Design of a supply chain network for determining the optimal number of items at the inventory groups based on ABC analysis: a comparison of exact and meta-heuristic methods

One of the most applicable techniques in the inventory management field is inventory classification based on ABC analysis, a well-known method to set the items in a different group, according to their importance and values. In this paper, a bi-objective mathematical model is proposed to improve the inventory grouping based on ABC analysis. The first objective function maximizes the total net profit of the items in the central stock, and the second objective function maximizes the total net profit of items in different wards. The proposed model simultaneously optimizes the service level, the number of inventory groups, and the number of assigned items. To solve the model in small and large dimensions, two exact methods (LP-metric and ε-constraint) and two meta-heuristic methods (NSGA-II and MOPSO) are used. Then, to compare those methods in terms of efficiency, the statistical analysis besides the AHP and VIKOR techniques is implemented. The results show the superiority of the ε-constraint among the exact methods and MOPSO among meta-heuristic methods. Finally, the proposed model has been implemented in two sets of numerical examples to demonstrate its applicability.