a hybrid meta-heuristic approach for the capacitated location-routing problem with hard time windows

the capacitated location-routing problem (clrp) is a new research area in logistics and distribution management. this problem combines two difficult problems: the facility location problem (flp) and vehicle routing problem (vrp). the goal of the clrp is to open a subset of depots, assign the customers into open facilities, and then design vehicle tours in order to minimize the total cost. the time windows constraint has numerous real-life applications, however there are little attention to this fact in the clrp. this paper, considers the clrp with hard time windows (clrphtw). at first, a mixed integer linear programming (milp) formulations for the clrphtw is presented, then a meta-heuristic approach based on variable neighborhood search for solving the clrphtw is proposed. in order to evaluate the performance of the suggested method, this framework is tested on a set of instances. the experimental results show the effectiveness of the proposed approach.