Cost analysis for machine repair problem under triadic policy with discouragement and multiple working vacations

This study portrays the steady-state assessment of controlling the service of two removable repairmen for a machine maintenance problem with discouragement and multiple working vacations under a triadic policy. The $L$L operating machines constitute the entire system, and it is believed that failing machines will be repaired in accordance with triadic policy and repairmen will take multiple working vacations. During the working vacation period, one repairman continues providing service and goes for another vacation as soon as queue of failed machines becomes empty. The system steady state equations are solved recursively and various performance metrics are established for constructing a system total expected cost function. Cost optimization is performed, and the optimal cost is compared using several approaches, including Particle Swarm Optimisation (PSO), the Artificial Bee Colony (ABC) algorithm, and the Genetic Algorithm (GA). The convexity behavior of the expected cost function, among choice variables with restricted region also presented graphically. Furthermore, the paper includes computational findings illustrating the impact of different parameters on the estimated optimal service rate and optimal thresholds, as well as a case study demonstrating the practical use of the designed model.