US20060259173A1 - Capacity management in a wafer fabrication plant - Google Patents
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- US20060259173A1 US20060259173A1 US11/127,314 US12731405A US2006259173A1 US 20060259173 A1 US20060259173 A1 US 20060259173A1 US 12731405 A US12731405 A US 12731405A US 2006259173 A1 US2006259173 A1 US 2006259173A1
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B19/00—Programme-control systems
- G05B19/02—Programme-control systems electric
- G05B19/418—Total factory control, i.e. centrally controlling a plurality of machines, e.g. direct or distributed numerical control [DNC], flexible manufacturing systems [FMS], integrated manufacturing systems [IMS], computer integrated manufacturing [CIM]
- G05B19/41865—Total factory control, i.e. centrally controlling a plurality of machines, e.g. direct or distributed numerical control [DNC], flexible manufacturing systems [FMS], integrated manufacturing systems [IMS], computer integrated manufacturing [CIM] characterised by job scheduling, process planning, material flow
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q10/00—Administration; Management
- G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
- G06Q10/063—Operations research, analysis or management
- G06Q10/0631—Resource planning, allocation, distributing or scheduling for enterprises or organisations
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/30—Nc systems
- G05B2219/32—Operator till task planning
- G05B2219/32263—Afo products, their components to be manufactured, lot selective
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/30—Nc systems
- G05B2219/32—Operator till task planning
- G05B2219/32294—Maximize throughput of cell
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
- Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
- Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]
Definitions
- the invention relates broadly to a method for the management of capacity in a wafer fabrication plant and to a computer program product for the management of capacity in a wafer fabrication plant.
- Semiconductor wafer fabrication plants typically produce thousands of devices per day and may be configurable to fabricate two, three or more different product groups/types. E.g. commercial 8 inch wafer fabrication plants costs typically US$1.5 billion to build, representing a significant capital investment for even the largest enterprises.
- Profitability is of vital importance to the operators and owners of wafer fabrication plants, and such people endeavour to improve profitability without relying only on further capital expense in installed equipment. There thus is a need to optimise the use of existing installed equipment.
- wafer fabrication plants will produce more than one semiconductor product.
- the mix of products being manufactured at any one time is based on a demand plan and a derived corresponding initial capacity plan.
- Such initial capacity plans are reactive to customer ordering, and associated with a tooling plan.
- conventional initial capacity plans are not optimised, and thus there is a need to improve upon them, with the goal of improved profitability or plant output.
- a method for the management of capacity in a wafer fabrication comprising the steps of (a) calculating a bottleneck capacity factor for a product group mix of an initial capacity plan; (b) calculating a respective maximum capacity for each product group in the capacity plan; (c) algorithmically determining a respective production value for different product group mixes, including for the product group mix of the initial capacity plan, subject to said bottleneck capacity factor and said respective maximum capacities not being exceeded; (d) determining a maximum one of said production values; and (e) determining the product group mix for said maximum production value.
- Said bottleneck capacity factor may be calculated as the sum of respective weighted maximum capacities for the individual product groups.
- Each said product group weighting may be proportional to the sum of passes of a bottleneck tool of said fabrication plant for each piece of the respective product group and is inversely proportional to a production rate of the respective product group.
- step (c) said respective production values may be a measure of total wafer output provided for the respective product group mixes.
- step (c) said respective production values may be a measure of profit provided for the respective product group mixes.
- a computer program product for the management of capacity in a wafer fabrication plant comprising a computer program stored on a storage medium, said computer program performing the steps of (a) calculating a bottleneck capacity factor for a product group mix of an initial capacity plan; (b) calculating a respective maximum capacity for each product group in the capacity plan; (c) algorithmically determining a respective production value for different product group mixes, including for the product group mix of the initial capacity plan, subject to said bottleneck capacity factor and said respective maximum capacities not being exceeded; (d) determining a maximum one of said production values; and (e) determining the product group mix for said maximum production value.
- Said bottleneck capacity factor may be calculated as the sum of respective weighted maximum capacities for the individual product groups.
