Abstract
This paper investigates the M/M/1 warm-standby machine repair problem with multiple vacations and working breakdowns. 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 optimization problem to find the maximum profit. The particle swarm optimization (PSO) algorithm is implemented to determine the optimal number of warm standbys and two variable service rates simultaneously at the optimal maximum profit. We compare the searching results of the PSO algorithm with those of Genetic algorithm (GA) and Exhaustive Search Method (ESM) to ensure the superior searching quality of the PSO algorithm. Sensitivity analysis with numerical illustrations is also provided to improve the design quality of system engineers.
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