A novel hybrid epsilon-constraint and NSGA-II method for bi-objective restructuring hierarchical facility location problem

Purpose A multi-objective mixed-integer linear program (MILP) model is developed to address this problem. The primary objective is to minimize the total restructuring cost, while the secondary objective aims to enhance the customer service level. To tackle the NP-hard nature of the problem, the non-dominated sorted genetic algorithm (NSGA-II) and a hybrid NSGA-II with the ɛ-constraint method are employed. The hybrid method combines the strengths of the ɛ-constraint method with NSGA-II. Various performance metrics, including the number of Pareto solutions (NPS), normalized set coverage and spacing metrics, are utilized to compare the characteristics of the non-dominated fronts obtained by NSGA-II and the hybrid methods. Design/methodology/approach The Restructuring Facility Location Problem involves the closure, resizing or opening of a group of facilities and the assignment of customers to these selected facilities. The objective is to provide the required service to customers while minimizing the overall restructuring costs. This paper introduces a novel multi-objective model for hierarchical facilities called the Multi-Objective Restructuring Hierarchical Facility Location Problem (MO-RHFLP). The model specifically includes primary- and secondary-level facilities, with the primary facility offering broad coverage. In MO-RHFLP, customers within the coverage range of the primary facility can receive service from there. Findings The results demonstrate that the NSGA-II-based method performs well in terms of normalized set coverage and spacing metrics. However, the hybrid method outperforms NSGA-II in these aspects. Additionally, the hybrid method achieves a mutation in the NPS metric. Originality/value The present study, from three perspectives, has continued the way of the previous studies in restructuring channels. First, the multi-objective problem of restructuring the bi-level network executed in this study contains both levels of the network opening, closing and resizing. Taking a different perspective, the MO-RHFLP problem is introduced through the formulation of a multi-objective MILP model. This model serves as a framework for addressing the MO-RHFLP. By developing the hybrid ɛ-constraint method with NSGA-II, we solve the proposed problem.