- Each said product group weighting may be proportional to the sum of passes of a bottleneck tool of said fabrication plant for each piece of the respective product group and is inversely proportional to a production rate of the respective product group.
- step (c) said respective production values may be a measure of total wafer output provided for the respective product group mixes.
- step (c) said respective production values may be a measure of profit provided for the respective product group mixes.
- FIG. 1 is a schematic block diagram embodying the invention.
- FIG. 2 is a tabulation of variables leading to the bottleneck capacity measure.
- FIG. 3 is a tabulation of variables for various mix combinations leading to maximum wafer output.
- FIG. 4 is a surface plot of the data of FIG. 3 .
- FIG. 5 is a contour plot of the data of FIG. 3 .
- FIG. 6 is a tabulation of variables leading to the profit margin for Product Groups.
- FIG. 7 is a tabulation of variables for various mix combinations leading to maximum profit.
- FIG. 8 is a surface plot of the data of FIG. 7 .
- FIG. 9 is a contour plot of the data of FIG. 7 .
- FIG. 10 is a schematic representation of a computer system suitable for performing the techniques described herein.
- a wafer fabrication plant typically produces semiconductor devices using a large number and variety of basic fabrication steps.
- the steps will depend upon the form (eg. MOS) of device being fabricated, the nature of the gate (eg. metal or polysilicon) and the substrate (eg. bulk silicon or silicon-on-sapphire).
- MOS metal or polysilicon
- the steps can include the definition of active regions, definition of depletion loads, polysilicon-defusion interconnect, definition of transistors and polysilicon-defusion contacts, defusion, polysilicon-metal and defusion-metal interconnects, metallisation and annealing and passivation. All of these processes and sub-processes require complex and expensive equipment or tools. It is often the case that one process step and corresponding tool is used for all product groups being fabricated.
- FIG. 1 shows a block flow diagram embodying capacity management in a wafer fabrication plant, according to the present invention.
- the capacity management process 10 begins with identifying an initial capacity plan based on a demand plan (step 12 ). For each Product Group in the initial capacity plan, a consumption sensitivity factor is defined (step 14 ). Next, a bottleneck capability variable is calculated (step 16 ). The capacity boundaries for each of the product groups are next determined (step 18 ).
- a determination of maximum wafer output is then performed for changing Product Group mixes to determine a maximum (step 20 ).
- the Product Group mix giving maximum wafer output is then determined for the fabrication plant (step 22 ).
- a determination of maximum profit is performed for changing Product Group mixes (step 24 ), then the Product Group mix giving maximum profit is determined for the fabrication plant (step 26 ).
- a known respective maximum capacity in e.g. pieces/month
- X max 15,300
- Y max 8,000
- Z max 5,000
- the determined output, OUT 0 thus is 24,800, in accordance with Equation 1.
- the initial percentage Product group mix according to the initial capacity plan of X %: Y %: Z % is equal to 100%: 33%: 16%.
- PASS x,y,z sum of passes of the process using bottleneck tool for each piece of product group X, Y, Z
- WPH x,y z weighted WPH of process passes for each product group X, Y, Z
- CAPA 0 aX 0 +bY 0 +cZ 0 3
- X max Max capacity of X product group due to dedicated tool(s)
- Y max Max capacity of Y product group due to dedicated tool(s)
- Z max Max capacity of Z product group due to dedicated tool(s)
- FIG. 3 shows a series of mix combinations of the Z Product and the Y Product with reference to the X Product. For each combination the wafer output is calculated according to Equation 1 and the bottleneck capability is calculated in accordance with Equation 3. Once these values are determined for all mixes, a maximum mix combination is determined for maximum wafer output subject to the bottleneck capability not being exceeded.
- the data shown in FIG. 3 is represented as a surface plot in FIG. 4 and as a contour plot in FIG. 5 .
- the profit margins for each Product Group are calculated by the difference in the selling price and cost, in accordance with Equations 7, 8 and 9.
