Optimal Feedback Production Planning in a Stochastic Two-Machine Flowshop

European Journal of Operational Research, Vol. 73, No. 2, pp. 331-345, March 1994

Posted: 8 Apr 2008 Last revised: 31 Jan 2019

See all articles by Sheldon Lou

Sheldon Lou

Independent

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Qing Zhang

University of Georgia - Department of Mathematics

Date Written: 1994

Abstract

In this paper, we consider a production planning problem in a two-machine flowshop subject to breakdown and repair of machines and subject to non-negativity constraints on work-in-process. The machine capacities and demand processes are assumed to be finite state Markov chains. The problem is to choose the rate of production over time so as to minimize the expected discounted cost of production and inventory/backlog over an infinite horizon. The problem is formulatred as a stochastic dynamic programming problem. It is shown that the value function of the problem is locally Lipschitz and is a viscosity solution to the dynamic programming equation together with certain boundary conditions. Optimal feedback control policies are obtained in terms of the `partial derivatives' of the value function. It is shown that the derived control policy is feasible on the boundary of the state space. The results establish the theoretical framework within which further analyses and/or numerical solutions of the problem can be attempted.

Keywords: Production planning; Dynamic programming; Viscosity solutions; State constraints, feedback controls, optimal control theory

JEL Classification: M11, C61

Suggested Citation

Lou, Sheldon and Sethi, Suresh and Zhang, Qing, Optimal Feedback Production Planning in a Stochastic Two-Machine Flowshop (1994). European Journal of Operational Research, Vol. 73, No. 2, pp. 331-345, March 1994. Available at SSRN: https://ssrn.com/abstract=1117280

Sheldon Lou

Independent ( email )

No Address Available

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

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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