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1、FixedChargeConstraints (BinaryVariables)HenryC.CoTechnologyandOperationsManagement,CaliforniaPolytechnicandStateUniversityDecisionvariablesx1=numberofshirtstoproducex2=numberofshortstoproducex3=numberofpantstoproduceAtmost150laborhoursand160squareyardsofclothareavailable.FixedCostPerWeekVariab
2、leCostsPerWeekSalesPriceLaborHoursCloth(Sq.Yds.)Shirts$200$6$1234Shorts$150$4$823Pants$100$8$1564Withoutlookingatthefixedcost,andignoringthefactthatthenumberofshirts,shorts,andpantstoproducemustbeintegers,thissimplifiestoanLPproblem:TheLPSolutionQuestion:Howcanwemodelthefixedcosts?Wedothisbyus
3、ingbinaryvariables.Introduceasetofinteger(binary)variablesasfollows:y1=1ifweproduceshirts(i.e.,ifx1>0),otherwise,y1=0.Y2=1ifweproduceshorts(i.e.,ifx2>0),otherwise,y2=0.Y3=1ifweproducepants(i.e.,ifx3>0),otherwise,y3=0.Howdowemodelthis?Integer(Binary)VariablesAUsefulTrickLetM=areasonablylargecon
4、stant.Forexample,M=themostnumberofshirtsyoumaywanttoproduce.Ifwestate:x1≤My1orequivalently,x1-My1≤0,thenIfx1>0,y1cannotbe0.Inotherwords,ifweproduceshirts,y1=1.WhatisM?IfweALLthelaborisusedtoproduceshirts,wecanproduce150/3=50shirts(note:thereare150availableandeachshirttakes3hourstomake).Ifallth
5、eclothisusedtoproduceshirts,wecanproduce160/4=4shirts(i.e.,thereare160sq.ydofclothandeachshirtneed4sq.yd).Thus,themostshirtswecanproduceisMinimum(50,40)=40.Followingthesameargument,themostpantswecanproduce=53,andthemostpantswecanproduce=25.FixedCostintheObjectiveFunctionAddthefollowingfixedcos
6、tstotheobjectivefunction:$200y1+$150y2+$100y3Plus3additionalconstraints:x1-40y1≤0x2-53y2≤0x3-25y3≤0BinaryVariablesinSolverDeclarey1,y2,andy3asbinaryvariablesbyaddingthefollowingconstraintsinSolver:IntegerVariablesinSolverIfneeded,youmayalsodeclarex1,x2,andx3asintegervariablesbyaddingthefollowi
7、ngconstraintsinSolver:PuttingEverythingTogether…
