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

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

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Title: Robustness of Order-Up-To Policies in Lost-Sales Inventory Systems
Author(s):
Bijvank, Marco;
Huh, Woonghee Tim;
Janakiraman, Ganesh;
Kang, Wanmo
Item Type: article
Keywords: Inventory control
Base stock
Lost sales
Order-up-to policies
Abstract: 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.
Publisher: INFORMS
ISSN: 0030-364X
Persistent Link: http://dx.doi.org/10.1287/opre.2014.1298
http://hdl.handle.net/10735.1/4241
Terms of Use: ©2014 INFORMS

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