Base-stock policies in capacitated assembly systems: Convexity properties

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...

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Bibliographic Details
Published inNaval research logistics Vol. 57; no. 2; pp. 109 - 118
Main Authors Huh, Woonghee Tim, Janakiraman, Ganesh
Format Journal Article
LanguageEnglish
Published Hoboken Wiley Subscription Services, Inc., A Wiley Company 01.03.2010
Subjects
Algorithms
Assembly
Base-stock
Convexity
Inventory
Logistics
Multi-Echelon
Naval
Optimization
Policies
Shortages
Stockpiling
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Summary: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.© 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2010
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ISSN:0894-069X
1520-6750
DOI:10.1002/nav.20386