Zero-Inventory Conditions For a Two-Part-Type Make-to-Stock(12)

We consider the dynamic scheduling of a two-part-type make-tostock production system using the model of Wein [12]. Exogenous demand for each part type is met from finished goods inventory; unmet demand is backordered. The control policy determines which pa

WeconsidertwotrajectoriesXπandXζgeneratedbypolicyπofSection

4.3andpolicyζ.Thestartingpointsofthetrajectoriesaretheirrespectivehedgingpoints.Weconsiderthensequencesofrealizationsofthearrivaltime

11222oftype1and2demands,t11,t2,...,tk,...,andt1,t2,...,tk,...respectively,ppπandofrealizationsoftheproductiontimetp1,t2,...,tk,....WecoupleX

andXζbyassumingthattheyaregeneratedbythesecommonrealizationsoftheunderlyingrandomvariables.

Figure3:Di erentSegmentsoftheCoupledTrajectoriesfortheRightEx-tension

Thecoupledtrajectoriescanbedividedinto4segments(seeFigure3): Segment1:

ζπInthissegment,X1=0,Xπ Xζ=e1(sothatX1=1).Bothpolicies

ππ<0,andidlewhenX2=0.Asaresult,theproducetype2whenX2

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