Abstract:
A method of determining a cell configuration in a print production environment may include identifying a set of print devices to assign to a cell, identifying a print device number, identifying one or more subsets of print devices from the set, where each subset includes a unique portion of the print devices in the set, and each subset includes a number of print devices equal to the print device number, performing a simulation of operation on each subset to determiner a subset performance metric for each subset, selecting one of the subsets based on the associated subset performance metric, decrementing the print device number by an amount, updating the set with the selected subset, and repeating the identifying one or more subsets, performing the simulation, selecting one of the subsets, decrementing the print device number and updating until no subset performance metric satisfies a performance constraint.

Description:
BACKGROUND 
     Assigning resources to a print production environment can be a complex and time consuming process. For N number of devices, there are 2^N possibilities, assuming N is known, which is not typically the case. Furthermore, each possibility requires a time consuming full discrete event simulation since there is no analytic model capable of expressing production process characteristics of interest, except in the simplest of cases. This disclosure describes methods and systems that are directed to improving such processes. 
     SUMMARY 
     This disclosure is not limited to the particular systems, methodologies or protocols described, as these may vary. The terminology used in this description is for the purpose of describing the particular versions or embodiments only, and is not intended to limit the scope. 
     As used in this document, the singular forms “a,” “an,” and “the” include plural reference unless the context clearly dictates otherwise. Unless defined otherwise, all technical and scientific terms used herein have the same meanings as commonly understood by one of ordinary skill in the art. All publications mentioned in this document are incorporated by reference. All sizes recited in this document are by way of example only, and the invention is not limited to structures having the specific sizes or dimension recited below. As used herein, the term “comprising” means “including, but not limited to.” 
     In an embodiment, a method of determining a cell configuration in a print production environment may include identifying a set comprising a plurality of print production devices. Each print production device may be available to be used in a cell of a print production environment. The method may include running a first simulation using the plurality of print production devices to determine a first primary performance metric value associated with assigning the plurality of print production devices to the cell, and a first secondary performance metric value associated with assigning the plurality of print production devices to the cell. The method may include determining whether the first primary performance metric value satisfies a first constraint and the first secondary performance metric value satisfies a second constraint, and in response to determining that the first primary performance metric value and the first secondary performance metric value satisfy the one or more constraints, identifying one or more subsets, where each subset includes a unique portion of the plurality of print production devices, and each portion includes a number of print production devices that is less than a number of print production devices in the plurality of print production devices, for each subset, running a second simulation using the print devices associated with the subset to determine a second primary performance metric value associated with assigning the print devices associated with the subset to the cell, and a second secondary performance metric value associated with assigning the print devices associated with the subset to the cell, selecting one of the subsets based on one or more of the associated second primary performance metric value and the second secondary performance metric value, determining one or more removed print production devices, where each removed production device is included in the set but not the selected subset, and removing the removed print production devices from the set to create a modified set. 
     In an embodiment, a method of determining a cell configuration in a print production environment may include identifying a set of print devices to assign to a cell, identifying a print device number, identifying one or more subsets of print devices from the set, where each subset includes a unique portion of the print devices in the set, and each subset includes a number of print devices equal to the print device number, performing a simulation of operation on each subset to determiner a subset performance metric for each subset, selecting one of the subsets based on the associated subset performance metric, decrementing the print device number by an amount, updating the set with the selected subset, and repeating the identifying one or more subsets, performing the simulation, selecting one of the subsets, decrementing the print device number and updating until no subset performance metric satisfies a performance constraint. 
     In an embodiment, a system of determining a cell configuration in a print production environment may include a computing device, and a computer-readable storage medium in communication with the computing device. The computer-readable storage medium may include one or more programming instructions that, when executed, cause the computing device to identify a set comprising a plurality of print production devices, where each print production device is available to be used in a cell of a print production environment, run a first simulation using the plurality of print production devices to determine a first primary performance metric value associated with assigning the plurality of print production devices to the cell, and a first secondary performance metric value associated with assigning the plurality of print production devices to the cell, determine whether the first primary performance metric value satisfies a first constraint and the first secondary performance metric value satisfies a second constraint, and in response to determining that the first primary performance metric value and the first secondary performance metric value satisfy the one or more constraints, identify one or more subsets, where