Optimal Feedback Production Planning in a Stochastic N-machine Flowshop

Posted: 6 May 2020

See all articles by Ernst Presman

Ernst Presman

Russian Academy of Sciences (RAS)

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Qing Zhang

Department of Mathematics, University of Georgia

Date Written: 1995

Abstract

We consider a production planning problem in an N-machine flowshop subject to breakdown and repair of machines and 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 rates of production on the N machines over time to minimize the expected discounted cost of production and inventory/backlog over an infinite horizon. It is formulated as a stochastic dynamic programming problem. We show that the value function of the problem is locally Lipschitz and is a solution to a dynamic programming equation together with a certain boundary condition. We provide an interpretation of the boundary condition. We also prove a verification theorem and derive the optimal feedback control policy in terms of the directional derivatives of the value function. Finally, we obtain a deterministic optimal control problem that is equivalent to the stochastic production planning problem under consideration.

Keywords: Manufacturing systems; optimal control: stochastic jump processes; feedback control; piecewise-deterministic processes; dynamic programming: flowshops

JEL Classification: C61, M11, M20

Suggested Citation

Presman, Ernst and Sethi, Suresh and Zhang, Qing, Optimal Feedback Production Planning in a Stochastic N-machine Flowshop (1995). Available at SSRN: https://ssrn.com/abstract=3590762

Ernst Presman

Russian Academy of Sciences (RAS) ( email )

Leninsky Ave, 14
Moscow, 119991
Russia

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
98
PlumX Metrics