Presenting a multi-objective locating-routing-arc model with a collaborative approach (a food distribution case study)

Transportation in the industrialized world plays an important role in the economic development of countries by enabling the consumption of products at very remote locations. Transportation costs are one of the most important parts of the finished products’ costs. In general, locating-routing-arc is highly important for industries that are heavily involved with the end customers such as the consumer product industries. In these industries, due to the insignificant difference between the products of the various companies, the maintenance of the market and the loyalty of customers depend on the timely availability of the required products. Hence, providing the customers ‘need at the right time and place with high level of responding is highly important to get customers’ satisfaction. In this study, the problem of locating-routing-arc is studied by using game theory. In the investigated problem, there are a number of demand points as customers, each of which has a specific demand (delivered, handover or return) of every type of products and each customer determines the delivery time for each product. To solve the Problem in Small dimensions, a mathematical model is presented in the form of the mixed integer, two-objective, multi-cyclic, and multi-commodity and for to solve the problem in big dimensions in the form of NP-HARD. The model is to test the validation of the proposed model, a ε-constraint method is used and Pareto solutions are calculated. Then due to the complexity of the problem in big dimensions. We used the meta-heuristics NSGA-II algorithm in cooperative and non-cooperative modes. Finally, the results if cooperative methods were used to allocate the amount of savings.