- PF X ASP X ⁇ STD COST X 7
- PF Y ASP Y ⁇ STD COST Y 8
- PF z ASP Z ⁇ STD COST Z 9
- Maximize Profit i X i *PF X +Y i *PF Y +Z i *PF z 10
- FIG. 7 shows the same tabulation as FIG. 3 , but with the profit calculation, according to Equation 10, performed and given in the last column.
- FIG. 8 is a surface plot representation of the percentage Y product and percentage said product mixes and the profit value.
- FIG. 9 is a contour plot of the same data of FIG. 8 .
- the maximum profit point is calculated by interpolation and gives maximum profit for the percentage Product Group mixes, X %: Y %: Z %, of 100%: 34.3%: 1.6%.
- the results obtained from the optimization processing in example embodiments of the present invention may be utilized in a number of ways.
- the optimized Product Group mix may be implemented instead of the nominal Product Group mix according to the initial capacity plan. In practice, this may involve the results being considered during capacity management planning and possible feedback and interact with the demand plan management.
- the results of the optimization processing in example embodiments may be utilized to facilitate forecasting in capacity management, and may also provide valuable feedback in terms of identifying higher and lower profitability Product Group mixes. This in turn may influence the type of product groups offered or focused on in the overall management of a wafer fabrication plant.
- FIG. 10 is a schematic representation of a computer system 100 suitable for executing computer software programs.
- Computer software programs execute under a suitable operating system installed on the computer system 100 , and may be thought of as a collection of software instructions for implementing particular steps.
- the components of the computer system 100 include a computer 120 , a keyboard 110 and mouse 115 , and a video display 190 .
- the computer 120 includes a processor 140 , a memory 150 , input/output (I/O) interface 160 , communications interface 165 , a video interface 145 , and a storage device 155 . All of these components are operatively coupled by a system bus 130 to allow particular components of the computer 120 to communicate with each other via the system bus 130 .
- the processor 140 is a central processing unit (CPU) that executes the operating system and the computer software program executing under the operating system.
- the memory 150 includes random access memory (RAM) and read-only memory (ROM), and is used under direction of the processor 140 .
- the video interface 145 is connected to video display 190 and provides video signals for display on the video display 190 .
- User input to operate the computer 120 is provided from the keyboard 110 and mouse 115 .
- the storage device 155 can include a disk drive or any other suitable storage medium.
- the computer system 100 can be connected to one or more other similar computers via a communications interface 165 using a communication channel 185 to a network, represented as the Internet 180 .
- the computer software program may be recorded on a storage medium, such as the storage device 155 .
- the computer software can be accessed directly from the Internet 180 by the computer 120 .
- a user can interact with the computer system 100 using the keyboard 110 and mouse 115 to operate the computer software program executing on the computer 120 .
- the software instructions of the computer software program are loaded to the memory 150 for execution by the processor 140 .
Abstract
Description
- The invention relates broadly to a method for the management of capacity in a wafer fabrication plant and to a computer program product for the management of capacity in a wafer fabrication plant.
- Semiconductor wafer fabrication plants typically produce thousands of devices per day and may be configurable to fabricate two, three or more different product groups/types. E.g. commercial 8 inch wafer fabrication plants costs typically US$1.5 billion to build, representing a significant capital investment for even the largest enterprises.
- Profitability is of vital importance to the operators and owners of wafer fabrication plants, and such people endeavour to improve profitability without relying only on further capital expense in installed equipment. There thus is a need to optimise the use of existing installed equipment.
- As mentioned, wafer fabrication plants will produce more than one semiconductor product. Conventionally, the mix of products being manufactured at any one time is based on a demand plan and a derived corresponding initial capacity plan. Such initial capacity plans are reactive to customer ordering, and associated with a tooling plan. But conventional initial capacity plans are not optimised, and thus there is a need to improve upon them, with the goal of improved profitability or plant output.
