A Fully Polynomial Time Approximation Scheme for Single-Item Stochastic Lot-Sizing Problems with Discrete Demand

18 Pages Posted: 16 Feb 2006

See all articles by James B. Orlin

James B. Orlin

Massachusetts Institute of Technology (MIT) - Sloan School of Management

Nir Halman

University of Illinois at Urbana-Champaign

Diego Klabjan

University of Illinois at Urbana-Champaign - Department of Mechanical and Industrial Engineering

Mohamed Mostagir

University of Michigan, Stephen M. Ross School of Business

David Simchi-Levi

Massachusetts Institute of Technology (MIT) - School of Engineering

Date Written: January 2006

Abstract

The single-item stochastic lot-sizing problem is to find an inventory replenishment policy in the presence of a stochastic demand under periodic review and finite time horizon. The computational intractability of computing an optimal policy is widely believed and therefore approximation algorithms should be considered. To the best of our knowledge, this is the first work that develops a fully polynomial time approximation scheme for this problem. In other words, we design a tractable polynomial time algorithm that finds a policy that is arbitrarily close in the relative sense to the value of an optimal policy. In addition, we formally prove that finding an optimal policy is intractable in the standard sense.

Keywords: Inventory Replenishment Policy

Suggested Citation

Orlin, James B. and Halman, Nir and Klabjan, Diego and Mostagir, Mohamed and Simchi-Levi, David, A Fully Polynomial Time Approximation Scheme for Single-Item Stochastic Lot-Sizing Problems with Discrete Demand (January 2006). MIT Sloan Research Paper No. 4582-06, Available at SSRN: https://ssrn.com/abstract=882101 or http://dx.doi.org/10.2139/ssrn.882101

James B. Orlin (Contact Author)

Massachusetts Institute of Technology (MIT) - Sloan School of Management ( email )

E53-357
Cambridge, MA 02142
United States
617-253-6606 (Phone)
617-258-7579 (Fax)

Nir Halman

University of Illinois at Urbana-Champaign ( email )

601 E John St
Champaign, IL 61820
United States

Diego Klabjan

University of Illinois at Urbana-Champaign - Department of Mechanical and Industrial Engineering ( email )

1206 West Green Street
Urbana, IL 61801
United States

Mohamed Mostagir

University of Michigan, Stephen M. Ross School of Business ( email )

701 Tappan Street
Ann Arbor, MI MI 48109
United States

David Simchi-Levi

Massachusetts Institute of Technology (MIT) - School of Engineering ( email )

MA
United States

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