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Base‐stock policies in capacitated assembly systems: Convexity properties
Author(s) -
Huh Woonghee Tim,
Janakiraman Ganesh
Publication year - 2010
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/nav.20386
Subject(s) - convexity , holding cost , stock (firearms) , stockout , time horizon , operations research , mathematical optimization , economic shortage , computer science , order (exchange) , economic order quantity , inventory cost , regular polygon , function (biology) , economics , operations management , business , mathematics , finance , supply chain , marketing , engineering , mechanical engineering , linguistics , philosophy , geometry , government (linguistics) , evolutionary biology , biology
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