A Systematic Review of Linear Programming Techniques as Applied to Diet Optimisation and Opportunities for Improvement

Table 1

Summary of details retrieved from articles that minimised cost.

Reference	Objective function (s)	Decision variable (s)	Constraint (s)	Focus	Mathematical approach used
Maillot et al. [42]	Minimum cost of diet that met increasing levels of nutritional constraints	Amount of food and energy cost	Nutrient, social acceptability	Demonstrate that foods with good nutritional quality compared to their cost can be easily identified using their nutrient profiles and energy cost	Linear programming
Pirički et al. [43]	Minimum price	Amount of food in FB	Nutrients, energy, and palatability (quantity of food consumed)	Design a diet that combines different food groups and has minimum fat (especially reduced saturated fatty acids) and cholesterol	Linear programming
Dibari et al. [44]	Lowest formulation price	Weights of the chosen commodities	UN recommendations for the macronutrient content of therapeutic food included palatability, texture, and maximum food ingredient weight criteria	Design a RUTF prototype for treating wasting in East African children and adults	Linear programming
Brimblecombe et al. [45]	The minimum cost of a diet	Amount of food consumed	Nutrient adequacy, nutrient density	To observe the dietary change required to achieve nutrient requirements at minimum cost	Linear programming
Ryan et al. [46]	Minimise ingredient cost of the ready-to-use therapeutic foods	Ingredient weight, the usage rate of foods available	Nutritional, product quality (food taste and processing considerations)	Novel ready-to-use therapeutic foods for Ethiopia	Linear programming
De Carvalho et al. [56]	The minimum cost of porridge mix	Weight/amount of food	Constraints on the weight of starch, limiting dry matter to 25%, a limit on the total mass of reconstituted porridge, and nutrient constraints	To extend LP methodology to food formulation by selecting ingredients to make up food with acceptable consistency for the intended consumer group	Linear programming
Parlesak et al. [57]	Cost-minimised nutritionally adequate food basket	Amount of food	Cultural, dietary guidelines, nutrient recommendations	FBDGs	Linear programming
Deptford et al. [58]	Least cost of diet	Energy and nutrient specifications, predefined groups within households, portion sizes, and currency conversion factors	Nutrient requirements and amounts per meal	Applying linear programming to understand better how poverty may affect people’s ability to meet their nutritional specifications	Linear programming
Brixi [59]	Low cost	Nutritional value, price, and water efficiency of suitable ingredients	Nutrient, flavour, crop water efficiency	Ready-to-use therapeutic foods optimised at low cost using locally grown crops	Linear programming
Nykänen et al. [1]	The sum of cost of eating food (minimum cost)	Weight of each food, cost of each food	Energy and nutrient recommendations, minimum deviations from the food balance sheet for Ghana	Food basket for a family of 4 (mother, father, and male and female children) that has low cost	Linear programming
Ghazaryan [60]	Minimise cost	Portion (amount/weight) of the food product	Nutrient (tolerable levels), an upper limit imposed on the quantity of food product	Achieve minimum cost of diet while satisfying some constraints	Linear programming
Faksová et al. [38]	The minimum cost of a diet	The amount of food	Nutrient deviations from eating patterns	Obtain a food basket for a family of four (mother, husband, son, and daughter)	Linear programming
Hamid et al. [29]	Minimise food cost	The portion size of the food	Nutritional (amount of nutrient), acceptability (portion size)	To determine if an ideal diet that meets nutrient intake for pregnant women and is affordable can be created from locally available foods in Malaysia	Linear programming
Gurmu et al. [61]	The minimum cost of the optimised food basket	Weight of food	Estimated energy requirement, recommended macro and micronutrient requirement	Develop a basis for food-based dietary guidelines for Ethiopia	Linear programming
Verly-Jr et al. [62]	Minimise cost while minimising negative and positive deviations	Amount of food	Constraints on nutrient (RDIs), constraints on food group selection	To estimate the possibility of meeting dietary requirements and measure the correlation between the cost of menus and their adequacy	Linear programming
Alaini et al. [63]	Lowest cost for cancer prevention diet	Amount of food and nutrient	Energy, portion size	This study is aimed to build a healthy and balanced menu with minimal cost based on individual needs and focused on preventing cancer (100 people from a university)	Linear programming
Ibrahim et al. [64]	The minimum cost of the healthiest menu from McDonald’s	Amount of food	Recommended nutrients, the lower and upper bound for nutrients	To find the minimum cost of McDonald’s healthy combinations	Linear programming
Lauk et al. [65]	Lowest cost	Amount of food in FB	Nutrient recommendations, acceptability (dietary patterns)	Optimise food basket for Estonian family of four	Linear programming
Mejos et al. [30]	The minimum cost of diet complementary feeding recommendations	Amount of food	Constraints on nutrients, the lower and upper limits	To recognise problem nutrients in complementary diets and formulate feeding recommendations for children aged 6 to 23 months in the rural Philippines	Linear programming
Bai et al. [66]	Least cost of diets	Quantity of foods	Constraints on nutrient requirements (lower and upper bounds)	Identify populations whose nutrient needs are difficult to meet with the current challenges of the food systems	Linear programming

FB—food basket, UN—United Nations, FBDGs—food-based dietary guidelines, and RDIs—recommended dietary intakes.