Profit optimisation of the multiple-vacation machine repair problem using particle swarm optimisation

This paper investigates a multiple-vacation M/M/1 warm-standby machine repair problem with an unreliable repairman. We first apply a matrix-analytic method to obtain the steady-state probabilities. Next, we construct the total expected profit per unit time and formulate an optimisation problem to find the maximum profit. The particle swarm optimisation (PSO) algorithm is implemented to determine the optimal number of warm standbys S* and the service rate μ* as well as vacation rate ν* simultaneously at the optimal maximum profit. We compare the searching results of the PSO algorithm with those of exhaustive search method to ensure the searching quality of the PSO algorithm. Sensitivity analysis with numerical illustrations is also provided.