each subset includes a unique portion of the plurality of print production devices, and each portion includes a number of print production devices that is less than a number of print production devices in the plurality of print production devices. The computer-readable storage medium may include one or more programming instructions that, when executed, cause the computing device to, for each subset, run a second simulation using the print devices associated with the subset to determine a second primary performance metric value associated with assigning the print devices associated with the subset to the cell, and a second secondary performance metric value associated with assigning the print devices associated with the subset to the cell, select one of the subsets based on one or more of the associated second primary performance metric value and the second secondary performance metric value, determine one or more removed print production devices, wherein each removed production device is included in the set but not the selected subset, and remove the removed print production devices from the set to create a modified set. 
     In an embodiment, a system of determining a cell configuration in a print production environment may include a computing device and a computer-readable storage medium in communication with the computing device. The computer-readable storage medium may include one or more programming instructions that, when executed, cause the computing device to identify a set of print devices to assign to a cell, identify a print device number, identify one or more subsets of print devices from the set, where each subset includes a unique portion of the print devices in the set, and each subset includes a number of print devices equal to the print device number, perform a simulation of operation on each subset to determiner a subset performance metric for each subset, select one of the subsets based on the associated subset performance metric, decrement the print device number by an amount, update the set with the selected subset, and repeating the identify one or more subsets, perform the simulation, select one of the subsets, decrement the print device number and update until no subset performance metric satisfies a performance constraint. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  illustrates an example of a production environment according to an embodiment. 
         FIG. 2  illustrates a flow chart of an example method of determining a cell configuration according to an embodiment. 
         FIGS. 3 and 4  illustrate example graphs of cost and turnaround time according to various embodiments. 
         FIG. 5  illustrates a flow chart of an example method of determining a cell configuration according to an embodiment. 
         FIG. 6  illustrates a block diagram of example hardware that may be used to contain or implement program instructions according to an embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     The following terms shall have, for purposes of this application, the respective meanings set forth below: 
     A “cell” refers to one or more production devices in a production environment that are capable of processing at least a portion of a job. For example, in a print shop, a cell may include one or more print production devices that are capable of processing at least a portion of a print job. 
     A “cell configuration” refers to the production devices that are selected or assigned to a cell. 
     A “computing device” refers to a device that includes a processor and tangible, computer-readable memory. The memory may contain programming instructions that, when executed by the processor, cause the computing device to perform one or more operations according to the programming instructions. Examples of computing devices include personal computers, servers, mainframes, gaming systems, televisions, and portable electronic devices such as smartphones, personal digital assistants, cameras, tablet computers, laptop computers, media players and the like. 
     A “job” refers to a logical unit of work that is to be completed for a customer. For example, in a print production environment, a job may include one or more print jobs from one or more clients. For example, a job in a vehicle production environment may include manufacturing a vehicle or a portion thereof. As another example, a job in a chemical production environment may include producing or processing a chemical product or a portion thereof. Similarly, a job in a computing device production environment may be to manufacture a computing device or a portion thereof such as, for example, a printer, a scanner or a copier. 
     A “performance metric” refers to a performance measure associated with a production environment. 
     A “print job” refers to a job processed in a print shop. For example, a print job may include producing credit card statements corresponding to a certain credit card company, producing bank statements corresponding to a certain bank, printing a document, or the like. Although the disclosed embodiments pertain to print jobs, the disclosed methods and systems can be applied to jobs in general in other production environments, such as automotive manufacturing, semiconductor production and the like. 
     A “production device” device refers to a device used to process at least a portion of a job. Examples of production devices in a print shop may include, without limitation, printers, inserters, binders, punchers, collators, multi-function devices or other similar equipment and/or the like. 
     A “production environment” refers to machine and/or human labor used to complete one or more jobs. A production environment may include one or more devices or other equipment that may be used to complete one or more jobs. Example production environments may include, without limitation, a print production environment, a chemical production environment, a vehicle production environment, a computing device manufacturing production environment, and/or other manufacturing production environments. 
     A production environment may include one or more autonomous production cells that each may include one or more production devices. In an embodiment, a cell may include one or more devices that are capable of delivering at least one type of job. For example, in a print shop, a cell may include production devices such as, for example, multiple printers, a shrink-wrapper and a computerized control system. A different cell may include printers, cutters and copiers. In an embodiment, print jobs may be intelligently routed to cells to provide desired load balancing and/or throughput. The use of cells may help decrease the amount of work in progress and labor and inventory costs associated with processing jobs, and may increase the utilization of the production devices in a production environment. 
