Hierarchical Decomposition of Production and Capacity Investment Decisions in Stochastic Manufacturing Systems

International Transactions in Operational Research, Vol. 1, No. 4, pp. 435-451, 1994

17 Pages Posted: 15 Jan 2008 Last revised: 14 May 2019

See all articles by Suresh Sethi

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

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

Date Written: 1994

Abstract

This paper is concernced with hierarchical decisions regarding production and investment in capacity in manufacturing systems with production subject to breakdown and repair. The production capacity can be increased by investing continuously in new capacity which is available upon completion. The decision variables are the rates of production and investment in capacity. The investment rate is assumed to have an upper bound. If, as assumed, the rates of breakdown and repair of production equipment are much larger than the rate of discounting of costs, the given problem can be approximated by a simpler problem in which the stochastic production capacity is replaced by the average capacity. Asymptotically optimal controls for the given problem are constructed from nearly optimal controls of the limiting problem. In addition, we analyze the behavior of the solution as the investment rate is allowed to become arbitrarily large.

Keywords: production, inventory, investment, capital budgeting, planning, optimization; control; systems, Markov, dynamic programming

JEL Classification: M11

Suggested Citation

Sethi, Suresh and Taksar, Michael I. and Zhang, Qing, Hierarchical Decomposition of Production and Capacity Investment Decisions in Stochastic Manufacturing Systems (1994). International Transactions in Operational Research, Vol. 1, No. 4, pp. 435-451, 1994 . Available at SSRN: https://ssrn.com/abstract=1083177

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

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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