Title: Failure-prone manufacturing systems with setups: feasibility and optimality under various hypotheses about perturbations and setup interplay

Authors: Vladimir Polotski; Jean-Pierre Kenné; Ali Gharbi

Addresses: Department of Mechanical Engineering, Ecole de Technololgie Superieure, 1100 Notre Dame Street West, Montreal, Quebec, H3C 1K3, Canada ' Department of Mechanical Engineering, Ecole de Technololgie Superieure, 1100 Notre Dame Street West, Montreal, Quebec, H3C 1K3, Canada ' Department of Automated Production Engineering, Ecole de Technololgie Superieure, 1100 Notre Dame Street West, Montreal, Quebec, H3C 1K3, Canada

Abstract: A failure-prone manufacturing system producing two part types and requiring a setup for switching from one part type to another is considered. Both setup cost and time are taken into account. Various hypotheses regarding the interactions between random perturbations (failures and repairs) and setup strategies are used in the scientific literature, without clarifications provided for their relationships and possible consequences. In this paper, we close this gap and address feasibility and optimality conditions under various hypotheses. The feasibility conditions are obtained and studied analytically, and are shown to be dependent on the choice of an adopted hypothesis. This finding will prevent feasibility conditions not matching the underlying hypothesis from being applied. Optimality conditions in the form of Hamilton-Jacobi-Bellman equations are obtained and shown to be also dependent on the adopted hypothesis. A numerical example illustrating a comparison of the results obtained with the solutions of HJB equations is presented.

Keywords: failure-prone manufacturing systems; stochastic process; setup costs; setup times; optimal control; numerical methods; feasibility conditions; random perturbations; random failures; random repairs; optimality conditions.

DOI: 10.1504/IJMOR.2015.072277

International Journal of Mathematics in Operational Research, 2015 Vol.7 No.6, pp.681 - 705

Received: 01 Feb 2014
Accepted: 14 Jun 2014
Published online: 08 Oct 2015 *

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