Diet models with linear goal programming: impact of achievement functions

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 pr...

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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
Online Access:Get full text
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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.
AbstractList 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, nd a range of solutions with various properties.
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. European Journal of Clinical Nutrition (2015) 69, 1272-1278; doi: 10.1038/ejcn.2015.56; published online 22 April 2015
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.BACKGROUND/OBJECTIVESDiet 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.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.SUBJECTS/METHODSWe 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.Choice of achievement function affects the results of diet models.RESULTSChoice of achievement function affects the results of diet models.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.CONCLUSIONSMinSum 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.
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.
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. European Journal of Clinical Nutrition (2015) 69, 1272-1278; doi: 10.1038/ejcn.2015.56; published online 22 April 2015
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.
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. 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. Choice of achievement function affects the results of diet models. 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.
Audience Professional
Academic
Author Gerdessen, J C
de Vries, J H M
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  surname: de Vries
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COPYRIGHT 2015 Nature Publishing Group
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  year: 2015
  text: 2015-11-01
  day: 01
PublicationDecade 2010
PublicationPlace London
PublicationPlace_xml – name: London
– name: England
PublicationTitle European journal of clinical nutrition
PublicationTitleAbbrev Eur J Clin Nutr
PublicationTitleAlternate Eur J Clin Nutr
PublicationYear 2015
Publisher Nature Publishing Group UK
Nature Publishing Group
Publisher_xml – name: Nature Publishing Group UK
– name: Nature Publishing Group
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Snippet Background/Objectives: Diet models based on goal programming (GP) are valuable tools in designing diets that comply with nutritional, palatability and cost...
Diet models based on goal programming (GP) are valuable tools in designing diets that comply with nutritional, palatability and cost constraints. Results...
BACKGROUND/OBJECTIVES: Diet models based on goal programming (GP) are valuable tools in designing diets that comply with nutritional, palatability and cost...
SUBJECTS/METHODS: We use small numerical examples to illustrate the 'mechanics' of achievement functions. Then, the EGP achievement function is demonstrated on...
Background/Objectives:Diet models based on goal programming (GP) are valuable tools in designing diets that comply with nutritional, palatability and cost...
Background/Objectives: Diet models based on goal programming (GP) are valuable tools in designing diets that comply with nutritional, palatability and cost...
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Enrichment Source
Publisher
StartPage 1272
SubjectTerms 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
Title Diet models with linear goal programming: impact of achievement functions
URI https://link.springer.com/article/10.1038/ejcn.2015.56
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