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1、Chapter9:SalesandOperationsPlanningWedefineacomprehensivesetofdecisionvariablesthatareutilizedinproblems9-1to9-3dependingontheproblemcontext.DecisionVariables:Ht=#ofworkershiredinmontht(t=1,..,12)Lt=#ofworkerslaid-offinmontht(t=1,..,12)Wt=#ofworkersemployedinmontht(t=
2、1,..,12)Ot=#ofhoursofovertimeinmontht(t=1,..,12)It=#ofunitsheldininventoryattheendofmontht(t=1,..,12)Ct=#ofunitssubcontractedinmontht(t=1,..,12)Pt=#ofunitsproducedinmontht(t=1,..,12)Parameters:Dt=#ofunitsdemandedintimeperiodt(t=1,…12)Problem9-1:MinimizeSubjectto:Inven
3、toryconstraints:Overtimeconstraints:Productionconstraints:Workforceconstraints:(a)Worksheet9-1providesthesolutiontothisproblemandthecorrespondingaggregateplan.Thetotalcostoftheplanis$16,820,000(b)FromthetablebelowwecanseethatitisbettertopromoteinAprilthaninJuly,asthep
4、rofitisslightlyhigher.Price=$125TotalCost NopromotionPromotion(April)Promotion(July)TotalCost=$16,820,000$17,059,400$17,367,300TotalRevenue=$28,500,000$28,916,625$29,198,750Profit=$11,680,000$11,857,225$11,831,450Profitincrease=$177,225$151,450(c)Ifasinkissoldat$250
5、,thentheprofitassociatedwithpromotioninJulyishigherthaninApril.So,astheproductmarginincreasesitismorebeneficialtoofferthediscountinhighdemandperiod.Price=$250TotalCost NopromotionPromotion(April)Promotion(July)TotalCost=$16,820,000$17,059,399.94$17,367,299.95TotalRe
6、venue=$57,000,000$57,833,250$58,397,500Profit=$40,180,000$40,773,850.06$41,030,200.05Profitincrease=$593,850.06$850,200.05Problem9-2:Wenowincludehiringandlayoffcostsinthemodel.Notethattheworkforcelevelconstraintsalsochange.MinimizeSubjectto:Inventoryconstraints:Overti
7、meconstraints:Productionconstraints:Workforceconstraints:(a)TotalCost=$16,571,000TotalRevenue=$28,500,000Profit=$11,929,000PeriodProduction0 120,000220,000320,000420,000520,000620,000720,000820,000920,0001018,0001115,0001215,000(b)PromotioninJulyisbetter.Profitincreas
8、esto$218,900.1TotalCost NopromotionPromotion(April)Promotion(July)TotalCost=$16,571,000$16,794,500$17,050,850TotalRevenue=
