Optimal feedback production planning in a stochastic N-machine flowshop

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 product...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Automatica (Oxford) Jg. 31; H. 9; S. 1325 - 1332
Hauptverfasser: Presman, Ernst, Sethi, Suresh, Zhang, Qing
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Ltd 01.09.1995
Schlagworte:
dynamic programming
feedback control
flowshops
Manufacturing systems
optimal control
piecewise-deterministic processes
stochastic jump processes
stochastic jump processes
flowshops
feedback control
dynamic programming
optimal control
piecewise-deterministic processes
Manufacturing systems
ISSN:0005-1098, 1873-2836
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung: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.
ISSN:0005-1098
1873-2836
DOI:10.1016/0005-1098(95)00040-4