Diet models with linear goal programming: impact of achievement functions

• Published in: European journal of clinical nutrition Vol. 69; no. 11; pp. 1272 - 1278
• Main Authors: Gerdessen, J C, de Vries, J H M
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 01.11.2015; Nature Publishing Group
• Subjects: 631/114/2397; 692/700/2814; Achievement; Body Weight; Bread; Chair Nutrition and Health over the Lifecourse; Clinical Nutrition; Constraint modelling; Costs and Cost Analysis; Decision making; Diet; Epidemiology; Food; Fuzzy Logic; Fuzzy sets; Global Nutrition; Goal programming; Goals; Health aspects; HNE Nutrition and Health over the Lifecourse; HNE Voeding en Gezondheid in de Levenscyclus; Humans; Internal Medicine; Leerstoelgroep Operationele research en logistiek; Linear programming; Mathematical models; Meat; Medicine; Medicine & Public Health; Metabolic Diseases; Models, Biological; Numerical methods; Nutrients; Nutrition; Nutritional Requirements; Nutritive Value; Operationele Research en Logistiek; Operations Research and Logistics; original-article; Palatability; Planning; Programming, Linear; Public Health; Taste; VLAG; Wereldvoeding; Netherlands
• ISSN: 0954-3007; 1476-5640; 1476-5640
• DOI: 10.1038/ejcn.2015.56

Background/Objectives: Diet models based on goal programming (GP) are valuable tools in designing diets that comply with nutritional, palatability and cost constraints. Results derived from GP models are usually very sensitive to the type of achievement function that is chosen. This paper aims to provide a methodological insight into several achievement functions. It describes the extended GP (EGP) achievement function, which enables the decision maker to use either a MinSum achievement function (which minimizes the sum of the unwanted deviations) or a MinMax achievement function (which minimizes the largest unwanted deviation), or a compromise between both. An additional advantage of EGP models is that from one set of data and weights multiple solutions can be obtained. Subjects/Methods: We use small numerical examples to illustrate the ‘mechanics’ of achievement functions. Then, the EGP achievement function is demonstrated on a diet problem with 144 foods, 19 nutrients and several types of palatability constraints, in which the nutritional constraints are modeled with fuzzy sets. Results: Choice of achievement function affects the results of diet models. Conclusions: MinSum achievement functions can give rise to solutions that are sensitive to weight changes, and that pile all unwanted deviations on a limited number of nutritional constraints. MinMax achievement functions spread the unwanted deviations as evenly as possible, but may create many (small) deviations. EGP comprises both types of achievement functions, as well as compromises between them. It can thus, from one data set, find a range of solutions with various properties.