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

Figure1:GeneralStructureofanOptimalPolicy

3StructureoftheOptimalPolicy

Inthissectionwepresentsomepropertiesfortheoptimalpoliciesthatwillbeneededtoestablishzero-inventoryconditions.Theyarebasedontheconjecturethattheoptimalpolicyhasahedgingpointform.ThisformhasbeenshownbyHa[3]whenµ1=µ2,andhasbeenextensivelynumericallyveri edwhenµ1=µ2.

Ahedgingpointpolicyischaracterizedbyahedgingpointandaswitchingcurve(Figure1).Thehedgingpointz=(z1,z2)≥0determinestheon-handinventorylevelsfromwhichthemachinedoesnotproduce.Theswitchingcurvesplitsthestatespaceintworegions,accordingtowhichtypeisprefered.Moreprecisely,followingVeatchandWein[9],wedenotebyIthesetofstates¯ibethesetofstatesininwhichthecontrolpolicyidlesthemachine.LetB

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