Application of the NSGA-II algorithm to a multi-period inventory-redundancy allocation problem in a series-parallel system
Abstract In this paper, we formulate a mixed-integer binary non-linear programming model to study a series-parallel multi-component multi-periodic inventory-redundancy allocation problem (IRAP). This IRAP is a novel redundancy allocation problem (RAP) because components (products) are purchased under an all unit discount (AUD) policy and then installed on a series-parallel system. The total budget available for purchasing the components, the storage space, the vehicle capacities, and the total weight of the system are limited. Moreover, a penalty function is used to penalize infeasible solutions, generated randomly. The overall goal is to find the optimal number of the components purchased for each subsystem so that the total costs including ordering cost, holding costs, and purchasing cost are minimized while the system reliability is maximized, simultaneously. A non-dominated sorting genetic algorithm-II (NSGA-II), a multi-objective particle swarm optimization (MOPSO), and a multi-objective harmony search (MOHS) algorithm are applied to obtain the optimal Pareto solutions. While no benchmark is available in the literature, some numerical examples are generated randomly to evaluate the results of NSGA-II on the proposed IRAP. The results are in favor of NSGA-II. Highlights An inventory control system employing an all-unit discount policy is considered in the proposed model. The proposed model considers limited total budget, storage space, transportation capacity, and total weight. Moreover, a penalty function is used to penalize infeasible solutions. The overall goal is to find the optimal number components purchased for each subsystem so that the total costs including ordering cost, holding cost and purchasing cost are minimized and the system reliability are maximized, simultaneously. A NSGA-II algorithm is derived where a multi-objective particle swarm optimization and a multi-objective harmony search algorithm are used to evaluate the NSGA-II results.
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