Turnpike Sets and Their Analysis in Stochastic Production Planning Problems

Mathematics of Operations Research, Vol. 17, No. 4, pp. 932-950, 1992

19 Pages Posted: 26 Feb 2008 Last revised: 7 Nov 2015

See all articles by Suresh Sethi

Suresh Sethi

University of Texas at Dallas - Naveen Jindal School of Management

Halil Mete Soner

Koc University - College of Administrative Sciences and Economics

Qing Zhang

University of Georgia - Department of Mathematics

Jiong Jiang

Independent

Date Written: 1992

Abstract

This paper considers optimal infinite horizon stochastic production planning problems with capacity and demand to be finite state Markov chains. The existence of the optimal feedback control is shown with the aid of viscosity solutions to the dynamic programming equations. Turnpike set concepts are introduced to characterize the optimal inventory levels. It is proved that the turnpike set is an attractor set for the optimal trajectories provided that the capacity is assumed to be fixed at a level exceeding the maximum possible demand. Conditions under which the optimal trajectories enter the convex closure of the set in finite time are given. The structure of turnpike sets is analyzed. Last but not least, it is shown that the turnpike sets exhibit a monotone property with respect to capacity and demand. It turns out that the monotonicity property helps in solving the optimal production problem numerically, and in some cases, analytically.

Keywords: production planning, stochastic optimal control, viscosity solutions, stocahstic manufacturing systems, threshold policy, turnpike sets, turnpike theory, hierarchical controls, asymptotic optimality

JEL Classification: C, C61, M11

Suggested Citation

Sethi, Suresh and Soner, Halil Mete and Zhang, Qing and Jiang, Jiong, Turnpike Sets and Their Analysis in Stochastic Production Planning Problems (1992). Mathematics of Operations Research, Vol. 17, No. 4, pp. 932-950, 1992. Available at SSRN: https://ssrn.com/abstract=1097464

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

Halil Mete Soner

Koc University - College of Administrative Sciences and Economics ( email )

Rumelifeneri Yolu
Sariyer 80910, Istanbul
Turkey

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/

Jiong Jiang

Independent ( email )

No Address Available

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