       FIG. 1  shows an example of a production environment  50 , in this case, example elements of a print shop. Print jobs may enter the print shop manually or electronically and be collected at an electronic submission system  55  such as a computing device and/or scanner. Jobs are sorted and batched at the submission system or another location before being delivered to one or more print engines such as a color printer  56 , black-and-white printer  57  and/or a continuous feed printer  58 . Jobs may exit the print engine and be delivered to one or more finishing devices or areas such as a collator  60 , cutter  62 , and/or binder  64 . The finishing areas may include automatic or manual areas for such finishing activities and they also may include an automatic or manual inserter  70 . Finally, jobs may move to a postage metering station  72  and/or shipping station  74 . Jobs may move from one location to another in the print shop by automatic delivery or manual delivery such as by hand or by one or more paper carts  81 - 85 . 
     In an embodiment, a cell configuration may be determined that satisfies one or more performance metrics. Example performance metrics may include, without limitation, a performance cost, turnaround time, and/or the like. In an embodiment, an algorithm may be used to identify a configuration that satisfies one or more performance metrics in a cellular production environment. The algorithm may be a greedy-type algorithm. A greedy-type algorithm is an algorithm that follows a solution technique that makes optimal decisions at each stage of a process with the goal of finding an optimal global solution. 
     In an embodiment, a cell configuration may be determined using a discrete event simulation. The simulation may be simulated with a known set of jobs over a certain time period. The approach may be applied in a top-down fashion, meaning that it begins with a sufficient or excess number of production devices in a cell to satisfy the performance metrics, and gradually reduces the number of production devices in the cell while still satisfying the performance metrics. In an alternate embodiment, the approach may be applied in a bottom-up fashion, meaning that it begins with an insufficient number of production devices in a cell to satisfy the performance metrics, and gradually increases the number of production devices in the cell until the performance metrics are satisfied. 
       FIG. 2  illustrates a flow chart of an example method of determining a cell configuration according to an embodiment. As illustrated by  FIG. 2 , one or more performance metrics may be identified  200 . In an embodiment, the method may involve the use of two performance metrics. One may be considered a primary performance metric, and it may be a performance metric that is to be minimized or maximized by a configuration. The other may be considered a secondary performance metric that is to have a value relative to a threshold value. For example, a secondary performance metric may have a value that falls below a threshold value, a value that exceeds a threshold value, a value that equals a threshold value and/or the like. 
     For purposes of  FIG. 2 , the performance metrics may be cost and job turnaround time. As such, a best performance may be a configuration having the least cost with a job turnaround time that does not exceed a threshold value. Additional and/or alternate performance metrics may be used within the scope of this disclosure. 
     In an embodiment, one or more available production devices may be identified  202 . An available production device may be a production device that may be selected for inclusion in a cell. In an embodiment, a simulation may be performed  204  with all of the identified production devices assigned to the cell. For example, if ten production devices, M, are identified, then a simulation with a configuration of {M 1 , M 2 , . . . , M 10 } may be performed  204 . In an embodiment, the simulation may yield one or more output values. In an embodiment, each output value may be associated with a performance metric. For instance, in this example, the simulation may produce output values for a turnaround time and a cost associated with the configuration. 
     In an embodiment, an output value corresponding to a secondary performance metric may be compared  206  to the corresponding threshold value to determine whether the associated constraint is satisfied. If the constraint is not satisfied, then the method may stop  208 . For instance, referring to the above example, a simulation with a configuration of {M 1 , M 2 , . . . , M 10 } may yield an output value associated with the secondary performance metric turnaround time. The turnaround time may be associated with an upper threshold value that specifies the maximum acceptable turnaround time. If the turnaround time output value exceeds the threshold value, the simulation may stop  208  because there is no solution that satisfies the given constraints. In this situation, the simulation may be restarted with a different number of production devices. For instance, referring back to the above example, the simulation may be restarted with eleven production devices {M 1 , M 2 , . . . , M 11 }. 
     In an embodiment, if the associated constraint is satisfied, one or more simulations may be run  210  using a subset of the production devices. In an embodiment, if an original set of production devices includes N number of devices, then N simulations may be run  210  using one or more combinations of N−1 production devices. For instance, in the above example, the original set of production devices includes ten production devices. As such, ten more simulations may be run  210  on one or more subsets of machines that each includes nine production devices. The first simulation may remove M 1  and retain {M 2 , . . . , M 10 }. The second simulation may remove M 2  and retain {M 1 , M 3 , M 4 , . . . , M 10 }, the third simulation may remove M 3  and retain {M 1 , M 2 , M 4 , . . . , M 10 } and so on. 
     In an embodiment, each simulation may yield output values for the primary and secondary performance constraints. Table 1 illustrates example output values for the simulations of the above example according to an embodiment. 
     
