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.

Development of healthy and sustainable food-based dietary guidelines for the Netherlands

“…Optimisation modelling is considered the preferred approach, since it captures the complexity of the diet as a whole (66) , and is applied by several other countries (13)(14)(15) . The use of an optimisation model requires a range of decisions that potentially can influence the outcome (67) . Examples are the definition of food groups and their nutrient composition, the criteria for Wheel of Five food groups, the type of optimisation function (quadratic, linear) and constraints for food groups.…”

Assessing the Carbon Emission Driven by the Consumption of Carbohydrate-Rich Foods: The Case of China

“…This result implies that a significant change in Chinese diets should be made to achieve environmental and health goals. Linear programming could help develop diets with lower impacts than diet scenario studies [20,22]. On the other hand, in this research, the consumption of G3 increased significantly in the two optimized diets.…”

“…If not well balanced, the dietary styles that tend to be most beneficial in environmental terms, such as a vegan and vegetarian diets, could lead to an insufficient supply of essential nutrients [19]. Many studies deal with this issue through linear programming, i.e., constraining environmental and health criteria together to generate qualified choices about diets [20]. Many diets, such as those in France [21], Netherlands [22], and the USA [23], have been optimized using linear programming.…”

Production Flow Optimization By Using Theory of Constraints

“…Product flow optimization is very important in the production process in industry, because it deals with the effectiveness and efficiency within a company [1,2]. It is known that production planning is very crucial in the success of the company, especially in the context of measuring the ability of a company to provide the products and its balance with the production process in the factory [3,4].…”