Multi-objective inventory planning using MOPSO and TOPSIS

One of the main characteristics of today's business tends to vary often. Under such environment, many decisions should be carefully pondered over from relevant aspects which are usually conflicting. Hence, inventory planning problems, which address how much and when to order what customers need at the least relevant cost while maintaining a desirable service level expected by customers, could be recast into a multi-objective optimization problem (MOOP). In a MOOP there are normally infinite numbers of optimal solutions in the Pareto front due to the conflicts among objectives. Unfortunately, most multi-objective inventory models have been solved by aggregation methods through a linear combination of specific weights or only one objective was optimized and the others were turned into constraints. Therefore, the challenges decision makers face are not only modeling the problem in a multi-objective context, but also the effort dedicated to build the Pareto front of MOOPs. This paper first employs the multi-objective particle swarm optimization (MOPSO) algorithm to generate the non-dominated solutions of a reorder point and order size system. A ranking method called technique for order preference by similarity to ideal solution (TOPSIS) is then used to sort the non-dominated solutions by the preference of decision makers. That is, a two-stage multi-criteria decision framework which consists of MOPSO and TOPSIS is presented to find out a compromise solution for decision makers. By varying the weights of various criteria, including minimization of the annual expected total relevant cost, minimization of the annual expected frequency of stock-out occasions, and minimization of the annual expected number of stock-outs, managers can determine the order size and safety stock simultaneously which fits their preference under different situations. (C) 2007 Elsevier Ltd. All rights reserved.