       
         
               
               
               
               
             
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                   
                   
                   
                 Turnaround  
               
               
                   
                   
                 Cost  
                 Time 
               
               
                   
                   
                 Per- 
                 Per- 
               
               
                   
                   
                 formance 
                 formance 
               
               
                 Ref. 
                 Production Device Subset 
                 Metric 
                 Metric 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 A 
                 {M 1 , . . . , M 10 } 
                 100,000 
                 60 
               
               
                 B 
                 {M 2 , . . . , M 10 } 
                  59,000 
                 170 
               
               
                 C 
                 {M 1 , M 3 , M 4 , . . . , M 10 } 
                  90,000 
                 90 
               
               
                 D 
                 {M 1 , M 2 , M 4 , M 5 , . . . , M 10 } 
                  63,000 
                 63 
               
               
                 E 
                 {M 1 , M 2 , M 3 , M 5 , . . . , M 10 } 
                 215,000 
                 86 
               
               
                 F 
                 {M 1 , M 2 , M 3 , M 4 , M 6 , M 7 , M 8 , M 9 , M 10 } 
                 125,000 
                 74 
               
               
                 G 
                 {M 1 , M 2 , M 3 , M 4 , M 5 , M 7 , M 8 , M 9 , M 10 } 
                 180,000 
                 78 
               
               
                 H 
                 {M 1 , M 2 , M 3 , M 4 , M 5 , M 6 , M 8 , M 9 , M 10 } 
                 245,000 
                 74 
               
               
                 I 
                 {M 1 , M 2 , M 3 , M 4 , M 5 , M 6 , M 7 , M 9 , M 10 } 
                 118,000 
                 87 
               
               
                 J 
                 {M 1 , M 2 , M 3 , M 4 , M 5 , M 6 , M 7 , M 8 , M 10 } 
                 180,000 
                 71 
               
               
                 K 
                 {M 1 , . . . , M 9 } 
                  53,000 
                 130,000 
               
               
                   
               
             
          
         
       
     
