Multi-objective optimization of a mixture inventory system using a MOPSO-TOPSIS hybrid approach

This paper studies a multi-objective mixture inventory problem for a pharmaceutical distributor. The work starts with a discussion of a mixture inventory model and three objectives, namely the minimization of: 1) ordering and holding costs, 2) number of units that stockout and 3) frequency of stockout occasions. Multi-objective particle swarm optimization (MOPSO) is used to determine the non-dominated solutions and generate Pareto curves for the inventory system. Two variants of MOPSO are proposed, based on the selection of inertia weight. The performance of the proposed MOPSO algorithms is evaluated in comparison with two robust algorithms like non-dominated sorting genetic algorithm II (NSGA-II) and multi-objective cuckoo search (MOCS). The metrics that are used for the performance measurement of the algorithms are error ratio, spacing and maximum spread. Furthermore, the technique of order preference by similarity to ideal solution (TOPSIS) is used to rank the non-dominated solutions and determine the best compromise solution among them. A factorial analysis develops the linear regression expressions of optimal cost, service level measures, lot size and safety stock factor for practitioners. Lastly, the results of the regression equations are compared using a MOPSO-TOPSIS approach and the validity of the developed equations are checked.