Hierarchical Capacity Expansion and Production Planning Decisions in Stochastic Manufacturing Systems

Journal of Operations Management, Vol. 12, No. 3-4, pp. 331-352, June 1995

22 Pages Posted: 19 Feb 2008 Last revised: 31 Jan 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: June 1, 1995

Abstract

We present an approach 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 shopfloor, 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 production decisions.

The results are obtained via an asymptotic analysis of hierarchical investment and production decisions in a manufacturing system with machines subject to breakdown and repair. The demand facing the system is assumed to be a deterministic monotone increasing function. The production capacity can be increased by purchasing a finite number of new machines over time. The control variables are a sequence of purchasing times and a production plan. The rate of change in machine states is assumed to be much larger than the rate of discounting of costs. This gives rise to a limiting problem in which the stochastic machine availability is replaced by the equilibrium mean availability. The value function for the original problem converges to the value function of the limiting problem. Three different methods are developed for constructing decisions for the original problem from the optimal solution of the limiting problem in a way which guarantees the asymptotic optimality of constructed decisions. Finally, it is shown that as the number of machine that could be purchased tends to infinity, the problem approximates the corresponding problem with no limit on number of machine purchases.

Keywords: Stochastic manufacturing systems, Hierarchical decisions, Capacity expansion,Production planning, Dynamic programming,Asymptotic optimality, Markov process, Singular perturbations, Near optimality, Strategic decisions, Operationa decisions, Decentralization

JEL Classification: C61, M11

Suggested Citation

Sethi, Suresh and Taksar, Michael I. and Zhang, Qing, Hierarchical Capacity Expansion and Production Planning Decisions in Stochastic Manufacturing Systems (June 1, 1995). Journal of Operations Management, Vol. 12, No. 3-4, pp. 331-352, June 1995. Available at SSRN: https://ssrn.com/abstract=1094597

Register