                             , 
                             j 
                             , 
                             1 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Expression 
                   ⁢ 
                       
                   17 
                 
               
             
           
         
       
     
     This constraint condition means that “an early shift is not to be assigned on the next day of a late shift”. 
     
       
         
           
               
             
               
                 TABLE 9 
               
             
            
               
                   
               
               
                 In the case where there are no constraint conditions 
               
            
           
           
               
               
            
               
                   
                 The Number 
               
               
                   
                 of Necessary 
               
               
                   
                 Operators 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                 Early 
                 Late 
               
               
                 Day 
                 Operator 1 
                 Operator 2 
                 Operator 3 
                 Operator 4 
                 Shift 
                 Shift 
               
               
                   
               
               
                 1st 
                 holiday 
                 early 
                 early 
                 ▴late 
                 2 
                 1 
               
               
                   
                   
                 shift 
                 shift 
                 shift 
               
               
                     2nd 
                 holiday 
                 early 
                 ▴late 
                 early 
                 2 
                 1 
               
               
                   
                   
                 shift 
                 shift 
                 shift 
               
               
                 3rd 
                 ▴late 
                 early 
                 holiday 
                 early 
                 2 
                 1 
               
               
                   
                 shift 
                 shift 
                   
                 shift 
               
               
                 4th 
                 early 
                 ▴late 
                 holiday 
                 holiday 
                 1 
                 1 
               
               
                   
                 shift 
                 shift 
               
               
                 5th 
                 early 
                 early 
                 ▴late 
                 holiday 
                 2 
                 1 
               
               
                   
                 shift 
                 shift 
                 shift 
               
               
                 6th 
                 ▴late 
                 holiday 
                 early 
                 early 
                 2 
                 1 
               
               
                   
                 shift 
                   
                 shift 
                 shift 
               
               
                 7th 
                 early 
                 holiday 
                 early 
                 ▴late 
                 2 
                 1 
               
               
                   
                 shift 
                   
                 shift 
                 shift 
               
               
                 8th 
                 holiday 
                 early 
                 ▴late 
                 early 
                 2 
                 1 
               
               
                   
                   
                 shift 
                 shift 
                 shift 
               
               
                 9th 
                 holiday 
                 ▴late 
                 early 
                 early 
                 2 
                 1 
               
               
                   
                   
                 shift 
                 shift 
                 shift 
               
               
                 10th  
                 ▴late 
                 early 
                 holiday 
                 early 
                 2 
                 1 
               
               
                   
                 shift 
                 shift 
                   
                 shift 
               
               
                 11th  
                 early 
                 ▴late 
                 holiday 
                 holiday 
                 1 
                 1 
               
               
                   
                 shift 
                 shift 
               
               
                 12th  
                 early 
                 holiday 
                 early 
                 ▴late 
                 2 
                 1 
               
               
                   
                 shift 
                   
                 shift 
                 shift 
               
               
                 13th  
                 early 
                 holiday 
                 early 
                 ▴late 
                 2 
                 1 
               
               
                   
                 shift 
                   
                 shift 
                 shift 
               
               
                 14th  
                 early 
                 early 
                 ▴late 
                 holiday 
                 2 
                 1 
               
               
                   
                 shift 
                 shift 
                 shift 
               
               
                 Days of 
                 7 
                 7 
                 6 
                 6 
               
               
                 Early 
               
               
                 Shift 
               
               
                 Days of 
                 3 
                 3 
                 4 
                 4 
               
               
                 Late 
               
               
                 Shift 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 10 
               
             
            
               
                   
               
               
                 In the case where there are constraint conditions 
               
            
           
           
               
               
            
               
                   
                 The Number 
               
               
                   
                 of Necessary 
               
               
                   
                 Operators 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                 Early 
                 Late 
               
               
                 Day 
                 Operator 1 
                 Operator 2 
                 Operator 3 
                 Operator 4 
                 Shift 
                 Shift 
               
               
                   
               
               
                 1st 
                 holiday 
                 early 
                 ▴late 
                 early 
                 2 
                 1 
               
               
                   
                   
                 shift 
                 shift 
                 shift 
               
               
                     2nd 
                 holiday 
                 early 
                 ▴late 
                 early 
                 2 
                 1 
               
               
                   
                   
                 shift 
                 shift 
                 shift 
               
               
                 3rd 
                 early 
                 early 
                 holiday 
                 ▴late 
                 2 
                 1 
               
               
                   
                 shift 
                 shift 
                   
                 shift 
               
               
                 4th 
                 early 
                 ▴late 
                 holiday 
                 holiday 
                 1 
                 1 
               
               
                   
                 shift 
                 shift 
               
               
                 5th 
                 early 
                 ▴late 
                 early 
                 holiday 
                 2 
                 1 
               
               
                   
                 shift 
                 shift 
                 shift 
               
               
                 6th 
                 ▴late 
                 holiday 
                 early 
                 early 
                 2 
                 1 
               
