Zero-Inventory Conditions For a Two-Part-Type Make-to-Stock(16)

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

Figure4:OptimalityoftheZero-InventoryPolicy

Typicallyρ1 1whentheseconditionsaremet,sowewillweaken(27)slightlybyreplacingρ1by0,giving

1 γ2≤ h1

h1+b2

(28)Alsosettingλ1=λ2,wehaveγ2=γ2.Thus,Condition4issimilarto

Condition3butcomparesparttypes:thehighpriorityholdingcostmustbelargerelativetothelowprioritybackordercost.

Speci cparametervalueswhereMTOisoptimalareshowninFigure4.Inthisexample,thetotalutilizationrateofthesystemisequalto0.4.Parttypesaresymmetricalindemandandproductionrates.Weseth2=1andb1/h1=b2/h2=b/handvaryb/handh1/h2.Increasingb/hmakesthesystemswitchesfromMTOtomake-to-stock(MTS).Whenparttypesaresimilar(h1/h2closeto1),thesystemswitchtoMTSonlywhenCondition

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