Multi-objective Location and Routing Problem: A Review

Context: The location and routing problem is one of the main issues in logistics and operations research oriented to minimize the system's total costs. However, in the supply chain management trend towards sustainability, most decisions introduce the optimization of several objectives simultaneously, including economic, social, and environmental perspectives, from which the multi-objective location and routing problem arises.Method: This study reviews 99 scientific articles about the multi-objective location and routing problem published between 1989 and 2022 in Scopus and Web of Science databases. The papers are selected according to specific criteria and classified based on their application.Results: This paper describes the most important characteristics of each application of the multi-objective location and routing problem in the literature. It reviews the articles according to their study objectives and solution methods to identify future research opportunities.Conclusions: First, most papers on the multi-objective location and routing problem have studied waste management, relief distribution, perishable products, green location and routing problems, cold chain, and beverage distribution. Cost minimization is the most implemented optimization objective, in combination with other goals: risk minimization, environmental impact, time minimization, customer satisfaction maximization, workload balance, and route reliability. Additionally, the problem is solved using exact and approximate multi-objective methods, with evolutionary algorithms being the most suitable for complex models. Finally, current research is oriented toward developing models under uncertainty and stochastic problems, multiple periods, time windows, multiple echelons, and heterogeneous vehicle fleets.