               
                   
                 shift 
                   
                 shift 
                 shift 
               
               
                 7th 
                 ▴late 
                 holiday 
                 early 
                 early 
                 2 
                 1 
               
               
                   
                 shift 
                   
                 shift 
                 shift 
               
               
                 8th 
                 holiday 
                 early 
                 ▴late 
                 early 
                 2 
                 1 
               
               
                   
                   
                 shift 
                 shift 
                 shift 
               
               
                 9th 
                 holiday 
                 early 
                 ▴late 
                 early 
                 2 
                 1 
               
               
                   
                   
                 shift 
                 shift 
                 shift 
               
               
                 10th  
                 early 
                 early 
                 holiday 
                 ▴late 
                 2 
                 1 
               
               
                   
                 shift 
                 shift 
                   
                 shift 
               
               
                 11th  
                 early 
                 ▴late 
                 holiday 
                 holiday 
                 1 
                 1 
               
               
                   
                 shift 
                 shift 
               
               
                 12th  
                 early 
                 holiday 
                 early 
                 ▴late 
                 2 
                 1 
               
               
                   
                 shift 
                   
                 shift 
                 shift 
               
               
                 13th  
                 early 
                 holiday 
                 early 
                 ▴late 
                 2 
                 1 
               
               
                   
                 shift 
                   
                 shift 
                 shift 
               
               
                 14th  
                 ▴late 
                 early 
                 early 
                 holiday 
                 2 
                 1 
               
               
                   
                 shift 
                 shift 
                 shift 
               
               
                 Days of 
                 7 
                 7 
                 6 
                 6 
               
               
                 Early 
               
               
                 Shift 
               
               
                 Days of 
                 3 
                 3 
                 4 
                 4 
               
               
                 Late 
               
               
                 Shift 
               
               
                   
               
            
           
         
       
     
     In the above tables, a symbol ▴ is prefixed to each late shift to make it easy to distinguish. As shown above, in the case where there is no constraint, there are many portions where an early shift is assigned on the next day of a late shift. It means that before the operator takes enough rest, the operator has to work on the next day. Thus, the work shifts of the month are not realistic. In contrast, in the case where the constraint was considered, either a late shift or a holiday is assigned on the next day of a late shift. Thus, the work shifts of the month are realistic. 
     Next, the result (Table 11) of creating a schedule on the premise that there is no constraint condition regarding the compatibility between operators (Expression 18: Combinations of only recruits shall be avoided &amp; an instructor shall be combined) and a schedule (Table 12) for the case where the constraint conditions are solved are shown. Here is shown an example of results of the constraint conditions regarding the compatibility between operators in work shifts of a month. 
     Here, this time, the “work type” is not mentioned, and thus, the variable x_(i,j) in which the subscript (k) related to the work type is omitted is considered. Here, the symbols A and B are adjusted integers. 
     
       
         
           
             [ 
             
               Expression 
               ⁢ 
                   
               18 
             
             ] 
           
         
       
       
         
           
             
               
                 
                   
                     min 
                     ⁢ 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           1 
                         
                         14 
                       
                       
                         
                           x 
                           
                             3 
                             , 
                             j 
                           
                         
                         ⁢ 
                         
                           x 
                           
                             4 
                             , 
                             j 
                           
                         
                       
                     
                   
                   - 
                   
                     A 
                     ⁢ 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           1 
                         
                         14 
                       
                       
                         
                           x 
                           
                             1 
                             , 
                             j 
                           
                         
                         ⁢ 
                         
                           x 
                           
                             3 
                             , 
                             j 
                           
                         
                       
                     
                   
                   - 
                   
                     B 
                     ⁢ 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           1 
                         
                         14 
                       
                       
                         
                           x 
                           
                             2 
                             , 
                             j 
                           
                         
                         ⁢ 
                         
                           x 
                           
                             4 
                             , 
                             j 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Expression 
                   ⁢ 
                       
                   18 
                 
               
             
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 11 
               
             
            
               
                   
               
               
                 In the case where there are no constraint conditions 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Operator 1 
                 Operator 2 
                   
                   
                   
               
               
                   
                 (Expert A) 
                 (Expert B) 
                 Operator 
                 Operator 
                 The 
               
               
                   
                 Instructor 
                 Instructor 
                 3 
                 4 
                 Number of 
               
               
                   
                 for 
                 for 
                 (Recruit 
                 (Recruit 
                 Necessary 
               
               
                 Day 
                 Recruit A 
                 Recruit B 
                 A) 
                 B) 
                 Operators 
               
               
                   
               
               
                  1st 
                 work 
                 holiday 
                 work 
                 work 
                 3 
               
               
                  2nd 
                 work 
                 holiday 
                 work 
                 work 
                 3 
               
               
                  3rd 
                 work 
                 work 
                 holiday 
                 holiday 
                 2 
               
