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The focus of this paper is the analysis of the constraint on the repair resources caused by breakdowns of components in large systems. The study has been conducted by creating a very efficient discrete-event simulator, based on a min-heap data structure, for determining the probability of constraint on the repair resources.In finding the right balance between the number of repairers and salary costs, an exact optimisation algorithm has been proposed for the first time. The algorithm determines the optimal number of repairers which guarantees that the probability of constraint on the repair resources will not exceed an acceptable tolerable level. In addition, an exact optimisation algorithm has been proposed for the first time, for determining the maximum size of the system that can be serviced by a specified number of repairers so that the probability of constraint on the repair resources remains below a specified tolerable level. Unlike heuristic optimisation algorithms, the proposed algorithms are exact and always guarantee optimal solutions.The presented results are of significant importance to operators of computer networks, production systems, transportation networks, water distribution systems, electrical distribution networks etc. They are a solid basis for management decisions regarding the optimal number of maintenance personnel needed to service the breakdowns in large systems. Increasing the number of repairers beyond the optimal level leads to high salary costs while reducing the number of repairers below the optimal number leads to a poor quality of service.

Constraint on Repair Resources, Optimal Number of Repairers and Optimal Size of a Serviced System