Designing a Food Supply Chain Network under Uncertainty and Solving by Multi-objective Metaheuristics

Short life cycle products, especially food products, require a certain type of supply chain management due to their particular specifications such as perishability. On the other hand, the food distribution also requires special considerations and imparts more complexity compared with the distribution of other goods because in food distribution the quality of the food delivered to the customer should be considered as well as transportation costs. Therefore, in this paper, a new mathematical model is developed for integrating decisions regarding food supply and distribution under conditions of uncertainty (vehicles’ travel time) with aims to minimize purchase and transportation costs and maximize customer satisfaction. Customer satisfaction relies upon the quality of the food delivered to the customers. The multi-objective model proposed in this paper is NP-hard. Hence, a developed version of NSGA-II called Multi-Objective Time Travel to History (MOTTH) algorithm, inspired from the idea of traveling through history, is proposed to solve the problem. In order to validate the performance of the proposed algorithm, the results of MOTTH algorithm are compared with the results obtained from an exact augmented epsilon-constraint method. Furthermore, a comparison is provided between the NSGA-II and MOTTH algorithms, the results of which indicate the superiority of the MOTTH metaheuristic algorithm.