               
                  4th 
                 holiday 
                 work 
                 holiday 
                 work 
                 2 
               
               
                  5th 
                 holiday 
                 work 
                 work 
                 work 
                 3 
               
               
                  6th 
                 work 
                 work 
                 holiday 
                 holiday 
                 2 
               
               
                  7th 
                 work 
                 work 
                 holiday 
                 holiday 
                 2 
               
               
                  8th 
                 work 
                 holiday 
                 work 
                 work 
                 3 
               
               
                  9th 
                 work 
                 holiday 
                 work 
                 work 
                 3 
               
               
                 10th 
                 work 
                 work 
                 holiday 
                 holiday 
                 2 
               
               
                 11th 
                 holiday 
                 work 
                 work 
                 holiday 
                 2 
               
               
                 12th 
                 work 
                 work 
                 holiday 
                 work 
                 3 
               
               
                 13th 
                 work 
                 work 
                 holiday 
                 holiday 
                 2 
               
               
                 14th 
                 holiday 
                 work 
                 work 
                 holiday 
                 2 
               
               
                 The 
                 10 
                 10 
                 7 
                 7 
                   
               
               
                 Number 
                   
                   
                   
                   
                   
               
               
                 of 
                   
                   
                   
                   
                   
               
               
                 Working 
                   
                   
                   
                   
                   
               
               
                 Shifts 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 12 
               
             
            
               
                   
               
               
                 In the case where there are constraint conditions 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Operator 1 
                 Operator 2 
                   
                   
                   
               
               
                   
                 (Expert A) 
                 (Expert B) 
                 Operator 
                 Operator 
                 The 
               
               
                   
                 Instructor 
                 Instructor 
                 3 
                 4 
                 Number of 
               
               
                   
                 for 
                 for 
                 (Recruit 
                 (Recruit 
                 Necessary 
               
               
                 Day 
                 Recruit A 
                 Recruit B 
                 A) 
                 B) 
                 Operators 
               
               
                   
               
               
                  1st 
                 work 
                 work 
                 holiday 
                 work 
                 3 
               
               
                  2nd 
                 work 
                 work 
                 work 
                 holiday 
                 3 
               
               
                  3rd 
                 work 
                 holiday 
                 work 
                 holiday 
                 2 
               
               
                  4th 
                 holiday 
                 work 
                 holiday 
                 work 
                 2 
               
               
                  5th 
                 work 
                 work 
                 holiday 
                 work 
                 3 
               
               
                  6th 
                 holiday 
                 work 
                 holiday 
                 work 
                 2 
               
               
                  7th 
                 work 
                 holiday 
                 work 
                 holiday 
                 2 
               
               
                  8th 
                 work 
                 work 
                 work 
                 holiday 
                 3 
               
               
                  9th 
                 work 
                 work 
                 work 
                 holiday 
                 3 
               
               
                 10th 
                 holiday 
                 work 
                 holiday 
                 work 
                 2 
               
               
                 11th 
                 holiday 
                 work 
                 holiday 
                 work 
                 2 
               
               
                 12th 
                 work 
                 work 
                 holiday 
                 work 
                 3 
               
               
                 13th 
                 work 
                 holiday 
                 work 
                 holiday 
                 2 
               
               
                 14th 
                 work 
                 holiday 
                 work 
                 holiday 
                 2 
               
               
                 The 
                 10 
                 10 
                 7 
                 7 
                   
               
               
                 Number 
                   
                   
                   
                   
                   
               
               
                 of 
                   
                   
                   
                   
                   
               
               
                 Working 
                   
                   
                   
                   
                   
               
               
                 Shifts 
               
               
                   
               
            
           
         
       
     
     As above, in the case where there is no constraint, there are “days on which two recruits attend at work on the same day”, “days on which recruit A attends at work but operator 1 who is the instructor for recruit A does not”, and “days on which recruit B attends at work but operator 2 who is the instructor for recruit B does not”. The work shifts of the month are not realistic. In contrast, in the case where the constraints were considered, the number of recruits that attend at work on each day is only one, and on the day when a recruit attends at work, the recruit&#39;s instructor always attends. Thus, the work shifts of the month are realistic. 
     Next, the result (Table 13) of creating a schedule on the premise that there is no constraint condition regarding reflection of operators&#39; requests (Expression 19: Operator 2 wants to take holidays during the period from 1st to 7th &amp; operator 3 wants to work on early shifts &amp; operator 4 wants to work on late shifts) and a schedule (Table 14) for the case where the constraint conditions are solved are shown. 
     
