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...

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Bibliographic Details
Published in:Automatica (Oxford) Vol. 31; no. 9; pp. 1325 - 1332
Main Authors: Presman, Ernst, Sethi, Suresh, Zhang, Qing
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.09.1995
Subjects:
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 Access:Get full text
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Summary: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