An allocation-packing model of customized food parcels to food banks: A system subject to nutritional and logistics conditions [Un modelo de asignación-empaque de despensas personalizadas para bancos de alimentos: Un sistema sujeto a condiciones nutricionales y logísticas]

Abstract

A food management and distribution system in a food bank (FB) implies the gathering, classification (good and bad conditions), allocation and distribution of the food to families living in poverty. Our research is part of a reengineering project of the food management-distribution system in a Food Bank (FB) of México. The problem of a diet configuration has been studied in the literature focusing mainly on selecting the food quantities that minimize the total cost of a diet, and satisfying the nutritional requirements specified in the diet. In the context of a supply chain, food-allocation to multiple families implies the extension of this problem subject to nutritional restrictions mainly, to other kind of limiting such as: resource availability, resource-allocation to multiple points, weight and volume restrictions due to the use of containers during distribution and the cost of the recovery of the set of products delivered to the client. This article presents a food allocation-packing mathematical model to simultaneously configure various food parcels customized per family, subject to nutritional and logistic restrictions. The contribution of this research lies in simultaneously consider the restrictions and characteristics of three problems that had been studied in the literature separately: the problem of the limited allocation of resources in a supply chain, the diet problem and the food-packing problem. The model is presented as a mixed-integer lineal programming problem, and solved using Lingo 13Zapotitlán. The validation of the model was performed through experiments in different operation scenarios using information provided by the FB of México. The search time of the solution is analyzed in each scenario and a non-parametric statistical analysis is executed comparing the nutritional and dimensional characteristics of the obtained pantries in each scenario.