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Food and health

Diet models with linear goal programming: impact of achievement functions

European Journal of Clinical Nutrition volume 69, pages 1272–1278 (2015)Cite this article

Subjects

Abstract

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.

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Acknowledgements

This research received no grant from any funding agency in the public, commercial or not-for profit sectors.

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Authors and Affiliations

  1. Group Operations Research and Logistics, Wageningen University, Wageningen, The Netherlands

    J C Gerdessen

  2. Division of Human Nutrition, Wageningen University, Wageningen, The Netherlands

    J H M de Vries

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  1. J C Gerdessen
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  2. J H M de Vries
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Correspondence to J C Gerdessen.

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Supplementary Information accompanies this paper on European Journal of Clinical Nutrition website

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Gerdessen, J., de Vries, J. Diet models with linear goal programming: impact of achievement functions. Eur J Clin Nutr 69, 1272–1278 (2015). https://doi.org/10.1038/ejcn.2015.56

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