Mathematical modeling of a two-echelon location–routing problem in a perishable food supply chain with disruption risk

Food supply chain management is very vital due to its high scale in industry, amount of wastage of food in theworld and relationship between wastage of food and under-nourishment. It consists of producing the food andmanufacturing companies, whole sale and distributors, brokers, food service places, restaurants and retail groceryfirms. Studying perishable goods in a supply chain can be helpful for industries that are related to these kinds ofgoods. Because of the important role of location and routing in a supply chain, unity of these elements leading toan efficient supply chain. Recently, multi-layer and multi-facility problems in a supply chain have been studiedin large scale. Connection between facilities (i.e., the best flow allocating between facilities and vehicle routingfor supplying the perishable foods) is one of the key subjects for this problem. This paper studies a perishable foodsupply chain network with disruption risk including the location of facilities, allocating flow between facilitiesand routing decisions. It also presents a multi-objective model to minimize the operational costs (e.g., openingcost, route repairing cost during the disruption and unsatisfied demands cost), minimize the response time, andmaximize the reliability of minimum routes. Validity of the model is investigated by the ε-constraint method inGams. Since this problem is an NP-hard one, the NSGA-II is used for solving this problem in large sizes. Finally,to show the efficiency of the proposed model, a real case study including 10 zone of district 1 of Tehran is applied.