Mixed Linear Programming Models for fruits and vegetables supply from family farms to rural schools as support for public politics

The School Feeding Program of Paraguay (PAEP) has the function of providing food for children in elementary schools. Because there are no efficient supply plans to aid local suppliers, we are interested in minimize the purchase and transport costs and maximize the local purchase subject to the school demand satisfaction in the benefited area. This study has identified sub-problems: (pp) the purchase of products from local family farms, the vehicle routing problems (VRP) for multi-products picking (C) from the farms and for multi-products delivery (D) to schools. In this study have been designed four mathematical models based on Mixed Linear Programming: a three-stage model pp + VRPC + VRPD, two two-stage models VRPCpp + VRPD and pp + VRPCD, and a one-stage model VRPCDpp. The experimental result (based on real data of a rural zone) shows that the multi-stage approaches use less computational time than one-stage; however, the economic costs grow slightly.