Design of a distribution network for the school lunch program

Abstract

The national school lunch program (NSLP) is crucial for providing healthy, inexpensive, or free lunches to children, thus benefiting society. Designing a distribution network for the program requires solving a location and routing problem. In this paper, first, we formulate a multi-objective non-linear integer programming formulation of the problem. Next, we develop a two-step approach since the problem is Np-hard. The first stage presents a K-mean clustering method that deals with routing decisions by determining the locations of food processing centers and allocating schools to these centers. The second stage offers a multi-objective mixed-integer linear mathematical model for finding the locations of distribution centers. Besides economic and environmental factors, we optimize travel time in the network as perishable items are involved. A weighted sum approach is presented for different weights of objectives. We provide a real case study in Turkey to demonstrate the applicability of the two-stage approach proposed in this study. The numerical results provide valuable information for decision-makers and authorities to prioritize and prepare action plans.