       FIG. 3  illustrates an example graph showing a plot of the cost performance metric and turnaround time performance metric from Table 1 according to an embodiment. 
     Referring back to  FIG. 2 , the system may analyze the performance metric or metrics for each of the subsets to determine  212  whether at least one of the subsets satisfies one or more constraints. For example, the system may analyze one or more performance metrics of one or more subsets to determine whether they satisfy a constraint on turnaround time, cost and/or the like. If no subset is associated with performance metrics that satisfy the appropriate constraints, the process may stop  208 . 
     In an embodiment, if at least one subset is associated with one or more performance metrics that satisfy the appropriate constraints, then one or more production devices may be removed  214  from a cell based on the simulations. The production device or devices that are removed  214  may be determined based on the values of the associated performance criteria. In an embodiment, a production device having a performance criterion value that violates one or more constraints may not be removed. For example, as illustrated by  FIG. 3 , a constraint restricting the turnaround time to no more than  210  minutes exists. The production device subsets represented by letters ‘E’ and ‘H’ violate this constraint. As such, production devices M4, which is not included subset E and M7, which is not included in subset ‘H’, may not be removed from set. 
     In an embodiment, if all of the subsets have a performance criteria value that violates one or more constraints, the process may be stopped because no further reduction in production devices is permissible. 
     In an embodiment, a production device that results in the largest reduction of a primary performance criteria without violating a constraint associated with the secondary performance criteria may be removed  214 . For example, referring to  FIG. 3 , Production Device Subset K is associated with the largest cost reduction that does not violate the turnaround time threshold constraint. As such, M 10  may be removed  214 . 
     In an embodiment, the production device that results in the smallest decrease in a secondary performance metric may be removed  214 . For example, referring to  FIG. 3 , Production Device Subset C is associated with the smallest decrease in turnaround time, so M 2  may be removed  214 . 
     In an embodiment, the production device that results in the greatest reduction of the primary performance criteria per unit increase or decrease of the secondary performance criteria may be removed  214 . For example, referring to  FIG. 3 , Production Device Subset D is associated with the greatest cost reduction per unit turnaround time adjustment, so M 3  may be removed  214 . Additional and/or alternate rules for determining what production device or devices to remove may be used within the scope of this embodiment. 
     In certain embodiments, more than one production device may be removed from a subset at a certain time. The production devices that are removed may be determined in a manner similar to that described above or in a combination of manners as described above. For example, if two production devices are removed from a subset, they may be the production devices that results in the largest and second largest reduction of a primary performance criteria without violating a constraint associated with the secondary performance criteria. Alternatively, one production device may be a device that results in the largest and second largest reduction of a primary performance criteria without violating a constraint associated with the secondary performance criteria, while the other may be the device that results in the smallest increase in a secondary performance metric. Additional and/or alternate combinations may be used within the scope of this disclosure. 
     As an example, one or more simulations may be run  210  using one or more subsets of the production devices in the modified cell. For instance, referring to the above example, assume that production device M 2  is removed from the production device set, thus creating the modified cell that includes {M 1 , M 3 , M 4 , . . . , M 10 }. One or more simulations may be run  210  using one or more subsets of the modified cell. In an embodiment, each simulation may yield output values for the primary and secondary performance constraints. Table 2 illustrates example output values for the simulations of the above example according to an embodiment. 
     
       
         
               
               
               
               
             
               
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                   
                   
                   
                 Turnaround  
               
               
                   
                   
                 Cost  
                 Time 
               
               
                   
                   
                 Per- 
                 Per- 
               
               
                   
                   
                 formance 
                 formance 
               
               
                 Ref. 
                 Production Device Subset 
                 Metric 
                 Metric 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 C 
                 {M 1 , M 3 , M 4 , . . . , M 10 } 
                 90,000 
                  90 
               
               
                 L 
                 {M 1 , M 4 , . . . , M 10 } 
                 76,000 
                 160 
               
               
                 M 
                 {M 1 , M 3 , M 5 , . . . , M 10 } 
                 71,000 
                 100 
               
               
                 N 
                 {M 1 , M 3 , M 4 ,M 6 , . . . , M 10 } 
                 75,000 
                 260 
               
               
                 0 
                 {M 1 , M 3 , M 4 , M 5 , M 7 , . . . , M 10 } 
                 83,000 
                 120 
               
               
                 P 
                 {M 1 , M 3 , M 4 , M 5 , M 6 , M 8 , . . . , M 10 } 
                 74,000 
                 200 
               
               
                 Q 
                 {M 1 , M 3 , M 4 , M 5 , M 6 , M 7 , M 9 , M 10 } 
                 95,000 
                 180 
               
               
                 R 
                 {M 1 , M 3 , M 4 , M 5 , M 6 , M 7 , M 8 , M 10 } 
                 94,000 
                 140 
               
               
                 S 
                 {M 1 , M 3 , M 4 , M 5 , M 6 , M 7 , M 8 , M 9 } 
                 64,000 
                 130 
               
               
                   
