Producing in a Manufacturing System with Minimum Average Cost

Nonlinear Analysis, Theory, Methods & Applications, Vol. 30, No. 7. pp. 4357-4363, 1997

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

We deal with a single or parallel machine manufacturing system with convex cost of holding and backlogging and develop a new rigorous analysis to address the problem. We provide the results needed for the vanishing discount approach used for aour analysis. In particular, we show that one can go from any point in the state space to any other point in a finite time. The Hamilton-Jacobi-Bellman (HJB) equation is specified for the average cost problem and a verification theorem for optimality over the class of admissible controls is given. We show that the HJB equation has a viscosity solution, which turns out in this case to be also a classical solution.

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, Producing in a Manufacturing System with Minimum Average Cost. Nonlinear Analysis, Theory, Methods & Applications, Vol. 30, No. 7. pp. 4357-4363, 1997. Available at SSRN: https://ssrn.com/abstract=1422137

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/

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