A Combined Stochastic Programming and Robust Optimization Approach for Location-Routing Problem and Solving it via Variable Neighborhood Search algorithm

The location-routing problem is one of the combined problems in the area of supply chain management that simultaneously make decisions related to location of depots and routing of the vehicles. In this paper, the single-depot capacitated location-routing problem under uncertainty is presented. The problem aims to find the optimal location of a single depot and the routing of vehicles to serve the customers when the parameters may change under different circumstances. To get closer to real-world situations, travel time of vehicles, the fixed cost of using vehicles and customers’ demand are considered as a source of uncertainty. A combined approach including robust optimization and stochastic programming was presented to deal with the uncertainty in the problem at hand. For this purpose, a mixed integer programming model is developed and a numerical example is provided to illustrate the solution procedure on the related network. To solve the problem, Variable Neighborhood Search is also proposed. The results obtained from solving sample problems using an exact and heuristic algorithm represent the acceptable performance of the proposed algorithm.