Hierarchical decision making in production and repair/replacement planning with imperfect repairs under uncertainties |
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Authors: | FI Dehayem Nodem JP Kenne A Gharbi |
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Institution: | 1. Mechanical Engineering Department, Production Technologies Integration Laboratory, École de Technologie Supérieure, 1100 Notre Dame Street West, Montréal, Que., Canada H3C 1K3;2. Automated Production Engineering Department, Production System Design and Control Laboratory, École de Technologie Supérieure, 1100 Notre Dame Street West, Montréal, Que., Canada H3C 1K3 |
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Abstract: | In this paper, we analyse an optimal production, repair and replacement problem for a manufacturing system subject to random machine breakdowns. The system produces parts, and upon machine breakdown, either an imperfect repair is undertaken or the machine is replaced with a new identical one. The decision variables of the system are the production rate and the repair/replacement policy. The objective of the control problem is to find decision variables that minimize total incurred costs over an infinite planning horizon. Firstly, a hierarchical decision making approach, based on a semi-Markov decision model (SMDM), is used to determine the optimal repair and replacement policy. Secondly, the production rate is determined, given the obtained repair and replacement policy. Optimality conditions are given and numerical methods are used to solve them and to determine the control policy. We show that the number of parts to hold in inventory in order to hedge against breakdowns must be readjusted to a higher level as the number of breakdowns increases or as the machine ages. We go from the traditional policy with only one high threshold level to a policy with several threshold levels, which depend on the number of breakdowns. Numerical examples and sensitivity analyses are presented to illustrate the usefulness of the proposed approach. |
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Keywords: | Manufacturing systems Numerical methods Optimal control Production planning Imperfect repairs Damage failures Replacement |
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