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

Overview

Journal Front Nutr

Specialty Nutritional Sciences

Date 2018 Jul 7

PMID 29977894

Citations 39

Authors

Corne van Dooren

Affiliations

Soon will be listed here.

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.

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References

Darmon N, Ferguson E, Briend A . 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. Am J Clin Nutr. 2002; 75(2):245-53. DOI: 10.1093/ajcn/75.2.245. View

Dibari F, Diop E, Collins S, Seal A . Low-cost, ready-to-use therapeutic foods can be designed using locally available commodities with the aid of linear programming. J Nutr. 2012; 142(5):955-61. DOI: 10.3945/jn.111.156943. View

Mertens E, Vant Veer P, Hiddink G, Steijns J, Kuijsten A . Operationalising the health aspects of sustainable diets: a review. Public Health Nutr. 2016; 20(4):739-757. PMC: 10261330. DOI: 10.1017/S1368980016002664. View

Briend A, Darmon N . Determining limiting nutrients by linear programming: A new approach to predict insufficient intakes from complementary foods. Pediatrics. 2000; 106(5):1288-9. View

Darmon N, Ferguson E, Briend A . Do economic constraints encourage the selection of energy dense diets?. Appetite. 2003; 41(3):315-22. DOI: 10.1016/s0195-6663(03)00113-2. View

Soden P, Fletcher L . Modifying diets to satisfy nutritional requirements using linear programming. Br J Nutr. 1992; 68(3):565-72. DOI: 10.1079/bjn19920115. View

Maillot M, Ferguson E, Drewnowski A, Darmon N . Nutrient profiling can help identify foods of good nutritional quality for their price: a validation study with linear programming. J Nutr. 2008; 138(6):1107-13. DOI: 10.1093/jn/138.6.1107. View

Drewnowski A, Specter S . Poverty and obesity: the role of energy density and energy costs. Am J Clin Nutr. 2003; 79(1):6-16. DOI: 10.1093/ajcn/79.1.6. View

Maes L, Vereecken C, Gedrich K, Rieken K, Sichert-Hellert W, De Bourdeaudhuij I . A feasibility study of using a diet optimization approach in a web-based computer-tailoring intervention for adolescents. Int J Obes (Lond). 2008; 32 Suppl 5:S76-81. DOI: 10.1038/ijo.2008.186. View

10.

Herforth A, Frongillo E, Sassi F, Mclean M, Arabi M, Tirado C . Toward an integrated approach to nutritional quality, environmental sustainability, and economic viability: research and measurement gaps. Ann N Y Acad Sci. 2014; 1332:1-21. DOI: 10.1111/nyas.12552. View

11.

Auestad N, Fulgoni 3rd V . What current literature tells us about sustainable diets: emerging research linking dietary patterns, environmental sustainability, and economics. Adv Nutr. 2015; 6(1):19-36. PMC: 4288277. DOI: 10.3945/an.114.005694. View

12.

Donati M, Menozzi D, Zighetti C, Rosi A, Zinetti A, Scazzina F . Towards a sustainable diet combining economic, environmental and nutritional objectives. Appetite. 2016; 106:48-57. DOI: 10.1016/j.appet.2016.02.151. View

13.

Maillot M, Vieux F, Ferguson E, Volatier J, Amiot M, Darmon N . To meet nutrient recommendations, most French adults need to expand their habitual food repertoire. J Nutr. 2009; 139(9):1721-7. DOI: 10.3945/jn.109.107318. View

14.

Vieux F, Soler L, Touazi D, Darmon N . High nutritional quality is not associated with low greenhouse gas emissions in self-selected diets of French adults. Am J Clin Nutr. 2013; 97(3):569-83. DOI: 10.3945/ajcn.112.035105. View

15.

Raffensperger J . The least-cost low-carbohydrate diet is expensive. Nutr Res. 2008; 28(1):6-12. DOI: 10.1016/j.nutres.2007.10.002. View

16.

Parlesak A, Tetens I, Jensen J, Smed S, Gabrijelcic Blenkus M, Rayner M . Use of Linear Programming to Develop Cost-Minimized Nutritionally Adequate Health Promoting Food Baskets. PLoS One. 2016; 11(10):e0163411. PMC: 5070943. DOI: 10.1371/journal.pone.0163411. View

17.

Santika O, Fahmida U, Ferguson E . Development of food-based complementary feeding recommendations for 9- to 11-month-old peri-urban Indonesian infants using linear programming. J Nutr. 2008; 139(1):135-41. DOI: 10.3945/jn.108.092270. View

18.

Horgan G, Perrin A, Whybrow S, Macdiarmid J . Achieving dietary recommendations and reducing greenhouse gas emissions: modelling diets to minimise the change from current intakes. Int J Behav Nutr Phys Act. 2016; 13:46. PMC: 4823893. DOI: 10.1186/s12966-016-0370-1. View

19.

Maillot M, Vieux F, Amiot M, Darmon N . Individual diet modeling translates nutrient recommendations into realistic and individual-specific food choices. Am J Clin Nutr. 2009; 91(2):421-30. DOI: 10.3945/ajcn.2009.28426. View

20.

Frega R, Lanfranco J, De Greve S, Bernardini S, Geniez P, Grede N . What linear programming contributes: world food programme experience with the "cost of the diet" tool. Food Nutr Bull. 2012; 33(3 Suppl):S228-34. DOI: 10.1177/15648265120333S212. View