A Dynamic Lot Size Problem with Multiple Customers: Customer-Specific Shipping and Backlogging Costs

IIE Transactions, Vol. 39, No. 11, November 2007

27 Pages Posted: 9 May 2009

See all articles by Suresh Chand

Suresh Chand

Purdue University

Vernon Hsu

Donald G. Costello College of Business at George Mason University

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Vinayak Deshpande

Purdue University - Krannert School of Management

Abstract

This paper considers a dynamic lot sizing problem faced by a producer who supplies a single product to multiple customers. Characterized by their backorder costs as well as shipping costs, a customer with a high backorder cost has a greater need for the product than a customer with a low backorder cost. We show that the general problem with time-varying customer-dependent backlogging and shipping costs is NP-hard in the strong sense. We then develop an efficient dynamic programming algorithm for an important instance of the problem when there is no speculative motive for backlogging. We also establish forecast horizon results for the case of stationary production and shipping costs, which help the decision maker determine a proper forecast horizon in a rolling-horizon planning process.

Keywords: Dynamic lot sizing model, dynamic programming, forecast horizon, multiple customers

JEL Classification: C61, M11

Suggested Citation

Chand, Suresh and Hsu, Vernon and Sethi, Suresh and Deshpande, Vinayak, A Dynamic Lot Size Problem with Multiple Customers: Customer-Specific Shipping and Backlogging Costs. IIE Transactions, Vol. 39, No. 11, November 2007, Available at SSRN: https://ssrn.com/abstract=1401578

Suresh Chand

Purdue University ( email )

610 Purdue Mall
West Lafayette, IN 47907
United States

Vernon Hsu

Donald G. Costello College of Business at George Mason University ( email )

Fairfax, VA 22030
United States

Suresh Sethi (Contact Author)

University of Texas at Dallas - Naveen Jindal School of Management ( email )

800 W. Campbell Road, SM30
Richardson, TX 75080-3021
United States

Vinayak Deshpande

Purdue University - Krannert School of Management ( email )

1310 Krannert Building
West Lafayette, IN 47907-1310
United States

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