Linear and nonlinear programming to optimize the nutrient density of a population’s diet: an example based on diets of preschool children in rural Malawi

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Abstract
Background: Food consumption surveys are often used to detect inadequate nutrient intakes but not to determine whether inadequate nutrient intakes are due to suboptimal use of locally available foods or to insufficient availability of nutrient-dense foods. Objectives: The objectives were to describe the use of linear programming as a method to design nutrient-adequate diets of optimal nutrient density and to identify the most stringent constraints in nutritional recommendations and food consumption patterns in a population's diet. Design: This analysis was conducted with the use of food consumption data collected during 2 seasons from rural Malawian children aged 3–6 y. Linear programming was used to select diets based on local foods that satisfied a set of nutritional constraints while minimizing the total energy content of the diet. Additional constraints on daily intakes of foods and food groups were also introduced to ensure that the diets were compatible with local food patterns. The strength of the constraints was assessed by analyzing nonlinear programming sensitivity. Results: In the harvest season, it was possible to satisfy nutritional recommendations with little departure from the local diet. In the nonharvest season, nutritional adequacy was impaired by the low availability of riboflavin- and zinc-rich animal or vegetable foods and by the high phytate content of other foods. Conclusions: This analysis suggests that nutrition education may help improve the diets of children in the harvest season, whereas changes in the range of available foods might be needed in the nonharvest season. Linear and nonlinear programming can be used to formulate recommendations with the use of data from local food consumption surveys.