Assembly of customized food pantries in a food bank by fuzzy optimization

Purpose: The contribution of this research is to propose a new problem of linear-mixed programming model (LMPM) for the allocation-packing of multiple pantries personalized for Food Banks (FB) considering the opinion of the Decision Maker (DM) in the selection of the best solution. Design/methodology/approach: A food allocation-packing system is modeled as a mixed integer problem (MIP) and a fuzzy mixed integer linear problem (FMILP). 250 families and 100 products were considered. The solutions were found using Lingo 13® (for both deterministic and fuzzy model). To select a good solution in the fuzzy model, this research adapted an interactive method proposed in the literature. The relevance of this modification is that the opinion of a decision maker (DM) is included and considered. Findings: The results for the deterministic and fuzzy model are compared in terms of their accomplishment of the restrictions (mainly nutritional and logistic) and the time needed to achieve a solution. Research limitations/implications: This paper was done considering quantity, weight and volume restrictions so that the pantry will contain a variety of products; it is not considered how the products will be stored into the pantry. Practical implications: This research proposes an alternative food management system at a food bank. The proposed system organizes the content of customized food pantries by the bias of a food allocation model. Social implications: Our paper analyzes a Food Bank (FB) in México. With this proposal, food will be distributed to families in poverty considering their particular nutritional needs. Originality/value: The main contribution of this article lies in the proposal of a new model of mixed integer linear problem (MILP) for the allocation-packing of food, solved with fuzzy possibilistic programming that simultaneously considers nutritional and logistic restrictions applied to a type of organization that has been little studied in the literature and where the opinion of Decision Maker (DM) is very important in the operational decisions involved in the Food Supply Chain (FSC) of a Food Bank (FB).