Aplicação da modelagem matemática para o planejamento de cardápios para restaurantes universitários

Abstract

Mathematical modeling is a feature of great utility and application in several contexts where focus is the optimization of resources. One of these contexts consists of feeding practiced by university students who commonly presents with important nutritional deficits that can affect their health and their performance, requiring interventions.In this way, the aim of this thesis is to apply mathematical modeling to the development of menus for university restaurants seeking the formulation of nutritionally adequate meals that meet the students' food preferences and present the lowest costs for students and institutions. The research was divided into five stages for its design. In the first stage, information was collected about nutritional needs for individuals, nutritional composition of foods and costs of food. In the second stage, seeking to justify the accomplishment of the present research, the nutritional analysis of meals served at the university restaurant during a four-week period was carried out. The results of this analysis showed that meals served at the university restaurant presented deficits in nutrients and high levels of cholesterol and energy. In the third stage of the study, a questionnaire was applied to 329 university students seeking to identify their food preferences in relation to a predetermined group of foods. Based on the previous results, in the fourth stage an integer linear programming model was elaborated for the generation of meals for university restaurants. The objective of the integer linear programming model is to reduce meal costs, taking into account the minimum and maximum nutritional requirements indicated for the public concerned. In the fifth stage, an algorithm was developed to enable the foods to be used by the linear programming model, where food preferences are considered and the generation of non-repetitive meals over a predetermined period of time is sought. In order to verify the functionality of the proposal, the mathematical model was applied to the generation of meals in a period of 10 days, it was verified with the results obtained that different meals were generated throughout the period, taking into account the nutritional requirements imposed. It is concluded that the methodological proposal is suitable to support the development of menus for university restaurants, and can be replicated to other contexts through the adaptation of the mathematical model constraints.