       
         
           
             [ 
             
               Expression 
               ⁢ 
                   
               19 
             
             ] 
           
         
       
       
         
           
             
               
                 
                   min 
                   - 
                   
                     
                       ∑ 
                       
                         j 
                         = 
                         1 
                       
                       7 
                     
                     
                       ( 
                       
                         1 
                         - 
                         
                           x 
                           
                             2 
                             , 
                             j 
                             , 
                             k 
                           
                         
                       
                       ) 
                     
                   
                   - 
                   
                     A 
                     ⁢ 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           1 
                         
                         14 
                       
                       
                         x 
                         
                           3 
                           , 
                           j 
                           , 
                           1 
                         
                       
                     
                   
                   - 
                   
                     B 
                     ⁢ 
                     
                       
                         ∑ 
                         
                           j 
                           = 
                           1 
                         
                         14 
                       
                       
                         x 
                         
                           4 
                           , 
                           j 
                           , 
                           2 
                         
                       
                     
                   
                 
               
               
                 
                   Expression 
                   ⁢ 
                       
                   19 
                 
               
             
           
         
       
     
     These constraint conditions mean “operator 2 wants to take holidays in the first half of the period (1st to 7th)”, “operator 3 wants to work on early shifts to the extent possible”, and “operator 4 wants to work on late shifts to the extent possible”. 
     
       
         
           
               
             
               
                 TABLE 13 
               
             
            
               
                   
               
               
                 In the case where there are no constraint conditions 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                 Operator 2 
                 Operator 3 
                 Operator 4 
                 The Number 
               
               
                   
                   
                 (wants to take 
                 (wants to 
                 (wants to 
                 of Necessary 
               
               
                   
                 Operator 1 
                 holidays in 
                 work on 
                 work on 
                 Operators 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 (no 
                 the first half 
                 early 
                 late 
                 Early 
                 Late 
               
               
                 Day 
                 requests) 
                 of the period) 
                 shifts) 
                 shifts) 
                 Shift 
                 Shift 
               
               
                   
               
               
                 1st 
                 holiday 
                 early 
                 ▴late 
                 early 
                 2 
                 1 
               
               
                   
                   
                 shift 
                 shift 
                 shift 
               
               
                     2nd 
                 holiday 
                 early 
                 ▴late 
                 early 
                 2 
                 1 
               
               
                   
                   
                 shift 
                 shift 
                 shift 
               
               
                 3rd 
                 early 
                 early 
                 holiday 
                 ▴late 
                 2 
                 1 
               
               
                   
                 shift 
                 shift 
                   
                 shift 
               
               
                 4th 
                 early 
                 ▴late 
                 holiday 
                 holiday 
                 1 
                 1 
               
               
                   
                 shift 
                 shift 
               
               
                 5th 
                 early 
                 ▴late 
                 early 
                 holiday 
                 2 
                 1 
               
               
                   
                 shift 
                 shift 
                 shift 
               
               
                 6th 
                 ▴late 
                 holiday 
                 early 
                 early 
                 2 
                 1 
               
               
                   
                 shift 
                   
                 shift 
                 shift 
               
               
                 7th 
                 ▴late 
                 holiday 
                 early 
                 early 
                 2 
                 1 
               
               
                   
                 shift 
                   
                 shift 
                 shift 
               
               
                 8th 
                 holiday 
                 early 
                 ▴late 
                 early 
                 2 
                 1 
               
               
                   
                   
                 shift 
                 shift 
                 shift 
               
               
                 9th 
                 holiday 
                 early 
                 ▴late 
                 early 
                 2 
                 1 
               
               
                   
                   
                 shift 
                 shift 
                 shift 
               
               
                 10th  
                 early 
                 early 
                 holiday 
                 ▴late 
                 2 
                 1 
               
               
                   
                 shift 
                 shift 
                   
                 shift 
               
               
                 11th  
                 early 
                 ▴late 
                 holiday 
                 holiday 
                 1 
                 1 
               
               
                   
                 shift 
                 shift 
               
               
                 12th  
                 early 
                 holiday 
                 early 
                 ▴late 
                 2 
                 1 
               
               
                   
                 shift 
                   
                 shift 
                 shift 
               
               
                 13th  
                 early 
                 holiday 
                 early 
                 ▴late 
                 2 
                 1 
               
               
                   
                 shift 
                   
                 shift 
                 shift 
               
               
                 14th  
                 ▴late 
                 early 
                 early 
                 holiday 
                 2 
                 1 
               
               
                   
                 shift 
                 shift 
                 shift 
               
               
                 The Number 
                 10 
                 10 
                 10 
                 10 
               
               
                 of Working 
               
               
                 Shifts 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 14 
               
             
            
               
                   
               
               
                 In the case where there are constraint conditions 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                 Operator 2 
                 Operator 3 
                 Operator 4 
                 The Number 
               
               
                   
                   
                 (wants to take 
                 (wants to 
                 (wants to 
                 of Necessary 
               
               
                   
                 Operator 1 
                 holidays in 
                 work on 
                 work on 
                 Operators 
               
            
           
           
               
               
               
               
               
               
               
            
               
