Asymptotic Optimal Feedback Controls in Stochastic Dynamic Two-Machine Flowshops

Sethi, Suresh; Yu Zhou, Xun

Asymptotic Optimal Feedback Controls in Stochastic Dynamic Two-Machine Flowshops

RECENT ADVANCES IN CONTROL AND OPTIMIZATION OF MANUFACTURING SYSTEMS, LECTURE NOTES IN CONTROL AND INFORMATION SCIENCES, G. Yin, Q. Zhang, eds., Vol. 214, pp. 147-180, Springer-Verlag, New York, 1996

23 Pages Posted: 15 Jan 2009 Last revised: 30 Mar 2014

See all articles by Suresh Sethi

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Xun Yu Zhou

University of Toronto

Date Written: January 14, 2009

Abstract

In this paper, we treat an optimal control problem of a stochastic two-machine flowshop with machines subject to random breakdown and repair. While the problem is difficult to solve, it can be approximated by a deterministic problem when the rates of machine failure and repair become large. Furthermore, beginning with the solution of the deterministic problem, we can construct a feedback control for the stochastic flowshop that is asymptotically optimal with respect to the rates of changes in machine states. We also show that a threshold type control known also as Kanban control is asymptotically optimal in some cases and not in others.

Keywords: Production Planning, Hierarchical Controls, Stochastic Manufacturing System, Dynamic Programming, Asymptotic Optimality, Feedback Controls, Kanban policy, Inventory problems, Flowshops, Threshold-type controls

JEL Classification: C00, C61, M11

Suggested Citation: Suggested Citation

Sethi, Suresh and Yu Zhou, Xun, Asymptotic Optimal Feedback Controls in Stochastic Dynamic Two-Machine Flowshops (January 14, 2009). RECENT ADVANCES IN CONTROL AND OPTIMIZATION OF MANUFACTURING SYSTEMS, LECTURE NOTES IN CONTROL AND INFORMATION SCIENCES, G. Yin, Q. Zhang, eds., Vol. 214, pp. 147-180, Springer-Verlag, New York, 1996 , Available at SSRN: https://ssrn.com/abstract=1328056