A new integrated mathematical model for a bi-objective multi-depot location-routing problem solved by a multi-objective scatter search algorithm

The location of manufacturing facilities is one of the most important strategic decisions considered in the design of logistic systems. Another important strategic decision is the structure and management of the fleets. Most often, even if two types of problem (i.e., location of facilities and vehicle routing) have occurred in a given scenario, they have been studied and solved separately. This paper presents a new integrated mathematical model for a bi-objective multi-depot location-routing problem where the total demand served is to be maximized and the total cost, consisting of start-up of the facility, fixed and variable depots and variable delivery cost, is to be minimized. Since this type of the problem is NP-hard, a new multi-objective scatter search (MOSS) algorithm is proposed to obtain the Pareto frontier for the given problem. To validate the performance of the proposed MOSS algorithm in terms of the solution quality and diversity level, various test problems are carried out and the efficiency of this algorithm based on some comparison metrics is compared with the elite tabu search (ETS). The computational results show that the proposed MOSS outperforms the ETS, especially in large-sized problems.