The food bank of Madrid: a linear model for optimal nutrition

This work proposes a mathematical linear programming model that addresses the food provisioning problem of the food bank of Madrid. It aims to determine the most appropriate weekly decisions to meet the macro-nutritional requirements of the beneficiaries of this social service, by minimizing the total cost considering third-party donations. The model has been applied to a realistic case study considering a sociological structure of beneficiaries categorized by age and gender and representing the first decile of incomes of the Spanish population. The demand of macronutrients is satisfied by means of nine different groups of food, used to provide some level of variability in the consumption patterns of the beneficiaries. The results provide insight on cost-cutting opportunities related to centralizing the decision-making process, indicating a 10% reduction both in provisioning costs and food quantities. This suggests that the proposed model might serve as a tool for designing new strategies for the provisioning or evaluation of economic and social support policies for the food bank of Madrid.