                   
                 (no 
                 the first half 
                 early 
                 late 
                 Early 
                 Late 
               
               
                 Day 
                 requests) 
                 of the period) 
                 shifts) 
                 shifts) 
                 Shift 
                 Shift 
               
               
                   
               
               
                 1st 
                 early 
                 holiday 
                 early 
                 ▴late 
                 2 
                 1 
               
               
                   
                 shift 
                   
                 shift 
                 shift 
               
               
                     2nd 
                 early 
                 holiday 
                 early 
                 ▴late 
                 2 
                 1 
               
               
                   
                 shift 
                   
                 shift 
                 shift 
               
               
                 3rd 
                 holiday 
                 early 
                 early 
                 ▴late 
                 2 
                 1 
               
               
                   
                   
                 shift 
                 shift 
                 shift 
               
               
                 4th 
                 early 
                 ▴late 
                 holiday 
                 holiday 
                 1 
                 1 
               
               
                   
                 shift 
                 shift 
               
               
                 5th 
                 early 
                 holiday 
                 early 
                 ▴late 
                 2 
                 1 
               
               
                   
                 shift 
                   
                 shift 
                 shift 
               
               
                 6th 
                 early 
                 holiday 
                 early 
                 ▴late 
                 2 
                 1 
               
               
                   
                 shift 
                   
                 shift 
                 shift 
               
               
                 7th 
                 ▴late 
                 early 
                 early 
                 holiday 
                 2 
                 1 
               
               
                   
                 shift 
                 shift 
                 shift 
               
               
                 8th 
                 ▴late 
                 early 
                 early 
                 holiday 
                 2 
                 1 
               
               
                   
                 shift 
                 shift 
                 shift 
               
               
                 9th 
                 holiday 
                 early 
                 early 
                 ▴late 
                 2 
                 1 
               
               
                   
                   
                 shift 
                 shift 
                 shift 
               
               
                 10th  
                 early 
                 early 
                 holiday 
                 ▴late 
                 2 
                 1 
               
               
                   
                 shift 
                 shift 
                   
                 shift 
               
               
                 11th  
                 ▴late 
                 early 
                 holiday 
                 holiday 
                 1 
                 1 
               
               
                   
                 shift 
                 shift 
               
               
                 12th  
                 holiday 
                 early 
                 early 
                 ▴late 
                 2 
                 1 
               
               
                   
                   
                 shift 
                 shift 
                 shift 
               
               
                 13th  
                 holiday 
                 early 
                 early 
                 ▴late 
                 2 
                 1 
               
               
                   
                   
                 shift 
                 shift 
                 shift 
               
               
                 14th  
                 early 
                 early 
                 holiday 
                 ▴late 
                 2 
                 1 
               
               
                   
                 shift 
                 shift 
                   
                 shift 
               
               
                 The Number 
                 10 
                 10 
                 10 
                 10 
               
               
                 of Working 
               
               
                 Shifts 
               
               
                   
               
            
           
         
       
     
     In the above tables, a symbol ▴ is prefixed to each late shift to make it easy to distinguish. 
     As shown above, in the case where there is no constraint, “there are holidays for operator 2 also in the latter half of the period”, “late shifts are assigned to operator 3”, “early shifts are assigned to operator 4”. Thus, the work shifts of the month are far from operators&#39; requests. In contrast, in the case where the constraints are considered, the work shifts of the month reflect the operators&#39; requests. 
     Next, the result (Table 15) of creating a schedule on the premise that there is no constraint condition regarding equal work between operators (Expression 20: The number of working hours shall be equal between operators) and a schedule (Table 16) for the case where the constraint condition is solved are shown. 
     
       
         
           
             [ 
             
               Expression 
               ⁢ 
                   
               20 
             
             ] 
           
         
       
       
         
           
             
               
                 
                   min 
                   - 
                   
                     
                       ∑ 
                       
                         i 
                         = 
                         1 
                       
                       4 
                     
                     
                       
                         [ 
                         
                           
                             
                               ∑ 
                               
                                 j 
                                 = 
                                 1 
                               
                               15 
                             
                             
                               x 
                               
                                 i 
                                 , 
                                 j 
                               
                             
                           
                           - 
                           D 
                         
                         ] 
                       
                       2 
                     
                   
                 
               
               
                 
                   Expression 
                   ⁢ 
                       
                   20 
                 
               
             
           
         
       
     
     This constraint condition means that “the number of working shifts of each operator shall be set to as close to a guideline D as possible. 
     
