A multi-objective and multi-level model for location-routing problem in the supply chain based on the customer’s time window

Today, logistics costs often make up a major part of large organizations’ expenses. These costs can be reduced with optimal design and its implementation in the supply chain. As a result, in present study, a two-objective mathematical location-routing model is presented, where an objective is to minimize the costs and the next is to maximize the reliability in order to deliver the goods timely to customer according to the probable time and time window. The proposed problem has two levels of distribution. The first level, which is called transportation level, points to the distribution of products from a factory to an open distribution center, and the latter is known as routing level, which is related to a part of the problem in which we deliver products from the warehouse to customers. The proposed mathematical model is solved by Epsilon-constraint and NSGA-II approaches in small and medium, and large scales problem, respectively. The present study has provided the following contributions: concurrent locating and routing in the supply chain in accordance with the customer’s time window, probable travel time in the supply chain and customer’s reliability in the supply chain. The assessment metric results indicate the proper performance of our proposed model.