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

Esther Frostig

doi:10.1017/S0269964800004113

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

Esther Frostig

Department of Statistics

Research output: Contribution to journal › Article › peer-review

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 λ_i and μ_jrespectively. All failure times and repair times are independent. Machine i earns c_iper 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≥ • • • ≥ c_N and c₁/λ₁≥ • • • > c_N/λ_Nthe 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 < • • - < λ_Nthen this policy maximizes, stochastically, the number of the most reliable machines at every time t.

Original language	English
Pages (from-to)	633-645
Number of pages	13
Journal	Probability in the Engineering and Informational Sciences
Volume	9
Issue number	4
DOIs	https://doi.org/10.1017/S0269964800004113
State	Published - Oct 1995

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Management Science and Operations Research
Industrial and Manufacturing Engineering

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title = "Optimal Allocation of Machines to Distinguishable Repairmen in Order to Maximize Some Reward Functions",

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 μjrespectively. All failure times and repair times are independent. Machine i earns ciper 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/λNthe 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 < • • - < λNthen this policy maximizes, stochastically, the number of the most reliable machines at every time t.",

author = "Esther Frostig",

year = "1995",

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N2 - 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 μjrespectively. All failure times and repair times are independent. Machine i earns ciper 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/λNthe 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 < • • - < λNthen this policy maximizes, stochastically, the number of the most reliable machines at every time t.

AB - 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 μjrespectively. All failure times and repair times are independent. Machine i earns ciper 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/λNthe 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 < • • - < λNthen this policy maximizes, stochastically, the number of the most reliable machines at every time t.

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

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