Robust production and maintenance planning in stochastic manufacturing systems

Boukas, El‐Kébir; Zhang, Q.; Yin, Gang

doi:10.1109/9.388692

Cited by 93 publications

(30 citation statements)

References 15 publications

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“…[4,5,6,7,9,10,19,20,21,22]. Our result differs, however, from the ones obtained in the references above and it can be regarded as an extension of the averaging technique developed for deterministic singularly perturbed optimal control problems (see, e.g.…”

Section: Introductioncontrasting

confidence: 55%

On asymptotic optimization of a class of nonlinear stochastic hybrid systems

Shi

Altman

Gaitsgory

1998

Mathematical Methods of Operations Research

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Abstract:We consider the problem of control for continuous time stochastic hybrid systems in finite time horizon. The systems considered are nonlinear: the state evolution is a nonlinear function of both the control and the state. The control parameters change at discrete times according to an underlying controlled Markov chain which has finite state and action spaces. The objective is to design a controller which would minimize an expected nonlinear cost of the state trajectory. We show using an averaging procedure, that the above minimization problem can be approximated by the solution of some deterministic optimal control problem. This paper generalizes our previous results obtained for systems whose state evolution is linear in the control.

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Section: Introductioncontrasting

confidence: 55%

On asymptotic optimization of a class of nonlinear stochastic hybrid systems

Shi

Altman

Gaitsgory

1998

Mathematical Methods of Operations Research

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“…Recent control models for maintenance under uncertainty include the works of Boukas and his colleagues (Boukas and Haurie 1990, Boukas et al 1995, Boukas and Liu 2001, who made use of Davis's (1984Davis's ( , 1993) piecewise deterministic Markov process and Sethi and Zhang (1994). In the earlier models of Boukas and his colleagues, transition probabilities (to failure) of their continuous-time, finite-state Markov chains depended directly on the age of the machine as a continuous variable.…”

Section: Introductionmentioning

confidence: 99%

Replacement Decisions with Maintenance Under Uncertainty: An Imbedded Optimal Control Model

Dogramaci

Fraiman

2004

Operations Research

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How should a manager make replacement decisions for a chain of machines over time if each is maintained by an optimal control model addressing uncertainty of machine breakdowns? A network representation of the problem involves arcs with interdependent costs. A solution algorithm is presented and replacement considerations under technological change are incorporated into a well-known optimal control model for maintenance under uncertainty (that of Kamien and Schwartz 1971). The method is illustrated by an example.

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“…For further details on this concept, we refer the reader to the age dependent hedging point concept presented by Boukas et al (1995b), Kenne et al (1997) and Kenne and Gharbi (2000). For large scale FMS, the derivation of suboptimal policies based on this concept seems to be difficult due to the computation of the threshold levels.…”

Section: Sommairementioning

confidence: 99%

Hierarchical control of production and maintenance rates in manufacturing systems

Kenné

Boukas

2003

Journal of Quality in Maintenance Engineering

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SOMMAIRELes systèmes de production sont en général constitués de plusieurs machines interconnectées qui produisent simultanément plusieurs types de pièces. Ces machines sont sujettes à des pannes et réparations aléatoires. La dynamique des pannes de ces machines dépend de leurs âges et leur disponibilité dépend des stratégies de maintenance adoptées. Dans ce contexte, le problème de planification de la production et de la maintenance de ces types de systèmes de production peut être formulé comme un HIERARCHICAL CONTROL OF PRODUCTION AND MAINTENANCE RATES IN MANUFACTURING SYSTEMS JEAN-PIERRE KENNE EL-KÉBIR BOUKAS ABSTRACTThis paper deals with the production and preventive maintenance planning control problem for a multi-machine flexible manufacturing system (FMS). A two-level hierarchical control model is developed according to the discrepancy between the time scale of the discounting cost event and the one of the machines states process. The proposed model extends the classical singular perturbation approach by considering age dependent machines failure rates and controlling both production and preventive maintenance rates. We replace the stochastic optimal control problem by a deterministic control problem called limiting control problem. With this approach, we compute an age dependent near-optimal control policy of the stochastic initial control problem from the optimal solution of the equivalent limiting control problem. A numerical example is used to illustrate the procedure and to show the reduction of the control problem size.

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Robust production and maintenance planning in stochastic manufacturing systems

Cited by 93 publications

References 15 publications

On asymptotic optimization of a class of nonlinear stochastic hybrid systems

On asymptotic optimization of a class of nonlinear stochastic hybrid systems

Replacement Decisions with Maintenance Under Uncertainty: An Imbedded Optimal Control Model

Hierarchical control of production and maintenance rates in manufacturing systems

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