       
         
           
               
             
               
                 TABLE 15 
               
             
            
               
                   
               
               
                 In the case where there are no constraint conditions 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                 The 
               
               
                   
                   
                   
                   
                   
                 Number of 
               
               
                 Time  
                 Operator 
                 Operator 
                 Operator 
                 Operator 
                 Necessary 
               
               
                 Slot 
                 1 
                 2 
                 3 
                 4 
                 Operators 
               
               
                   
               
               
                 9:00 to 
                 work 
                 work 
                 holiday 
                 holiday 
                 2 
               
               
                 9:10 
                   
                   
                   
                   
                   
               
               
                 9:10 to 
                 work 
                 work 
                 holiday 
                 holiday 
                 2 
               
               
                 9:20 
                   
                   
                   
                   
                   
               
               
                 9:20 to 
                 work 
                 work 
                 holiday 
                 holiday 
                 2 
               
               
                 9:30 
                   
                   
                   
                   
                   
               
               
                 9:30 to 
                 work 
                 work 
                 holiday 
                 holiday 
                 2 
               
               
                 9:40 
                   
                   
                   
                   
                   
               
               
                 9:40 to 
                 work 
                 work 
                 work 
                 holiday 
                 3 
               
               
                 9:50 
                   
                   
                   
                   
                   
               
               
                 9:50 to 
                 work 
                 work 
                 work 
                 holiday 
                 3 
               
               
                 10:00 
                   
                   
                   
                   
                   
               
               
                 10:00 to 
                 work 
                 work 
                 work 
                 work 
                 4 
               
               
                 10:10 
                   
                   
                   
                   
                   
               
               
                 10:10 to 
                 work 
                 work 
                 work 
                 work 
                 4 
               
               
                 10:20 
                   
                   
                   
                   
                   
               
               
                 10:20 to 
                 work 
                 work 
                 work 
                 work 
                 4 
               
               
                 10:30 
                   
                   
                   
                   
                   
               
               
                 10:30 to 
                 work 
                 work 
                 work 
                 holiday 
                 3 
               
               
                 10:40 
                   
                   
                   
                   
                   
               
               
                 10:40 to 
                 work 
                 work 
                 work 
                 holiday 
                 3 
               
               
                 10:50 
                   
                   
                   
                   
                   
               
               
                 10:50 to 
                 work 
                 work 
                 holiday 
                 holiday 
                 2 
               
               
                 11:00 
                   
                   
                   
                   
                   
               
               
                 11:00 to 
                 work 
                 work 
                 holiday 
                 holiday 
                 2 
               
               
                 11:10 
                   
                   
                   
                   
                   
               
               
                 11:10 to 
                 work 
                 work 
                 work 
                 holiday 
                 3 
               
               
                 11:20 
                   
                   
                   
                   
                   
               
               
                 11:20 to 
                 work 
                 work 
                 work 
                 holiday 
                 3 
               
               
                 11:30 
                   
                   
                   
                   
                   
               
               
                 Actual 
                 15 
                 15 
                 9 
                 3 
                   
               
               
                 Number of 
                   
                   
                   
                   
                   
               
               
                 Working 
                   
                   
                   
                   
                   
               
               
                 Shifts 
                   
                   
                   
                   
                   
               
               
                 Guideline 
                 10 
                 10 
                 10 
                 10 
                   
               
               
                 of The 
                   
                   
                   
                   
                   
               
               
                 Number of 
                   
                   
                   
                   
                   
               
               
                 Working 
                   
                   
                   
                   
                   
               
               
                 Shifts 
               
               
                   
               
            
           
         
       
     
     
       
         
           
               
             
               
                 TABLE 16 
               
             
            
               
                   
               
               
                 In the case where there are constraint conditions 
               
            
           
           
               
               
               
               
               
               
            
               
                   
                   
                   
                   
                   
                 The 
               
               
                   
                   
                   
                   
                   
                 Number of 
               
               
                 Time  
                 Operator 
                 Operator 
                 Operator 
                 Operator 
                 Necessary 
               
               
                 Slot 
                 1 
                 2 
                 3 
                 4 
                 Operators 
               
               
                   
               
               
                 9:00 to 
                 work 
                 rest 
                 rest 
                 work 
                 2 
               
               
                 9:10 
                   
                   
                   
                   
                   
               
               
                 9:10 to 
                 work 
                 rest 
                 rest 
                 work 
                 2 
               
               
                 9:20 
                   
                   
                   
                   
                   
               
               
                 9:20 to 
                 work 
                 rest 
                 work 
                 rest 
                 2 
               
               
                 9:30 
                   
                   
                   
                   
                   
               
               
                 9:30 to 
                 rest 
                 work 
                 work 
                 rest 
                 2 
               
               
                 9:40 
                   
                   
                   
                   
                   
               
               
                 9:40 to 
                 rest 
                 work 
                 work 
                 work 
                 3 
               
               
                 9:50 
                   
                   
                   
                   
                   
               
               
                 9:50 to 
                 rest 
                 work 
                 work 
                 work 
                 3 
               
               
                 10:00 
                   
                   
                   
                   
                   
               
               
                 10:00 to 
                 work 
                 work 
                 work 
                 work 
                 4 
               
               
                 10:10 
                   
                   
                   
