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Robustness of Order-Up-to Policies in Lost-Sales Inventory Systems

Marco Bijvank¹; Woonghee Tim Huh²; Ganesh Janakiraman³; Wanmo Kang⁴

¹ Haskayne School of Business, University of Calgary, Calgary, Alberta T2N 1N4, Canada; · ² Sauder School of Business, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada · ³ Naveen Jindal School of Management, University of Texas at Dallas, Richardson, Texas 75080; · ⁴ Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Daejeon, 305-701, South Korea

We study an inventory system under periodic review when excess demand is lost. It is known (Huh et al. 2009) that the best base-stock policy is asymptotically optimal as the lost-sales penalty cost parameter grows. We now show that this result is robust in the following sense: Consider the base-stock level which is optimal in a backordering system (with a per-unit-per-period backordering cost) in which the backorder cost parameter is a function of the lost-sales parameter in the original system. Then there is a large family of functions (mapping the lost-sales cost parameter to the backorder cost parameter) such that the resulting base-stock policy is asymptotically optimal. We also demonstrate the robustness phenomenon through a second result. We consider the base-stock level which is optimal in a backordering system in which a unit of backorder is charged a penalty cost only once (such a system has been studied by Rosling). We show that this base-stock policy is also asymptotically optimal. Furthermore, we show that a modification suggested by Archibald of this base-stock level also results in an asymptotically optimal policy. Finally, we numerically test the performance of this heuristic policy for a wide spectrum of values for the lost-sales penalty cost parameter and illustrate the superior performance of Archibald's method.

DOI

10.1287/opre.2014.1298

Volume

62 (5)

Pages

1040-1047

Language

en

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