Optimal Production Planning in a Stochastic Manufacturing System with Long-Run Average Cost

Journql of Optimization Theory and Applications, Vol. 92, No. 1, pp. 161-188, January 1997

28 Pages Posted: 21 Jun 2009 Last revised: 31 Jan 2019

See all articles by Suresh Sethi

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Wulin Suo

Smith School of Business

Michael I. Taksar

University of Missouri at Columbia - Department of Mathematics (Deceased) ; State University of New York (SUNY), Stony Brook, College of Engineering and Applied Sciences, Department of Applied Mathematics and Statistics (Deceased)

Qing Zhang

University of Georgia - Department of Mathematics

Abstract

This paper is concerned with the optimal production planning in a dynamic stochastic manufacturing system consisting of a single machine that is failure prone and facing a constant demand. The objective is to choose the rate of production over time in order to minimize the long-run average cost of production and surplus. The analysis proceeds with a study of the corresponding problem with a discounted cost. It is shown using the vanishing discount approach that the Hamilton-Jacobi-Bellman equation for the average cost problem has a solution giving rise to the minimal average cost and the so-called potential function. The result helps in establishing a verification theorem. Finally, the optimal control policy is specified in terms of the potential function.

Keywords: Production planning, stochastic dynamic programming, vanishing discount approach, optimal control, long-run average cost

JEL Classification: M11, C61

Suggested Citation

Sethi, Suresh and Suo, Wulin and Taksar, Michael I. and Zhang, Qing, Optimal Production Planning in a Stochastic Manufacturing System with Long-Run Average Cost. Journql of Optimization Theory and Applications, Vol. 92, No. 1, pp. 161-188, January 1997. Available at SSRN: https://ssrn.com/abstract=1421488

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

Wulin Suo

Smith School of Business ( email )

Smith School of Business - Queen's University
143 Union Street
Kingston, Ontario K7L 3N6
Canada

Michael I. Taksar

University of Missouri at Columbia - Department of Mathematics (Deceased)

State University of New York (SUNY), Stony Brook, College of Engineering and Applied Sciences, Department of Applied Mathematics and Statistics (Deceased)

Qing Zhang

University of Georgia - Department of Mathematics ( email )

Athens, GA 30602
United States
(706) 542-2616 (Phone)
(706) 542-2573 (Fax)

HOME PAGE: http://www.math.uga.edu/~qingz/

Register to save articles to
your library

Register

Paper statistics

Downloads
1
Abstract Views
422
PlumX Metrics