A Dynamic Inventory Model with the Right of Refusal

Management Science, Vol. 56, Vol. 12, pp. 2265-2281

39 Pages Posted: 2 Jun 2008 Last revised: 29 Oct 2015

See all articles by Sreekumar R. Bhaskaran

Sreekumar R. Bhaskaran

Southern Methodist University (SMU) - Information Technology and Operations Management Department (ITOM)

Karthik Ramachandran

Georgia Institute of Technology - Scheller College of Business

John H. Semple

Southern Methodist University (SMU) - Information Technology and Operations Management Department (ITOM)

Date Written: 2010

Abstract

We consider a dynamic inventory (production) model with general order (production) costs and excess demand that can be backordered or refused by the firm. A unit backordered incurs a backorder cost, a unit refused incurs a lost sales charge. Endogenizing the sales decision is necessary in the presence of general convex order costs so that the firm is not forced to backorder a unit whose subsequent procurement would reduce total profits. In each period, the firm must determine the optimal order/production and sales strategy. We show that the optimal policy is characterized by an optimal buy up to level that increases with the initial inventory level and an order quantity that decreases with the initial inventory level. More importantly, we show the optimal sales strategy is characterized by a critical threshold, a backorder limit, that dictates when to stop selling. This threshold is independent of the initial inventory level and the amount purchased. We investigate various properties of this new policy. As demand stochastically increases, the amount purchased increases but the amount backordered decreases, reflecting a shift in the way excess demand is managed. We develop two regularity conditions, one that ensures some backorders are allowed in each period, and another that ensures the amount backordered is nondecreasing in the length of the planning horizon. We bound the buy up to levels in our model using buy up to levels from the pure lost sales and pure backlogging models. We illustrate our findings and results using several numerical examples.

Keywords: dynamic programming, inventory and production, convex order costs, backorder limit

Suggested Citation

Bhaskaran, Sreekumar R. and Ramachandran, Karthik and Semple, John H., A Dynamic Inventory Model with the Right of Refusal (2010). Management Science, Vol. 56, Vol. 12, pp. 2265-2281. Available at SSRN: https://ssrn.com/abstract=1138758

Sreekumar R. Bhaskaran (Contact Author)

Southern Methodist University (SMU) - Information Technology and Operations Management Department (ITOM) ( email )

Dallas, TX 75275
United States

Karthik Ramachandran

Georgia Institute of Technology - Scheller College of Business ( email )

800 West Peachtree St.
Atlanta, GA 30308
United States
(404) 894-8631 (Phone)

HOME PAGE: http://www.prism.gatech.edu/~karthik37/

John H. Semple

Southern Methodist University (SMU) - Information Technology and Operations Management Department (ITOM) ( email )

Dallas, TX 75275
United States
214-768-2546 (Phone)
214-768-4099 (Fax)

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