Base‐stock policies in capacitated assembly systems: Convexity properties

Base‐stock policies in capacitated assembly systems: Convexity properties

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Article ID: iaor20101074
Volume: 57
Issue: 2
Start Page Number: 109
End Page Number: 118
Publication Date: Mar 2010
Journal: Naval Research Logistics
Authors: ,
Keywords: inventory: storage
Abstract:

We study an assembly system with a single finished product managed using an echelon base‐stock or order‐up‐to policy. Some or all operations have capacity constraints. Excess demand is either backordered in every period or lost in every period. We show that the shortage penalty cost over any horizon is jointly convex with respect to the base‐stock levels and capacity levels. When the holding costs are also included in the objective function, we show that the cost function can be written as a sum of a convex function and a concave function. Throughout the article, we discuss algorithmic implications of our results for making optimal inventory and capacity decisions in such systems.

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