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BDM Cheat Sheet.docx

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University of Ottawa

GOAL PROGRAMMING Decide what to produce over the next quarter A product INTEGER PROGRAMMING Product can be made on only 1 of 2 machines x1 or x2 cannot be produced unless the associated setup cost is paid If the setup cost is paid the Machines have different process req profitcost structures Differencesamount of a product which is produced is limited by the associated capacity Product B is MachineProfitUnit Setup CostRaw Mat 1 unitRaw Mat 2unitalways packaged in quantities of 100if produced either 100 200 or 300 units However the other products have no such packaging requirements If all 4 products produced an X1502502 lbs4 quartsextra charge of 1000 is incurred for trainingX2402103 lbs2 quartsThere are three goals equally weighted1 total profit should be at least 80002 total setup cost should be at most 950 Determine whether all output should be produced on one of machines or split between INTEGER PROGRAMMING Want to determine locations for cab waiting points3 exactly three products should be producedtwo machines Maximize contribution to profit 30 lbs of raw mat 1 and 36 quarts of rawThe objective as usual is to minimize the sum of the appropriate deviations ie the LocatioCan Serve AreasCost Daymat 2 available for the production rundeviations which are deemed to be undesirable FORMULATE the above problem n Let A B C and D denote the number of units of each of the products produced x1 units to produce machine 1x2 units produce machine 2 Let yA yB yC and yD1 if the corresponding product is produced 0 otherwise 1A E400y11 if machine 1 used 0 otherwisey21 if machine 2 used 0 otherwise Let zi1 if 100i units of C are produced 0 otherwise i1232A C D500 Let w1 if all four products are produced 0 otherwise Let di and di denote the amounts by which the ith goal is overunderachieved 3B C E450 Minimize d1d2d3d3A400yA B300yB C500yCD250yD4B D440 B100z1200z2300z3z1z2z315D E430 yAyByCyD3w 10A8B6C7D1200yA600yB700yC 1000w8000d1d1 Wants to be sure all areas can be served and wants done for as little cost as possible 1200yA600yB700yC950d2d2 Determine choice of locations to accomplish this goalyAyByCyD3d3d3 A B C and D either0 or integer deviation variables0 yi zi w binary Xi1 if location 1 used 0 if otherwise i 1 to 5d underachievement of the profit target1 Min Z400x1400x2450x3440x4430x5d overachievement of the profit target1As much profit above 3000 as possible dFully utilize available wiring dArea A x1x21Area D x2x4x51Avoid overtime in assembly dMeet contract to
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