A Bi-Objective Mathematical Programming Model for a Maximal Covering Hub Location Problem Under Uncertainty

Properly locating these facilities is a substantial factor in the success of the logistics systems. In this paper, a bi-objective mathematical model for a maximal covering hub location problem is presented to minimize time and environmental risks. The Goal Attainment method was employed to solve the small-sized problems for model validation. Since the problem is NP-Hard, the Multi-Objective Imperialist Competitive Algorithm (MOICA) meta-heuristic algorithm was exploited for solving the medium and large-sized problems. The performance of MOICA was compared with the performance of the Goal Attainment method and the Multi-Objective Particle Swarm Optimization (MOPSO) algorithm to validate the proposed model and solution approach. This paper can direct the logistics companies to reduce the cost, time, and environmental effects of their transportation networks. In addition, this research can optimize energy consumption in the transportation sector for the continuation of low-cost services and reduce fuel consumption, which leads to reducing environmental pollution.