- In accordance with a first aspect of the present invention there is provided a method for the management of capacity in a wafer fabrication, the method comprising the steps of (a) calculating a bottleneck capacity factor for a product group mix of an initial capacity plan; (b) calculating a respective maximum capacity for each product group in the capacity plan; (c) algorithmically determining a respective production value for different product group mixes, including for the product group mix of the initial capacity plan, subject to said bottleneck capacity factor and said respective maximum capacities not being exceeded; (d) determining a maximum one of said production values; and (e) determining the product group mix for said maximum production value.
- Said bottleneck capacity factor may be calculated as the sum of respective weighted maximum capacities for the individual product groups.
- Each said product group weighting may be proportional to the sum of passes of a bottleneck tool of said fabrication plant for each piece of the respective product group and is inversely proportional to a production rate of the respective product group.
- In step (c), said respective production values may be a measure of total wafer output provided for the respective product group mixes.
- In step (c), said respective production values may be a measure of profit provided for the respective product group mixes.
- In accordance with a second aspect of the present invention there is provided a computer program product for the management of capacity in a wafer fabrication plant comprising a computer program stored on a storage medium, said computer program performing the steps of (a) calculating a bottleneck capacity factor for a product group mix of an initial capacity plan; (b) calculating a respective maximum capacity for each product group in the capacity plan; (c) algorithmically determining a respective production value for different product group mixes, including for the product group mix of the initial capacity plan, subject to said bottleneck capacity factor and said respective maximum capacities not being exceeded; (d) determining a maximum one of said production values; and (e) determining the product group mix for said maximum production value.
- Said bottleneck capacity factor may be calculated as the sum of respective weighted maximum capacities for the individual product groups.
- Each said product group weighting may be proportional to the sum of passes of a bottleneck tool of said fabrication plant for each piece of the respective product group and is inversely proportional to a production rate of the respective product group.
- In step (c), said respective production values may be a measure of total wafer output provided for the respective product group mixes.
- In step (c), said respective production values may be a measure of profit provided for the respective product group mixes.
-
FIG. 1 is a schematic block diagram embodying the invention. -
FIG. 2 is a tabulation of variables leading to the bottleneck capacity measure. -
FIG. 3 is a tabulation of variables for various mix combinations leading to maximum wafer output. -
FIG. 4 is a surface plot of the data ofFIG. 3 . -
FIG. 5 is a contour plot of the data ofFIG. 3 . -
FIG. 6 is a tabulation of variables leading to the profit margin for Product Groups. -
FIG. 7 is a tabulation of variables for various mix combinations leading to maximum profit. -
FIG. 8 is a surface plot of the data ofFIG. 7 . -
FIG. 9 is a contour plot of the data ofFIG. 7 . -
FIG. 10 is a schematic representation of a computer system suitable for performing the techniques described herein. - Overview
- A wafer fabrication plant typically produces semiconductor devices using a large number and variety of basic fabrication steps. The steps will depend upon the form (eg. MOS) of device being fabricated, the nature of the gate (eg. metal or polysilicon) and the substrate (eg. bulk silicon or silicon-on-sapphire). In silicon-gate processes a number of discrete sub-processes are performed. By way of broad example, the steps can include the definition of active regions, definition of depletion loads, polysilicon-defusion interconnect, definition of transistors and polysilicon-defusion contacts, defusion, polysilicon-metal and defusion-metal interconnects, metallisation and annealing and passivation. All of these processes and sub-processes require complex and expensive equipment or tools. It is often the case that one process step and corresponding tool is used for all product groups being fabricated.
-
FIG. 1 shows a block flow diagram embodying capacity management in a wafer fabrication plant, according to the present invention. Thecapacity management process 10 begins with identifying an initial capacity plan based on a demand plan (step 12). For each Product Group in the initial capacity plan, a consumption sensitivity factor is defined (step 14). Next, a bottleneck capability variable is calculated (step 16). The capacity boundaries for each of the product groups are next determined (step 18). - Thereafter, in the first of two branches, a determination of maximum wafer output is then performed for changing Product Group mixes to determine a maximum (step 20). The Product Group mix giving maximum wafer output is then determined for the fabrication plant (step 22). In the second branch, a determination of maximum profit is performed for changing Product Group mixes (step 24), then the Product Group mix giving maximum profit is determined for the fabrication plant (step 26).
