Maintenance Optimization of Repairable Systems Under a Diffusion Approximation Scheme

In this paper we study maintenance optimization of the repairman problem. The temporal description of this problem is given by a Markov process of birth-and-death type. The maintenance consideration of this problem, considering all states, is difficult. Based on a diffusion approximation we formulat...

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Bibliographic Details
Published in:Methodology and computing in applied probability Vol. 27; no. 4; p. 87
Main Authors: Chetouani, Hassan, Limnios, Nikolaos, Shen, Jingyuan
Format: Journal Article
Language:English
Published: New York Springer US 01.12.2025
Springer Nature B.V
Subjects:
Approximation
Business and Management
Cost function
Economics
Electrical Engineering
Equilibrium
Life Sciences
Maintenance
Markov analysis
Markov processes
Mathematics and Statistics
Normal distribution
Optimization
Queuing theory
Random variables
Statistics
Diffusion approximation
Repairman problem
60J20
Maintenance optimization
90B2
60J605
ISSN:1387-5841, 1573-7713
Online Access:Get full text
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Summary:In this paper we study maintenance optimization of the repairman problem. The temporal description of this problem is given by a Markov process of birth-and-death type. The maintenance consideration of this problem, considering all states, is difficult. Based on a diffusion approximation we formulate the maintenance policy and then we optimize it in a much easier way. The associated cost includes cost for lack of repairmen, cost for busy repairmen, cost of excess of spare items, and cost of lack of spare items. Based on the limit process obtained by the diffusion approximation of the original Markov process, we optimize the maintenance by minimizing the cost function. A numerical example is given with more than one hundred states.
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ISSN:1387-5841
1573-7713
DOI:10.1007/s11009-025-10212-3