               
             
          
         
       
     
       FIG. 4  illustrates an example graph showing a plot of the cost performance metric and turnaround time performance metric from Table 2 according to an embodiment. 
     Referring back to  FIG. 2 , in an embodiment, one or more production devices may be removed  214  from a modified cell based on the simulations. In an embodiment, one or more production devices may be removed  214  from a modified cell in a manner similar to that described above for removing one or more production devices from a cell. 
     In certain embodiments, a cell configuration may be determining using a bottom-up approach.  FIG. 5  illustrates an example flow chart of a bottom-up approach according to an embodiment. As illustrated by  FIG. 5 , one or more performance metrics may be identified  500 . The performance metrics may be considered a primary performance metric and a secondary performance metric. For purposes of  FIG. 5 , the performance metrics may be cost and job turnaround time. As such, a best performance may be a configuration having the least cost with a job turnaround time that does not exceed a threshold value. Additional and/or alternate performance metrics may be used within the scope of this disclosure. 
     In an embodiment, one or more available production devices may be identified  502 . An available production device may be a production device that may be selected for inclusion in a cell. In an embodiment, a simulation may be performed  504  with one of the identified production devices assigned to the cell. In an embodiment, the simulation may yield one or more output values. In an embodiment, each output value may be associated with a performance metric. For instance, in this example, the simulation may produce output values for a turnaround time and a cost associated with the configuration. 
     In an embodiment, an output value corresponding to a secondary performance metric may be compared  506  to the corresponding threshold value to determine whether the associated constraint is satisfied. If the constraint is not satisfied, then the one or more of the identified production devices may be assigned  508  to the cell. If the constraint is satisfied, the process may stop  510 . 
     In an embodiment, a determination of which production device or devices to added to the cell may be based on one or more simulated device utilization levels. For example, if a production device is utilized a high percentage of time, then it is likely that adding an additional such production device would be beneficial. In an embodiment, a production device that results in the greatest benefit to cost tradeoff may be added to a cell. 
     One or more simulations may be run  504  on the new set of the production devices. Production devices may be added to the cell configuration, and simulations may be run on the new configurations until a configuration is identified that satisfies all associated constraints. 
     The following example illustrates the described approach of determining a cell configuration (referred to as a greedy approach) compared with a brute force approach according to an embodiment. This example assumes two cells and six production devices as illustrated in Table 3. 
     
       
         
               
             
               
               
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 Print Shop One 
               
             
          
           
               
                   
                 Cell 
                 Station 
                 Fixed Cost 
               
               
                   
                   
               
               
                   
                 Cell One 
                 Printer A  
                 2448874 
               
               
                   
                 Cell One 
                 Inserter A 
                  423366 
               
               
                   
                 Cell One  
                 Inserter B 
                  143304 
               
               
                   
                 Cell One  
                 Printer B 
                 2448874 
               
               
                   
                 Cell Two 
                 Printer C  
                 3000000 
               
               
                   
                 Cell Two 
                 Inserter B 
                 1443304 
               
               
                   
                   
               
             
          
         
       
     
     The number of stations in a cell may be varied between 1 and 3, which results in 729 (3^6) configurations. The brute force approach visits all configurations and identifies the least cost configuration with a job turnaround-time metric less than or equal to 5 hours. 
     The greedy approach initially starts with a solution having the maximum number of equipment of each type in each cell (e.g., three production devices) and by following the approach described above, converges to the optimal solution. Table 4 illustrates the optimal configuration and computation time using the brute force approach as compared to the greedy approach according to an embodiment. 
     
