Capacity and Production Decisions in Stochastic Manufacturing Systems: An Asymptotic Optimal Hierarchical Approach

Production and Operations Management, Vol. 1, No. 4, pp. 367-392, Fall 1992

26 Pages Posted: 12 Feb 2008

See all articles by Michael I. Taksar

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

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Abstract

We present a new paradigm of hierarchical decision making in production planning and capacity expansion problems under uncertainty. We show that under reasonable assumptions, the strategic level management can base the capacity decision on aggregated information from the shop floor, and the operational level management, given this decision, can derive a production plan for the system, without too large a loss in optimality when compared to simultaneous determination of optimal capacity and The results are obtained via an asymptotic analysis of a manufacturing system with convex costs, constant demand, and with machines subject to random breakdown and repair. The decision variables are purchase time of a new machine at a given fixed cost and production plans before and after the costs of investment, production, inventories, and backlogs. If the rate of change in machine states such as up and down is assumed to be much larger than the rate of discounting costs, one obtains a simpler limiting mean. We develop methods for constructing asymptotically optimal decisions for the original problem from the optimal decisions for the limiting problem. We obtain error estimates for these constructed decisions.

Keywords: Hierarchical Decision Making, Capacity Expansion, Production Planning, Dynamic Progrramming, Markov Processes, Near-Optimal Decisions

JEL Classification: C61,M11

Suggested Citation

Taksar, Michael I. and Zhang, Qing and Sethi, Suresh, Capacity and Production Decisions in Stochastic Manufacturing Systems: An Asymptotic Optimal Hierarchical Approach. Production and Operations Management, Vol. 1, No. 4, pp. 367-392, Fall 1992. Available at SSRN: https://ssrn.com/abstract=1092210

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/

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

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