A Mathematical Model of Hub Location for War Equipment under Uncertainty Using Meta-Heuristic Algorithms

By providing timely transportation and dispatch of raw materials and finished goods, freight transport plays an essential role in industries, commercial activities, and trade war industries. It also has a significant impact on the overall performance of associated organizations and the ultimate costs of their products. Therefore, freight transport providers are under pressure to decrease costs and increase their service levels and should overcome these pressures by redesigning and improving their logistics processes on strategic, tactical, and operational levels. In this research, a multi-objective model is proposed for hub location in the field of war equipment under uncertainty. The first objective is to minimize costs, the second objective is to maximize the fulfillment of demands, and the third objective is to minimize congestion on the routes. Taking into account the parameters in the state of uncertainty, the mathematical model is modeled in a robust state and a robust counterpart model of the problem is proposed. In order to solve the problem on a small scale, the exact epsilon constraint method is used in GAMS software. Also, meta-heuristic approaches of grey wolf optimizer (GWO) and non-dominated sorting genetic algorithm (NSGA-II) are used to solve the model in medium and large dimensions. Next, the solution time of two algorithms was compared. 10 numerical experiments with different dimensions were designed and implemented through GWO and NSGAII algorithms. The results showed that the time to solve the GWO problem is less than the other algorithm. Finally, proper performance indicators are used to compare the performance of the used algorithms, and as a result of solving several numerical examples and calculating their performance indicator, it is concluded that the GWO algorithm has a better performance in solving the model.