       
         
               
               
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                   
                 Brute Force 
                   
               
               
                   
                 Approach 
                 Greedy Algorithm 
               
             
          
           
               
                   
                 Optimal Solution 
                 Run 1 
                 Run 2 
                 Run 3 
               
               
                   
               
             
          
           
               
                 No. of Printer A in Cell One 
                 1 
                 1 
                 1 
                 1 
               
               
                 No. of Inserter A in Cell One 
                 1 
                 1 
                 1 
                 1 
               
               
                 No. of Inserter B in Cell One 
                 3 
                 3 
                 3 
                 3 
               
               
                 No. of Printer B in Cell One 
                 1 
                 1 
                 1 
                 1 
               
               
                 No. of Printer C in Cell Two 
                 1 
                 1 
                 1 
                 1 
               
               
                 No. of Inserter B in Cell Two 
                 2 
                 2 
                 2 
                 2 
               
               
                 Total Station Cost ($) 
                 15568553 
                 15567043 
                 15567083 
                 15567045 
               
               
                 Number of Simulations 
                 21870 
                 72 
                 72 
                 72 
               
               
                 Tim in Hours or Minutes 
                 29.94 hours 
                 8.48 mins 
                 8.6 mins 
                 8.73 mins 
               
               
                   
               
             
          
         
       
     
     The following example illustrates the described approach of determining a cell configuration (referred to as a greedy approach) compared with a brute force approach according to an embodiment. This example assumes two cells and eleven production devices as illustrated in Table 5. 
     
       
         
               
             
               
               
               
               
             
           
               
                 TABLE 5 
               
             
             
               
                   
               
               
                 Print Shop Two 
               
             
          
           
               
                   
                 Cell 
                 Station 
                 Fixed Cost 
               
               
                   
                   
               
               
                   
                 Cell One 
                 BW Printer 1 
                  50000 
               
               
                   
                 Cell One 
                 Tab 
                  32000 
               
               
                   
                 Cell One 
                 Punch 
                  30000 
               
               
                   
                 Cell One 
                 Tape Bind 
                  35000 
               
               
                   
                 Cell One 
                 Staple 
                  40000 
               
               
                   
                 Cell Two 
                 Laminate 
                  53000 
               
               
                   
                 Cell Two 
                 Wire Punch 
                  40000 
               
               
                   
                 Cell Two 
                 Color Printer 
                  75000 
               
               
                   
                 Cell Two 
                 BW Printer  
                 250000 
               
               
                   
                 Cell Two 
                 Poster Print 
                  55000 
               
               
                   
                 Cell Two 
                 Wire Bind 
                  38000 
               
               
                   
                   
               
             
          
         
       
     
     The number of stations in a cell may be varied between 1 and 2, which results in 2,048 (2^11) configurations. The brute force approach visits all configurations and identifies the least cost configuration with a job turnaround-time metric less than or equal to 4 hours. 
     The greedy approach initially starts with a solution having the maximum number of equipment of each type in each cell (e.g., two production devices) and by following the approach described above, converges to the optimal solution. Table 6 illustrates the optimal configuration and computation time using the brute force approach as compared to the greedy approach according to an embodiment. 
     
       
         
               
               
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 6 
               
             
             
               
                   
               
               
                   
                 Brute Force 
                   
               
               
                   
                 Approach 
                 Greedy Algorithm 
               
             
          
           
               
                   
                 Optimal Solution 
                 Run 1 
                 Run 2 
                 Run 3 
               
               
                   
               
             
          
           
               
                 No. of BW Printer 1 in Cell 
                 2 
                 2 
                 2 
                 2 
               
               
                 One 
                   
                   
                   
                   
               
               
                 No. of Tab in Cell One 
                 1 
                 1 
                 1 
                 1 
               
               
                 No. of Punch in Cell One 
                 1 
                 1 
                 1 
                 1 
               
               
                 No. of Tape Bind in Cell One 
                 1 
                 1 
                 1 
                 1 
               
