Turnpike sets in stochastic production planning problems

S. P. Sethi; H. M. Soner; Q. Zhang; J. Jiang

doi:10.1109/cdc.1990.203664

Turnpike sets in stochastic production planning problems

S. P. Sethi, H. M. Soner, Q. Zhang, J. Jiang

Research output: Contribution to journal › Conference article › peer-review

1 Scopus citations

Abstract

Optimal infinite-horizon stochastic production planning problems with capacity and demand are considered to be finite state Markov chains. Turnpike set concepts are introduced to characterize the optimal inventory levels. It is shown 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 described, and 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.

Original language	English (US)
Pages (from-to)	590-595
Number of pages	6
Journal	Proceedings of the IEEE Conference on Decision and Control
Volume	2
DOIs	https://doi.org/10.1109/cdc.1990.203664
State	Published - 1990
Externally published	Yes
Event	Proceedings of the 29th IEEE Conference on Decision and Control Part 6 (of 6) - Honolulu, HI, USA Duration: Dec 5 1990 → Dec 7 1990

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Modeling and Simulation
Control and Optimization

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10.1109/cdc.1990.203664

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title = "Turnpike sets in stochastic production planning problems",

abstract = "Optimal infinite-horizon stochastic production planning problems with capacity and demand are considered to be finite state Markov chains. Turnpike set concepts are introduced to characterize the optimal inventory levels. It is shown 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 described, and 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.",

author = "Sethi, {S. P.} and Soner, {H. M.} and Q. Zhang and J. Jiang",

year = "1990",

doi = "10.1109/cdc.1990.203664",

language = "English (US)",

volume = "2",

pages = "590--595",

journal = "Proceedings of the IEEE Conference on Decision and Control",

issn = "0191-2216",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

note = "Proceedings of the 29th IEEE Conference on Decision and Control Part 6 (of 6) ; Conference date: 05-12-1990 Through 07-12-1990",

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TY - JOUR

T1 - Turnpike sets in stochastic production planning problems

AU - Sethi, S. P.

AU - Soner, H. M.

AU - Zhang, Q.

AU - Jiang, J.

PY - 1990

Y1 - 1990

N2 - Optimal infinite-horizon stochastic production planning problems with capacity and demand are considered to be finite state Markov chains. Turnpike set concepts are introduced to characterize the optimal inventory levels. It is shown 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 described, and 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.

AB - Optimal infinite-horizon stochastic production planning problems with capacity and demand are considered to be finite state Markov chains. Turnpike set concepts are introduced to characterize the optimal inventory levels. It is shown 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 described, and 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.

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DO - 10.1109/cdc.1990.203664

M3 - Conference article

AN - SCOPUS:0025567897

SN - 0191-2216

VL - 2

SP - 590

EP - 595

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

T2 - Proceedings of the 29th IEEE Conference on Decision and Control Part 6 (of 6)

Y2 - 5 December 1990 through 7 December 1990

ER -

Turnpike sets in stochastic production planning problems

Abstract

All Science Journal Classification (ASJC) codes

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