The multi-depot capacitated location-routing problem with fuzzy travel times

This paper addresses the fuzzy version of Capacitated Location Routing Problem (CLRP). The proposed CLRP is defined considering opening costs for depots, limited capacities of vehicles and a set of customers with known demands. There are some potential nodes to locate depots, fuzzy travel times between nodes, and also a time window to meet the demand of each customer. Although there exists several papers, manuscripts and technical reports in the literature concerning Location Routing Problem (LRP) extensions and solution procedures, most of them assume the variables to be crisp. In this paper, we present a multi-depot capacitated LRP (MDCLRP) in which travel time between two nodes is a fuzzy variable. A simulation-embedded Simulated Annealing (SA) procedure is proposed in order to solve the problem. The proposed framework is tested using a standard test problem of MDCLRP and results are analyzed and justified. This numerical example shows that the proposed method is robust and could be used in real world problems.