A Review of the Use of Linear Programming to Optimize Diets, Nutritiously, Economically and Environmentally

Abstract

The "Diet Problem" (the search of a low-cost diet that would meet the nutritional needs of a US Army soldier) is characterized by a long history, whereas most solutions for comparable diet problems were developed in 2000 or later, during which computers with large calculation capacities became widely available and linear programming (LP) tools were developed. Based on the selected literature (52 papers), LP can be applied to a variety of diet problems, from food aid, national food programmes, and dietary guidelines to individual issues. This review describes the developments in the search for constraints. After nutritional constraints, costs constraints, acceptability constraints and ecological constraints were introduced. The 12 studies that apply ecological constraints were analyzed and compared in detail. Most studies have used nutritional constraints and cost constraints in the analysis of dietary problems and solutions, but such research begin showing weaknesses under situations featuring a small number of food items and/or nutritional constraints. Introducing acceptability constraints is recommended, but no study has provided the ultimate solution to calculating acceptability. Future possibilities lie in finding LP solutions for diets by combining nutritional, costs, ecological and acceptability constraints. LP is an important tool for environmental optimization and shows considerable potential as an instrument for finding solutions to a variety of very complex diet problems.

Keywords: diet costs; environmental constraints (EC); linear programming; nutritional quality; sustainable diet.

Figure 1

Concept of linear programming: The constraints (x_i; purple lines) result in a feasible solution set (yellow area). The objective function (k; yellow line) results in the highest possible solution at the edge of the solution area.

Figure 2

Selection of papers through the PRISMA protocol for systematic literature research.

Figure 3

Example of the application of acceptability constraints and the effects on the environmental impact of different diet scenarios (M, males; F, females). The lower the penalty score is, the closer the diet is to the current diet and the more acceptable (21). The red line is called the “possibilities frontier.” It indicates the possibilities with the lowest penalty score for a certain environmental constraint (21).