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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Vydáno v:Automatica (Oxford) Ročník 31; číslo 9; s. 1325 - 1332
Hlavní autoři: Presman, Ernst, Sethi, Suresh, Zhang, Qing
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Ltd 01.09.1995
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ISSN:0005-1098, 1873-2836
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Abstract 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.
AbstractList 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.
Author Sethi, Suresh
Zhang, Qing
Presman, Ernst
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  givenname: Qing
  surname: Zhang
  fullname: Zhang, Qing
  organization: Department of Mathematics, University of Georgia, Athens, GA 30602, U.S.A
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Issue 9
Keywords stochastic jump processes
flowshops
feedback control
dynamic programming
optimal control
piecewise-deterministic processes
Manufacturing systems
Language English
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Snippet We consider a production planning problem in an N-machine flowshop subject to breakdown and repair of machines and to non-negativity constraints on...
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SubjectTerms dynamic programming
feedback control
flowshops
Manufacturing systems
optimal control
piecewise-deterministic processes
stochastic jump processes
Title Optimal feedback production planning in a stochastic N-machine flowshop
URI https://dx.doi.org/10.1016/0005-1098(95)00040-4
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