Mathematical modeling the location routing problem considering capacity and diversity for vehicles with restriction of their movement and presentaton a solving model based on ant colony

The location routing problem (LRP) is presented with the aim of specifying both routing and location decision simultaneously and coordinate these two matters is very important in designing distribution networks of supply chain. This importance is for that the suitable coordinating between location and routing has a powerfuul affect on supply chain performance in distribution systems and also can improve it’s efficiency indexes. Although for simplifying، these two matters are usually analyzed and solved in two separated phase، but this would cause to lost the ideal benefit and global optimum solution. In this paper، the routing and location problem with considering real word conditions and restrictions like diversity of vehicles and restrictions of some vehicles movement in specified route are investigated concurrently. After presenting summery of previous research، we investigate the problem that mentioned earlier and relevant variables and parameters will be declared. Then mathematical model will be extended. In addition، mathematical model with modeling software GAMS will be implemented. With assuming this problem is kind of NP-hard problem، thus we solve this problem in small scale. In order to solve the considered problem in larg scale، a model will be presented based on ant colony. So with our specific parameters، diverse testing problems will be designed and outcome of these problems will be analyzed to show the algorithm efficiency.