Multi-commodity Location-routing Problem with Vehicle Accessible Time and Maximum Capacity Constraints

Distribution and transportation system design is one of the most important problems faced by distribution companies. In recent years, two major problems in distribution and transportation networks design i.e. distribution centers location and vehicle routing are considered simultaneously, so location-routing problem (LRP) has been created. Since LRP is composed of two NP-hard problems, it is NP-hard too. In this research, in order to actualize problem, more constraints have been considered, therefore there are multiple commodities in distribution network and vehicles are capacitated and time-constrained. The respected mathematical model is proposed and then due to problem’s magnitude, only small instances are generated and solved by LINGO 8.0.