Bi-Objective Goal Programming for Balancing Costs versus Nutritional Adequacy

The Diet Optimization Problem is a classical Linear Programming problem which
finds, from a set of available food commodities, the most affordable diet that meets an individual’s nutritional requirements. It is, however, not always possible to create a feasible diet, as certain nutritional requirements are difficult to be met (e.g. iron for adolescent females). In that case, Goal Programming is used to minimize nutritional deviations in order to obtain a near feasible diet. The cost of the diet is, however, often overlooked or neglected. Therefore, we focus in our paper on finding all tradeoffs between the cost and nutritional adequacy of a diet. To do so, we present a bi-objective approach based on the NISE method that is able to find all efficient tradeoffs between two linear objectives. To the best of our knowledge, this approach bridges the current gap between diet optimization and multicriteria optimization, as we are the first to address how to obtain all efficient trade-offs of two linear objectives in a dietary context. In order to show what type of insights can be gained from this approach, two analyses are presented using data collected in Ebonyi, Nigeria. In the first analysis a diet with a restriction on the exact energy intake is considered where all nutrient intakes except energy are allowed to deviate from their prescription. This analysis is especially helpful when one needs to make decisions in case there is a restrictive budget or when a
nutritionally adequate diet is either unaffordable or unattainable. The second analysis only relaxes the exact energy intake, where the other nutrients are kept within their requirements, to investigate how the energy intake affects the cost of a diet. Here, we describe in what situations the so-called more-for-less paradox takes place, which can be induced by the exact energy intake.