                   
                   
               
               
                 10:10 to 
                 work 
                 work 
                 work 
                 work 
                 4 
               
               
                 10:20 
                   
                   
                   
                   
                   
               
               
                 10:20 to 
                 work 
                 work 
                 work 
                 work 
                 4 
               
               
                 10:30 
                   
                   
                   
                   
                   
               
               
                 10:30 to 
                 work 
                 work 
                 work 
                 rest 
                 3 
               
               
                 10:40 
                   
                   
                   
                   
                   
               
               
                 10:40 to 
                 rest 
                 work 
                 work 
                 work 
                 3 
               
               
                 10:50 
                   
                   
                   
                   
                   
               
               
                 10:50 to 
                 rest 
                 work 
                 rest 
                 work 
                 2 
               
               
                 11:00 
                   
                   
                   
                   
                   
               
               
                 11:00 to 
                 work 
                 rest 
                 rest 
                 work 
                 2 
               
               
                 11:10 
                   
                   
                   
                   
                   
               
               
                 11:10 to 
                 work 
                 rest 
                 work 
                 work 
                 3 
               
               
                 11:20 
                   
                   
                   
                   
                   
               
               
                 11:20 to 
                 work 
                 work 
                 work 
                 rest 
                 3 
               
               
                 11:30 
                   
                   
                   
                   
                   
               
               
                 Actual 
                 10 
                 10 
                 11 
                 11 
                   
               
               
                 Number of 
                   
                   
                   
                   
                   
               
               
                 Working 
                   
                   
                   
                   
                   
               
               
                 Shifts 
                   
                   
                   
                   
                   
               
               
                 Guideline 
                 10 
                 10 
                 10 
                 10 
                   
               
               
                 of The 
                   
                   
                   
                   
                   
               
               
                 Number of 
                   
                   
                   
                   
                   
               
               
                 Working 
                   
                   
                   
                   
                   
               
               
                 Shifts 
               
               
                   
               
            
           
         
       
     
