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A 2-Approximation Algorithm for Stochastic Inventory Control Models with Lost Sales

Sloan School of Management, MIT, Cambridge, Massachusetts 02139
IOMS-OM Group, Stern School of Business, New York University, New York, New York 10012
Sauder School of Business, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada
retsef{at}mit.edu
gjanakir{at}stern.nyu.edu
mahesh.nagarajan{at}sauder.ubc.ca

In this paper, we describe the first computationally efficient policies for stochastic inventory models with lost sales and replenishment lead times that admit worst-case performance guarantees.

In particular, we introduce dual-balancing policies for lost-sales models that are conceptually similar to dual-balancing policies recently introduced for a broad class of inventory models in which demand is backlogged rather than lost. That is, in each period, we balance two opposing costs: the expected marginal holding costs against the expected marginal lost-sales cost. Specifically, we show that the dual-balancing policies for the lost-sales models provide a worst-case performance guarantee of two under relatively general demand structures. In particular, the guarantee holds for independent (not necessarily identically distributed) demands and for models with correlated demands such as the AR(1) model and the multiplicative autoregressive demand model. The policies and the worst-case guarantee extend to models with capacity constraints on the size of the order and stochastic lead times. Our analysis has several novel elements beyond the balancing ideas for backorder models.

Key Words: inventory; approximation; dual balancing; algorithms; lost sales
History: Received: November 2, 2005; revision received: March 11, 2007;

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