Lost Sales Inventory Models: Some Recent Results
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Date: 09-30-2008
Start Time:
1:00pm
End Time: 2:00pm
Speaker: Ganesh Janakiraman, Stern School of Business: New York University
Location: 303 Mudd
ABSTRACT
In the area of stochastic inventory theory, there are two fundamental assumptions about the consequence of stock-outs. The first assumption, called backordering, is that any demand that exceeds supply in a time period is carried over to the next period. The second assumption, called lost sales, is that such excess demand is not carried over. Although the second model is at least as important as the first, it has received far less attention from researchers than the first, in models where supply replenishment is not instantaneous. This is because lost sales inventory models are much less analytically tractable than backorder models. In particular, it is known that a simple class of replenishment policies, called order-up-to policies, is optimal for backorder models. The optimal replenishment policies for lost sales models have only been partially characterized; most importantly, it is known that order-up-to policies are not optimal in these models. The focus of this seminar is the following set of new results for lost sales inventory systems. For a specific order-up-to policy we propose, the ratio of the cost incurred by using this policy to the optimal cost can be bounded using the mean residual life of the lead time demand distribution. Under mild distributional assumptions, this ratio converges to one asymptotically as the shortage cost parameter grows. In several real inventory systems where the lost sales model is more appropriate, the shortage cost is substantially larger than the holding cost; our bounds indicate that the specific order-up-to policy we propose performs well in such settings. These results are part of a working paper by Huh, Janakiraman, Muckstadt and Rusmevichientong. A related result, comparing the optimal costs of a lost sales inventory system with the cost of a backorder inventory system, due to Janakiraman, Seshadri and Shanthikumar (2005), will also be discussed.
BIO
Ganesh Janakiraman is an Assistant Professor of Operations Management in the Department of Information, Operations and Management Sciences at the Stern School of Business, New York University. He obtained his doctoral degree in Operations Research from Cornell University. He works in the area of Stochastic Inventory Theory and has published in Operations Research, Management Science and Operations Research Letters.