     As shown above, in the case where there is no constraint, the working hours are uneven between operators, and the table shows a mixture of operators having no rest time and operators having too many rests. Thus, the timetable is unrealistic. In contrast, in the case where the constraint was considered, the number of working hours is approximately equal between operators. Thus, the timetable is fair and realistic. 
     Note that, for example, it will be preferable if in case of emergency, such as a shortage of operators due to a sudden demand increase or abrupt absence of operators, the schedule creation assisting device  100  obtains a constraint condition corresponding to the event from the user terminal  200  and executes the foregoing procedure. 
     As a constraint condition in such a situation, for example, a constraint condition on the premise in which an operator who is allocated to a different operation in the same time slot on the same day in the latest created schedule is to “attend at work” or like conditions can be assumed. 
     In that case, the schedule creation assisting device  100  executes step s 11  according to the constraint condition to generate a constraint condition function, and solves an Ising model regarding the corresponding objective function. 
     Although the best mode and the like for carrying out the present invention has been specifically described above, the present invention is not limited to these, but various modifications can be made without departing from the spirit of the invention. 
     The present embodiment described above makes it possible to create a schedule efficiently considering nonlinear constraint conditions regarding a large number of workers who work in cooperation. 
     The description of the present specification makes at least the following things clear. Specifically, in the schedule creation assisting device of the present embodiment, the computation unit may include, in the terms of the objective function, the constraint condition function concerning at least one of an upper limit or a lower limit of continuous working time length, seeking to increase continuous work, and restricting continuous work, which are the constraint conditions regarding continuous work, and compute the Ising model. 
     This makes it possible to efficiently create a schedule that minimizes labor costs and in which conditions regarding continuous work of each worker (Example: The workers&#39; requests and the rules of their organization. The same applies in the following) are taken into account as much as possible. This in turn makes it possible to create more efficiently a schedule with nonlinear constraint conditions taken into account for a large number of workers who work in cooperation. 
     In the schedule creation assisting device of the present embodiment, the computation unit may include, in the terms of the objective function, the constraint condition function concerning at least one of an upper limit or a lower limit of intervals of work timings, seeking to increase consecutive holidays, and restricting consecutive holidays, which are the constraint conditions regarding discontinuous work, and compute the Ising model. 
     This makes it possible to efficiently create a schedule that minimizes labor costs and in which conditions regarding discontinuous work of each worker are taken into account as much as possible. This in turn makes it possible to create more efficiently a schedule with nonlinear constraint conditions taken into account for a large number of workers who work in cooperation. 
     In the schedule creation assisting device of the present embodiment, the computation unit may include, in the terms of the objective function, the constraint condition function concerning at least one of prohibition of continuous work in a specified time slot and prohibition of work in a predetermined time slot immediately after working in the specified time slot, which are the constraint conditions regarding a prohibited pattern, and compute the Ising model. 
     This makes it possible to efficiently create a schedule that minimizes labor costs and in which conditions regarding prohibited patterns of work for each worker (Example: A day shift immediately after a midnight shift shall be prohibited) are taken into account as much as possible. This in turn makes it possible to create more efficiently a schedule with nonlinear constraint conditions taken into account for a large number of workers who work in cooperation. 
     In the schedule creation assisting device of the present embodiment, the computation unit may include, in the terms of the objective function, the constraint condition function concerning at least one of seeking a state in which workers having specified attributes work at the same time or avoiding the state, which are the constraint conditions regarding the compatibility of workers, and compute the Ising model. 
     This makes it possible to efficiently create a schedule that minimizes labor costs and in which conditions regarding the compatibility of each worker with other workers (Example: A recruit and a worker capable of giving instruction to the recruit shall attend at work on the same shift. A worker and a certain worker shall not attend at work on the same shift) are taken into account as much as possible. This in turn makes it possible to create more efficiently a schedule with nonlinear constraint conditions taken into account for a large number of workers who work in cooperation. 
     In the schedule creation assisting device of the present embodiment, the computation unit may include, in the terms of the objective function, the constraint condition function concerning seeking work shifts in a specified pattern, which is the constraint condition regarding workers&#39; requests, and compute the Ising model. 
     This makes it possible to efficiently create a schedule that minimizes labor costs and in which conditions regarding requests from each worker (Example: A certain shift should be assigned if possible on a specified day) are taken into account as much as possible. This in turn makes it possible to create more efficiently a schedule with nonlinear constraint conditions taken into account for a large number of workers who work in cooperation. 
     In the schedule creation assisting device of the present embodiment, the computation unit may include, in the terms of the objective function, the constraint condition function concerning seeking a state in which the work time length in each work pattern is equal between the workers, which is the constraint condition regarding equality between workers, and compute the Ising model. 
     This makes it possible to efficiently create a schedule that minimizes labor costs and in which conditions regarding equality between workers are taken into account as much as possible. This in turn makes it possible to create more efficiently a schedule with nonlinear constraint conditions taken into account for a large number of workers who work in cooperation. 
     The schedule creation assisting device of the present embodiment may be a CMOS annealing machine that solves a combinatorial optimization problem regarding the Ising model. 
     This makes it possible to efficiently calculate, at room temperature, a practical solution of a combinatorial optimization problem with constraint conditions affecting one another, in other words, nonlinear constraint conditions taken into account, by simulating the operation of an Ising model, using a circuit including semiconductors such as devices of complementary metal oxide semiconductors (CMOS) or the like. This in turn makes it possible to create much more efficiently a schedule with nonlinear constraint conditions taken into account for a large number of workers who work in cooperation. 
     In the schedule creation assisting method in the present embodiment, the information processing device may include, in the terms of the objective function, the constraint condition function concerning at least one of an upper limit or a lower limit of continuous working time length, seeking to increase continuous work, and restricting continuous work, which are the constraint conditions regarding continuous work, and compute the Ising model. 
     In the schedule creation assisting method in the present embodiment, the information processing device may include, in the terms of the objective function, the constraint condition function concerning at least one of an upper limit or a lower limit of intervals of work timings, seeking to increase consecutive holidays, and restricting consecutive holidays, which are the constraint conditions regarding discontinuous work, and compute the Ising model. 
     In the schedule creation assisting method in the present embodiment, the information processing device may include, in the terms of the objective function, the constraint condition function concerning at least one of prohibition of continuous work in a specified time slot and prohibition of work in a predetermined time slot immediately after working in the specified time slot, which are the constraint conditions regarding a prohibited pattern, and compute the Ising model. 
     In the schedule creation assisting method in the present embodiment, the information processing device may include, in the terms of the objective function, the constraint condition function concerning at least one of seeking a state in which workers having specified attributes work at the same time or avoiding the state, which are the constraint conditions regarding the compatibility of workers, and compute the Ising model. 
     In the schedule creation assisting method in the present embodiment, the information processing device may include, in the terms of the objective function, the constraint condition function concerning seeking work shifts in a specified pattern, which is the constraint condition regarding workers&#39; requests, and compute the Ising model. 
     In the schedule creation assisting method in the present embodiment, the information processing device may include, in the terms of the objective function, the constraint condition function concerning seeking a state in which the work time length in each work pattern is equal between the workers, which is the constraint condition regarding equality between workers, and compute the Ising model. 
     In the schedule creation assisting method in the present embodiment, the information processing device may be a CMOS annealing machine that solves a combinatorial optimization problem regarding the Ising model. 
     REFERENCE SIGNS LIST 
     
         
           10  network 
           100  schedule creation assisting device (annealing machine) 
           101  storage unit 
           102  program 
           1021  Ising model 
           103  memory 
           104  computation unit 
           105  communication unit 
           125  basic information table 
           126  constraint condition table 
           200  user terminal