chapter07 - Chapter 7 More Models from McCarl and Spreen...

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Chapter 7 More Models from McCarl and Spreen
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The Assembly Problem Objective : Maximize the return summed over all the final products produced less the cost of the component parts purchased. Constraints : The first type of constraint equation is a supply‑demand balance and constrains the usage of the component parts to be less than or equal to inventory plus purchases. The second type of constraint limits the resources used in manufacturing final products and purchasing component parts to the exogenous resource endowment. The last type of constraint imposes a minimum sales requirement on final product production
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Algebra ij j ik kj j j k k j j k k k j k i j k k j j j k e X f Q b X a X - w Q h for a g for all j for al X , Q 0 for all k,j Max c X l - i Q d l l k + X is product, Q is component
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Example: “Computer Express” Computer Excess (CE) can assemble six different computer types: XT, AT, 80386-25, 80386-33, 80486-SX, and 80486-33. Each different type of computer requires a specific set of component parts. The parts considered: 360K floppy disks, 1.2 Meg floppy disks, 1.44 Meg floppy disks, hard disks, monochrome graphics setups, color graphics setups, plain cases, and fancy cases. Assembly information and resource requirements are given in table 7.1. The resource endowment is 550 hours labor, 240 units of system space and 590 units of shelf space.
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Computer Express – Assembly Information Table 7.1. Data for Computer Excess Example Components Required to Assemble a System XT AT 386SX 38633 486SX 48633 360FLOPPY 1 1 12MFLOPPY 1 1 2 1 1 1 144MFLOPPY 1 1 1 HARDDISK 1 1 1 1 1 MONO 1 1 1 COLORVGA 1 1 1 PLAINCASE 1 1 1 FANCYCASE 1 1 1
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Name Cost Inventory Labor Shelf Space 360KFLOPPY 35 20 0.01 0.01 12MFLOPPY 49 29 0.01 0.01 144MFLOPPY 52 32 0.01 0.01 HARDDISK 245 45 0.03 0.03 MONO 102 15 0.07 1.5 COLORVGA 302 45 0.1 2 PLAINCASE 41 11 0.15 1.7 FANCYCASE 80 12 0.12 1.7 Component Parts Information Table 7.1, continued.
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Final Products Assembly and Sales Information Sales Minimum Assembly Name Price Sales Cost Labor Space XT 689 1 59 2 1 AT 992 3 102 2.05 1 386SX 1200 2 100 2.21 1 38633 1400 4 300 2.24 1 486SX 1500 2 400 2.18 1 48633 1800 2 700 2.12 1 Table 7.1, continued.
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Table 7.2. XT AT 386SX 38633 486SX 48633 360k 12M 144M HARD MONO CVGA PLAIN FANCY rhs used OBJECTIVE 630 890 1100 1100 1100 1100 -35 -49 -52 -245 -102 -302 -41 -80 Max 155330.10 360KFLOPPY 1 1 -1 le 20 4.00 0.00 12MFLOPPY 1 1 2 1 1 1 -1 le 29 29.00 50.89 144MFLOPPY 1 1 1 -1 le 32 32.00 53.89 HARDDISK 1 1 1 1 1 -1 le 45 45.00 250.67 MONO 1 1 1 -1 le 15 15.00 385.38 COLORVGA 1 1 1 -1 le 45 45.00 343.38 PLAINCASE 1 1 1 -1 le 11 11.00 362.17 FANCYCASE 1 1 1 -1 le 12 12.00 401.17 LABOR 2 2.05 2.21 2.24 2.18 2.12 0.01 0.01 0.01 0.03 0.07 0.1 0.15 0.12 le 550 537.69 0.00 SHELFSPACE 0.01 0.01 0.01 0.03 1.5 2 1.7 1.7 le 590 590.00 188.92 SYSTEMSPC 1 1 1 1 1 1 le 240 221.89 0.00 b1 1 ge 1 1.00 -168.44 b2 1 ge 3 3.00 -159.11 b3 1 ge 2 172.89 0.00 b4 1 ge 4 4.00
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chapter07 - Chapter 7 More Models from McCarl and Spreen...

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