A framework to study nearly optimal solutions of linear programming models developed for agricultural land use exploration

A framework to study nearly optimal solutions of linear programming models developed for... Nearly optimal solutions of linear programming models provide useful information when some of the relevant objectives and constraints are not explicitized in the models. This paper presents a three steps framework to study nearly optimal solutions of linear programming models developed for land use exploration. The first step is to define low dimensional vectors called ‘aspects’ to summarize the solutions. The second step is to generate a group of optimal and of nearly optimal solutions. Three methods are proposed for generating nearly optimal solutions. Method i proceeds by minimization of sums of decision variables that are non-zero in the optimal solution and in previously generated nearly optimal solutions. Method ii proceeds by maximization of sums of randomly selected decision variables. Method iii is targeted at searching nearly optimal solutions with very different values for the aspects. Finally, the third step of the framework is to present graphically the values of the aspects of the generated solutions. The framework is illustrated with a case study in which a linear programming model developed for land use exploration at the European level is presented. First, an optimal solution is calculated with the model by minimizing nitrogen loss with constraints on area, water use, product balances, and manure balances. Then, 52 nearly optimal solutions are generated by using methods i , ii , and iii with a deviation tolerance of 5% from the optimal value of nitrogen loss. Each solution is summarized by three different aspects that represent the allocations of the agricultural area among two regions, among five types of crop rotation, and among five production orientations respectively. Graphical presentation of these aspects and principal component analysis show that nearly optimal solutions can be very different from the optimal solution in terms of land use allocations. For example, the agricultural area allocated to the north of the European Community varies from 10.9 to 50.2×10 6 ha among the 52 generated nearly optimal solutions, whereas this area is equal to 26.5×10 6 ha in the optimal solution. The comparison of methods i , ii , and iii shows that the solutions generated with method iii are quite more contrasted than the solutions generated with methods i and ii . The case study presented in this paper illustrates how our methodological framework can be used to allow a stakeholder to select a satisfactory solution according to issues that cannot be quantified in a model. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Ecological Modelling Elsevier

A framework to study nearly optimal solutions of linear programming models developed for agricultural land use exploration

Loading next page...
 
/lp/elsevier/a-framework-to-study-nearly-optimal-solutions-of-linear-programming-1GMree5f1f
Publisher
Elsevier
Copyright
Copyright © 2000 Elsevier Science B.V.
ISSN
0304-3800
eISSN
1872-7026
D.O.I.
10.1016/S0304-3800(00)00249-0
Publisher site
See Article on Publisher Site

Abstract

Nearly optimal solutions of linear programming models provide useful information when some of the relevant objectives and constraints are not explicitized in the models. This paper presents a three steps framework to study nearly optimal solutions of linear programming models developed for land use exploration. The first step is to define low dimensional vectors called ‘aspects’ to summarize the solutions. The second step is to generate a group of optimal and of nearly optimal solutions. Three methods are proposed for generating nearly optimal solutions. Method i proceeds by minimization of sums of decision variables that are non-zero in the optimal solution and in previously generated nearly optimal solutions. Method ii proceeds by maximization of sums of randomly selected decision variables. Method iii is targeted at searching nearly optimal solutions with very different values for the aspects. Finally, the third step of the framework is to present graphically the values of the aspects of the generated solutions. The framework is illustrated with a case study in which a linear programming model developed for land use exploration at the European level is presented. First, an optimal solution is calculated with the model by minimizing nitrogen loss with constraints on area, water use, product balances, and manure balances. Then, 52 nearly optimal solutions are generated by using methods i , ii , and iii with a deviation tolerance of 5% from the optimal value of nitrogen loss. Each solution is summarized by three different aspects that represent the allocations of the agricultural area among two regions, among five types of crop rotation, and among five production orientations respectively. Graphical presentation of these aspects and principal component analysis show that nearly optimal solutions can be very different from the optimal solution in terms of land use allocations. For example, the agricultural area allocated to the north of the European Community varies from 10.9 to 50.2×10 6 ha among the 52 generated nearly optimal solutions, whereas this area is equal to 26.5×10 6 ha in the optimal solution. The comparison of methods i , ii , and iii shows that the solutions generated with method iii are quite more contrasted than the solutions generated with methods i and ii . The case study presented in this paper illustrates how our methodological framework can be used to allow a stakeholder to select a satisfactory solution according to issues that cannot be quantified in a model.

Journal

Ecological ModellingElsevier

Published: Jun 30, 2000

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create folders to
organize your research

Export folders, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off