- Specific Example
- Assume X,Y,Z . . . are Product Groups in the Fabrication plant. Then, the reference fabrication output (OUT0) is given by:
OUT0 =X 0 +Y 0 +Z 0+ 1
For the purposes of illustration, three Product Groups will be assumed, although there can, of course, be any desired number. - Referring to
FIG. 2 , for the three Product Groups X,Y,Z a known respective maximum capacity (in e.g. pieces/month) is given: Xmax=15,300, Ymax=8,000 and Zmax=5,000. The initial capacity plan specifies an initial capacity for each Product Group: X0=14,000, Y0=6,800 and Z0=4,000. The determined output, OUT0, thus is 24,800, in accordance withEquation 1. The initial percentage Product group mix according to the initial capacity plan of X %: Y %: Z % is equal to 100%: 33%: 16%. - For each of the Product Groups, the sum of passes (PASSx,y,z) for the process using the bottleneck tool, together with the weighted wafer per hour (WPHx,y,z), are given as:
- PASSx,y,z: sum of passes of the process using bottleneck tool for each piece of product group X, Y, Z
- WPHx,y z: weighted WPH of process passes for each product group X, Y, Z
- The values of PASSx,y,z and WPHx,y,z are given in
FIG. 2 . - A Product Group Consumption Sensitivity Factor for each Product Group is defined as:
- The values of a, b and c are also given in
FIG. 2 . - Therefore the maximum Bottleneck Capability (CAPA0) in the example embodiment is calculated as:
CAPA 0 =aX 0 +bY 0 +cZ 0 3 - Therefore, the maximum Bottleneck Capability for the data shown in
FIG. 2 , calculated in accordance withEquation 3, gives the value 5,657 as available machine hours per month in the example embodiment. - The Product Groups'Capacity Boundaries Xmax, Ymax, Zmax are defined as:
- Xmax=Max capacity of X product group due to dedicated tool(s)
- Ymax=Max capacity of Y product group due to dedicated tool(s)
- Zmax=Max capacity of Z product group due to dedicated tool(s)
- Maximum Wafer Output
- The objective is to maximize wafer output in accordance with
Equation 4 for Product Group mix combinations. This determination is subject to boundary conditions given byEquations 5 and 6:
Maximize OUTi =X i +Y i +Z i where i: anymix combination 4
Boundary(1): CAPA i =aX i +bY i +cZ i ≦CAPA 0 6
Boundary(2): X i ≦X max , Y i ≦Y max , Z i ≦Z max 5 -
FIG. 3 shows a series of mix combinations of the Z Product and the Y Product with reference to the X Product. For each combination the wafer output is calculated according toEquation 1 and the bottleneck capability is calculated in accordance withEquation 3. Once these values are determined for all mixes, a maximum mix combination is determined for maximum wafer output subject to the bottleneck capability not being exceeded. The data shown inFIG. 3 is represented as a surface plot inFIG. 4 and as a contour plot inFIG. 5 . - By mathematical process of interpolation, the maximum wafer output is given for a percentage Product Group mix of X %: Y %: Z %=100%: 25.2%: 19.6%. This represents an optimized Product Group mix, compared with the initial mix from the initial capacity plan.
- The result of the analysis is that a maximized wafer output of 25,445 units is achieved by an optimized mixed combination, as opposed to 24,800 units according to the mix of the initial capacity plan.
