Hierarchical Investment and Production Decisions in Stochastic Manufacturing Systems

Stochastic Theory and Adaptive Control, T. Duncan and B. Pasik-Duncan (Eds.), Springer-Verlag, New York 1992, 426-435

Posted: 6 May 2020

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

Department of Mathematics, University of Georgia

Date Written: 1992

Abstract

This paper presents 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 given constant. The production capacity can be increased by purchasing a new machine at a fixed cost at some time in the future. The control variables are a pair of a Markov time to purchase the new machine 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. Moreover, three different methods are developed for constructing controls for the original problem from the optimal controls of the limiting problem in a way which guarantees their asymptotic optimality. The convergence rate of the value function for the original problem to that of the limiting problem is also found. This helps in providing error estimates for the constructed asymptotically optimal controls.

Keywords: Original Problem, Admissible Control, Production Decision, Hierarchical Control, Asymptotic Optimality

JEL Classification: C61, M11, M20

Suggested Citation

Sethi, Suresh and Taksar, Michael I. and Zhang, Qing, Hierarchical Investment and Production Decisions in Stochastic Manufacturing Systems (1992). Stochastic Theory and Adaptive Control, T. Duncan and B. Pasik-Duncan (Eds.), Springer-Verlag, New York 1992, 426-435, Available at SSRN: https://ssrn.com/abstract=3592604

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

Department of Mathematics, University of Georgia ( email )

Athens, GA 30602-6254
United States

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Abstract Views
77
PlumX Metrics