TECHNICAL NOTE---Inventory Systems with a Generalized Cost Model

Woonghee Tim Huh (), Ganesh Janakiraman (), Alp Muharremoglu () and Anshul Sheopuri ()
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Woonghee Tim Huh: Sauder School of Business, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada
Ganesh Janakiraman: School of Management, The University of Texas at Dallas, Richardson, Texas 75080
Alp Muharremoglu: Graduate School of Business, Columbia University, New York, New York 10027
Anshul Sheopuri: IBM T. J. Watson Research Center, Yorktown Heights, New York 10598

Operations Research, 2011, vol. 59, issue 4, 1040-1047

Abstract: We study a single-stage inventory system with a generalized shortage penalty cost that includes the following three components: (i) a cost that is an increasing function of the number of backordered units in a period, (ii) a fixed cost incurred for each period in which there is a backorder irrespective of how many units are backordered, and finally (iii) a cost that is an increasing function of the number of periods a customer is backordered. We show the problem can be transformed into one in which the backorder cost depends on the inventory position only. Then we present two sets of conditions; the first one restricts our attention to a special case of the generalized penalty cost model while the second one restricts our attention to stationary demand models with some distributional assumptions. Under the first (resp. second) set of conditions, we show that the expected cost in a period can be expressed as a convex (resp. quasiconvex) function of the after-ordering inventory position. We use this property to prove the optimality of order-up-to policies under both sets of conditions and discuss extensions to the cases where either a fixed ordering cost or a batch ordering constraint is present.

Keywords: inventory/production systems; backordering cost; base-stock policies (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (3)

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