Cost Optimization of Machine Repair Problem with Differentiated Retrials and Repair-Facility Breakdown under ACFP

A double-orbit retrial (DOR) machine repair problem under Markovian assumptions is investigated, incorporating an admission control F -policy (ACFP) and an unreliable repair-facility to serve incoming failed machines. The system has a finite capacity K and a limited machine population M , with K ≤ M . Incoming failed machines that find the repair-facility busy are directed to one of two distinct retrial orbits, each governed by a distinct retrial intensity. The ACFP helps in managing congestion from failed machines in queueing systems by halting new arrivals when the system is saturated and resuming only when failures in repair-facility falls below a predefined threshold level, F . A two-stage restoration process is available for repair-facility breakdown, allowing recovery in the first stage or, if needed, in the second. The model also incorporates a feedback mechanism wherein inadequately serviced machines re-enter the system by joining the queue for another service attempt. The system’s behavior is examined by formulating Chapman-Kolmogorov difference equations, which are then solved recursively to determine steady-state probabilities for all system states. These probabilities form the basis for evaluating the model’s key performance measures. The system’s total operational cost is constructed using relevant parameters and minimized via the quasi-Newton method to determine optimal service rates. Numerical experiments analyze the impact of parameter changes on the system’s performance measures. The practical justification of developed model is illustrated through its application to a hydraulic cylinder repair workshop, where machines like gantry cranes and launching gantries arrive for and receive service under the proposed model.