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1、Chapter8:AggregatePlanninginaSupplyChainExerciseSolutions :Wedefineacomprehensivesetofdecisionvariablesthatareutilizedinproblems8-1to8-3dependingontheproblemcontext.DecisionVariables:Ht=#ofworkershiredinmontht(t=1,..,12)Lt=#ofworkerslaid-offinmontht(t=1,..,12)Wt=#ofworker
2、semployedinmontht(t=1,..,12)Ot=#ofhoursofovertimeinmontht(t=1,..,12)It=#ofunits(000s)heldininventoryattheendofmontht(t=1,..,12)Ct=#ofunits(000s)subcontractedinmontht(t=1,..,12)Pt=#ofunits(000s)producedinmontht(t=1,..,12)Parameters:Dt=#ofunits(000s)demandedintimeperiodt(t=
3、1,…12)Problem8-1:MinimizeSubjectto:Inventoryconstraints:Overtimeconstraints:Productionconstraints:Workforceconstraints:(a)Worksheet8.1providesthesolutiontothisproblemandthecorrespondingaggregateplan.Thetotalcostoftheplanis$360,400,000.(b)Ifthenumberofovertimehoursperemplo
4、yeewereincreasedfrom20to40itwouldresultindecreasingthetotalcostto$356,450,000.So,itisadvantageoustodoit.(c)Ifthenumberofemployeesisdecreasedto1200andtheovertimehoursperemployeeareheldat20and40thenthetotalcostsoftheplanare$363,324,000and$357,422,000,respectively.Ifthenumbe
5、rofemployeesisincreasedto1300andtheovertimehoursperemployeeareheldat20and40thenthetotalcostsoftheplanare$358,790,000and$356,270,000,respectively.So,thevalueofadditionalovertimeincreasesasworkforcesizedecreases.(d)Weaddanewconstraint:.Thecostwillbe$363,049,982.Problem8-2:W
6、enowincludethesubcontractoptioninthemodel:MinimizeSubjectto:Inventoryconstraints:Overtimeconstraints:Productionconstraints:Workforceconstraints:Worksheet8-2providesthesolutiontothisproblem.(a)Withoutthesubcontractoptionthetotalcostis$360,400,000(fromproblem8-1)andthetotal
7、numberofunitsproducedis14,900,000.Thus,thecostperunitis$24.19.(b)Thirdpartyproductionmustbeusedinperiods5,6,7,and10foratotalof1,050,000units.Ifthesubcontractcostperunitdecreasesto$25perunitthenatotalof1,650,000unitsmustbeacquiredfromthisoption.(c)Ifthesubcontractcostincre
8、asesto$28perunitthenatotalof700,000unitsmustbeacquiredfromthisoption.(d)Thetotalnumberofunitspro
