Modeling the split delivery open location routing problem and solving it by simulated annealing

Location-routing problem is one of the most challenging problems in supply chain management. In real world، many companies hire vehicles for servicing demands of customers، so these vehicles do not return to these companies after ending services. On the other hand، managers are constantly faced with the problem of whether serving each costumer’s demand by one vehicle will result in higher benefits or delivering their demands by more than one vehicle will lead to increased profits. Therefore، in response to this challenge and in order to get closer to the real world، a new problem which is called split delivery open location-routing problem is modeled in this study. Since the problem is a NP-Hard، Tabu search and simulated annealing algorithms are used for solving it. The mathematical model is run by cplex10. 1 software for the small size instances. In addition، in order to improve the proposed solution algorithms، a heuristic algorithm for generating suitable initial solution is presented. Finally، after generating the new experimental instances and tuning parameters of the proposed algorithms، the numerical results of the problem solving by cplex10. 1 software and the suggested algorithm are analyzed. The results show the efficiency of the two algorithms and superiority of simulated annealing algorithm over tabu search algorithm. The results also indicate that considering the assumption of split delivery lead to final cost reduction، especially when the demand variance is relatively small and the mean is greater than half the vehicle capacity and less than three quarters of the vehicle capacity.