JOINT OPTIMIZATION OF REDUNDANCY AND MAINTENANCE STAFF ALLOCATION FOR MULTI-STATE SERIES-PARALLEL SYSTEMS

Multi-state system (MSS), as a kind of complex system consisting of elements with different performance levels, widely exists in engineering practices. In this paper, redundancy and maintenance staff allocation problems for repairable MSS with series-parallel configuration are considered simultaneously. The traditional redundancy allocation problem (RAP) for MSS always assumes that maintenance resources are unlimited. However in many practical situations, maintenance resources are limited due to the budget and/or time. To maximize the system availability under a certain demand, there are two feasible ways: (1) designing an optimal system configuration with available elements, and (2) allocating more maintenance staffs to reduce waiting time for repair. With the assistance of Markov queue model, the availabilities of identical version elements with the pre-assigned number of maintenance staffs can be evaluated. The universal generation function (UGF) is employed to assess the availability of entire MSS under a certain demand. Two optimization formulas considering the limited maintenance resources are proposed. One regards the limitation of maintenance resources as a constraint, and the other considers minimizing the total system cost including both the system elements and maintenance staff fees. The system redundancy and staffs allocation strategies are jointly optimized under required availability. A numerical case is presented to illustrate the efficiency of the proposed models. The Firefly Algorithm (FA), which is a recently developed metaheuristic optimization algorithm, is employed to seek the global optimal strategy.