Hierarchical Controls in Stochastic Manufacturing Systems with Convex Costs

Journal of Optimizztion Theory and Applications, Vol. 80, No. 2, pp. 299-317, FEBRUARY 1994

19 Pages Posted: 21 Jun 2009 Last revised: 25 Jul 2017

See all articles by Suresh Sethi

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Qing Zhang

University of Georgia - Department of Mathematics

Xun Yu Zhou

University of Toronto

Date Written: February 1994

Abstract

This paper presents an extension of earlier research on heirarchical control of stochastic manufacturing systems with linear production costs. A new method is introduced to construct asymptotically optimal open-loop and feedback controls for manufacturing systems in which the rates of machine breakdown and repair are much larger than the rate of fluctuation in demand and rate of discounting of cost. This new approach allows us to carry out an asymptotic analysis on manufacturing systems with convex inventory/backlog and production costs as well as obtain error bound estimates for constructed open loop controls. Under appropriate conditions, an asymptotically optimal Lipschitz feedback control law is obtained.

Keywords: Stochastic manufacturing systems, convex production planning, hierarchical control, dynamic programming, viscosity solutions, convergence rates, error bounds

JEL Classification: M11, C61

Suggested Citation

Sethi, Suresh and Zhang, Qing and Yu Zhou, Xun, Hierarchical Controls in Stochastic Manufacturing Systems with Convex Costs (February 1994). Journal of Optimizztion Theory and Applications, Vol. 80, No. 2, pp. 299-317, FEBRUARY 1994. Available at SSRN: https://ssrn.com/abstract=1421450

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/

Xun Yu Zhou

University of Toronto

Toronto, Ontario M5S 3G8
Canada

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