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Optimal Allocation of Machines to Distinguishable Repairmen in Order to Maximize Some Reward Functions

Published online by Cambridge University Press:  27 July 2009

Esther Frostig
Esther Frostig
Affiliation:
Department of Statistics, University of Haifa, Mount Carmel, Haifa, Israel, 31905
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Abstract

We consider N unreliable machines that are maintained by M repairmen. The time until failure of machine i, and its repair by repairman j, are exponentially distributed random variable with parameters λi, and μj, respectively. All failure times and repair times are independent. Machine i earns ci, per unit time, while it is working. We wish to maximize the expected total discounted reward. It is shown that when the following conditions are satisfied — c1 ≥ … ≥ cN and c1/λ1≥…≥cN/λN, the policy that assigns the fastest repairman to the machine with the lowest index is optimal. Moreover, it is shown that when the second condition is replaced by λ≤ … ≤λN, then this policy maximizes, stochastically, the number of the most reliable machines at every time t.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 9 , Issue 4 , October 1995 , pp. 633 - 645
Copyright
Copyright © Cambridge University Press 1995

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