- Maximum Profit
- Taking into account the profit maximization aspect, the profit margins for each Product Group are calculated by the difference in the selling price and cost, in accordance with
Equations
PF X =ASP X −STD COST X 7
PF Y =ASP Y −STD COST Y 8
PF z =ASP Z −STD COST Z 9
Again, using the consumption sensitivity factors and capacity boundaries:
Maximize Profiti =X i *PF X +Y i *PF Y +Z i *PF z 10 -
- where i=any mix combination
Boundary(1): CAPA i =aX i +bY i +cZ i ≦CAPA 0 11
Boundary(2): X i ≦X max ,Y i ≦Y max , Z i ≦Z max 12
- where i=any mix combination
- In the present example, this is shown in
FIG. 6 as the values PFx=300, PFy=500 and PFz=100. - Maximizing profit is determined algorithmically for mix combinations of Product Groups, in accordance with
Equation 10. The profit margins act as weightings. The calculation is subject to the boundary conditions of the bottleneck capacity not exceeding the initial value (Equation 11), and that the mix components do not exceed respective maximum values (Equation 12). -
FIG. 7 shows the same tabulation asFIG. 3 , but with the profit calculation, according toEquation 10, performed and given in the last column.FIG. 8 is a surface plot representation of the percentage Y product and percentage said product mixes and the profit value.FIG. 9 is a contour plot of the same data ofFIG. 8 . The maximum profit point is calculated by interpolation and gives maximum profit for the percentage Product Group mixes, X %: Y %: Z %, of 100%: 34.3%: 1.6%. - The result of this analysis is that a maximum profit of approximately $US8.63 million is a achievable by an optimized Product Group mix as opposed to the US$8 million profit that would be achieved by the nominal Product Group mix according to the initial capacity plan.
- It will be appreciated that the results obtained from the optimization processing in example embodiments of the present invention may be utilized in a number of ways. For example, where possible, the optimized Product Group mix may be implemented instead of the nominal Product Group mix according to the initial capacity plan. In practice, this may involve the results being considered during capacity management planning and possible feedback and interact with the demand plan management. It will further be appreciated that the results of the optimization processing in example embodiments may be utilized to facilitate forecasting in capacity management, and may also provide valuable feedback in terms of identifying higher and lower profitability Product Group mixes. This in turn may influence the type of product groups offered or focused on in the overall management of a wafer fabrication plant.
- Computer Implementation
-
FIG. 10 is a schematic representation of acomputer system 100 suitable for executing computer software programs. Computer software programs execute under a suitable operating system installed on thecomputer system 100, and may be thought of as a collection of software instructions for implementing particular steps. - The components of the
computer system 100 include acomputer 120, akeyboard 110 and mouse 115, and avideo display 190. Thecomputer 120 includes aprocessor 140, amemory 150, input/output (I/O)interface 160,communications interface 165, avideo interface 145, and astorage device 155. All of these components are operatively coupled by a system bus 130 to allow particular components of thecomputer 120 to communicate with each other via the system bus 130. - The
processor 140 is a central processing unit (CPU) that executes the operating system and the computer software program executing under the operating system. Thememory 150 includes random access memory (RAM) and read-only memory (ROM), and is used under direction of theprocessor 140. - The
video interface 145 is connected tovideo display 190 and provides video signals for display on thevideo display 190. User input to operate thecomputer 120 is provided from thekeyboard 110 and mouse 115. Thestorage device 155 can include a disk drive or any other suitable storage medium. - The
computer system 100 can be connected to one or more other similar computers via acommunications interface 165 using acommunication channel 185 to a network, represented as theInternet 180. - The computer software program may be recorded on a storage medium, such as the
storage device 155. Alternatively, the computer software can be accessed directly from theInternet 180 by thecomputer 120. In either case, a user can interact with thecomputer system 100 using thekeyboard 110 and mouse 115 to operate the computer software program executing on thecomputer 120. During operation, the software instructions of the computer software program are loaded to thememory 150 for execution by theprocessor 140. - Other configurations or types of computer systems can be equally well used to execute computer software that assists in implementing the techniques described herein. In the example embodiment, the optimization processing was implemented utilizing a Microsoft® Excel application program, including the Solver function in that application program.
- It will be appreciated by a person skilled in the art that numerous variations and/or modifications may be made to the present invention as shown in the specific embodiments without departing from the spirit or scope of the invention as broadly described. The present embodiments are, therefore, to be considered in all respects to be illustrative and not restrictive.
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