               
                 No. of Staple in Cell One 
                 1 
                 1 
                 1 
                 1 
               
               
                 No. of Laminate in Cell Two 
                 1 
                 1 
                 1 
                 1 
               
               
                 No. of Wire Punch in Cell Two 
                 1 
                 1 
                 1 
                 1 
               
               
                 No. of Color Printer in Cell 
                 2 
                 2 
                 2 
                 2 
               
               
                 Two 
                   
                   
                   
                   
               
               
                 No. of BW Printer 2 in Cell 
                 1 
                 1 
                 1 
                 1 
               
               
                 Two 
                   
                   
                   
                   
               
               
                 No. of Poster Print in Cell Two 
                 1 
                 1 
                 1 
                 1 
               
               
                 No. of Wire Bind in Cell Two 
                 1 
                 1 
                 1 
                 1 
               
               
                 Total Station Cost 
                 623,000 
                 623,000 
                 623,000 
                 623,000 
               
               
                 Number of Simulations 
                 20,480 
                 76 
                 76 
                 76 
               
               
                 Time in Hours or Minutes 
                 17.06 hours 
                 3.2 mins 
                 3.36 mins 
                 3.35 mins 
               
               
                   
               
             
          
         
       
     
     The described methods and systems identify a cell configuration in a production environment that reduces cost while still satisfying one or more performance metrics. In an embodiment, the process of identifying a cell configuration may initially starts with a sufficient number of devices in one or more cells, and removes one or more production devices from one or more cells without violating performance criteria. This process is repeated until no further cost reduction is possible. The device that is chosen to be removed at each iteration may be the production device with the best, in a heuristic rule sense, cost-to-benefit tradeoff. 
     In another embodiment, the process of identifying a cell configuration may start with an insufficient number of devices in one or more cells, and may add one or more production devices to satisfy performance criteria. This process is repeated until no further cost reduction is possible. The device that is chosen to be added at each iteration may be the production device with the best, in a heuristic rule sense, cost-to-benefit tradeoff. 
       FIG. 6  depicts a block diagram of hardware that may be used to contain or implement program instructions. A bus  600  serves as the main information highway interconnecting the other illustrated components of the hardware. CPU  605  is the central processing unit of the system, performing calculations and logic operations required to execute a program. CPU  605 , alone or in conjunction with one or more of the other elements disclosed in  FIG. 6 , is an example of a production device, computing device or processor as such terms are used within this disclosure. Read only memory (ROM)  610  and random access memory (RAM)  615  constitute examples of non-transitory computer-readable storage media. 
     A controller  620  interfaces with one or more optional non-transitory computer-readable storage media  625  to the system bus  600 . These storage media  625  may include, for example, an external or internal DVD drive, a CD ROM drive, a hard drive, flash memory, a USB drive or the like. As indicated previously, these various drives and controllers are optional devices. 
     Program instructions, software or interactive modules for providing the interface and performing any querying or analysis associated with one or more data sets may be stored in the ROM  610  and/or the RAM  615 . Optionally, the program instructions may be stored on a tangible non-transitory computer-readable medium such as a compact disk, a digital disk, flash memory, a memory card, a USB drive, an optical disc storage medium, such as a Blu-ray™ disc, and/or other recording medium. 
     An optional display interface  630  may permit information from the bus  600  to be displayed on the display  635  in audio, visual, graphic or alphanumeric format. Communication with external devices, such as a printing device, may occur using various communication ports  640 . A communication port  640  may be attached to a communications network, such as the Internet or an intranet. 
     The hardware may also include an interface  645  which allows for receipt of data from input devices such as a keyboard  650  or other input device  655  such as a mouse, a joystick, a touch screen, a remote control, a pointing device, a video input device and/or an audio input device. 
     It will be appreciated that various of the above-disclosed and other features and functions, or alternatives thereof, may be desirably combined into many other different systems or applications or combinations of systems and applications. Also that various presently unforeseen or unanticipated alternatives, modifications, variations or improvements therein may be subsequently made by those skilled in the art which are also intended to be encompassed by the following claims.