Asymptotic Optimal Controls in Stochastic Manufacturing Systems With Machine Failures Dependent on Production Rates

Stochastics and Stochastics Reports, 48, 1994, 97-121

Posted: 6 May 2020

See all articles by Suresh Sethi

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Qing Zhang

Department of Mathematics, University of Georgia

Date Written: 1994

Abstract

This paper is concerned with hierarchical control of stochastic manufacturing systems with machines whose capacity states are governed by a Markov process dependent on the rates of production. The objective is to choose production rates that minimize the total inventory/shortage and production costs over the infinite horizon. The problem is formulated as a control problem of piecewise-deterministic processes. When the rates of machine breakdown and repair are much larger than the rate of fluctuation in demand and rate of discounting of costs, we show that the original problem can be approximated by a limiting problem obtained by replacing the stochastic machine capacity by its averaged machine capacity and by appropriately modifying the cost function. Asymptotically optimal controls for the original problem are constructed by using optimal controls of the limiting problem.

Keywords: Stochastic manufacturing systems, production planning, hierarchical control, dynamic programming, viscosity solutions

JEL Classification: C61, M11, M20

Suggested Citation

Sethi, Suresh and Zhang, Qing, Asymptotic Optimal Controls in Stochastic Manufacturing Systems With Machine Failures Dependent on Production Rates (1994). Stochastics and Stochastics Reports, 48, 1994, 97-121, Available at SSRN: https://ssrn.com/abstract=3590766

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

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
80
PlumX Metrics