Multi-echelon transportation location and routing problem for designing school lunch distribution network

The National School Lunch Program (NSLP) provides school children nutritious lunches. NSLP benefits health, obesity, and school attendance rates. Developing a distribution network for the program requires solving the multi-echelontransportation location and routing problem to design a distribution network. The first two echelons comprise the distribution of agricultural products from farmers to food processing centers (FPCs) through distribution centers (DC). The third echelon involves determining the locations of food processing centers and routes between schools as part of a multi-depot location routing problem. Since the consider problem is NP-Hard, we propose a two stage solution approach. We aim to minimize the total transportation cost in all echelons and the fixed costs of distribution and food processing centers. A Simulated Annealing Algorithm (SA) is used in the first stage of the process to handle the routing decisions of the third echelon. As part of the second stage, a mixed-integer linear mathematical model is presented that determines the locations of the distribution centers and provides a solution to the transportation problem at the first echelon. Several hypothetical problems are used to test the performance of the proposed method. According to the computational results, SA can be considered an effective and efficient solution algorithm that reduces the computational cost and enhances the quality of the solution.