A comparison between simultaneous and hierarchical approaches to solve a multi-objective location-routing problem

This paper deals with a multi-objective location-routing problem (MO-LRP) and follows the idea of sectorization to simplify the solution approaches. The MO-LRP consists of sectorization, sub-sectorization, and routing sub-problems. In the sectorization sub-problem, a subset of potential distribution centres (DCs) is opened and a subset of customers is assigned to each of them. Each DC and the customers assigned to it form a sector. Afterward, in the sub-sectorization stage customers of each DC are divided into different sub-sector. Then, in the routing sub-problem, a route is determined and a vehicle is assigned to meet demands. To solve the problem, we design two approaches, which adapt the sectorization, sub-sectorization and routing sub-problems with the non-dominated sorting genetic algorithm (NSGA-II) in two different manners. In the first approach, NSGA-II is used to find non-dominated solutions for all sub-problems, simultaneously. The second one is similar to the first one but it has a hierarchical structure, such that the routing sub-problem is solved with a solver for binary integer programming in MATLAB optimization toolbox after solving sectorization and sub-sectorization sub-problem with NSGA-II. Four benchmarks are used and based on a comparison between the obtained results it is shown that the first approach finds more non-dominated solutions. Therefore, it is concluded that the simultaneous approach is more effective than the hierarchical approach for the defined problem in terms of finding more non-dominated solutions.