Which efficient solution in multi objective programming problem should be taken?

In practical problems, which can be stated in the form of multi objective programming problem, we have usually a large set of efficient solutions. So, which solution from this set should be taken, appears as a natural question here. In the paper we propose some sustainable principles and simple nume...

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Bibliographic Details
Published in:Central European journal of operations research Vol. 29; no. 3; pp. 967 - 987
Main Authors: Matejas, Josip, Peric, Tunjo, Mlinaric, Danijel
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2021
Springer
Springer Nature B.V
Subjects:
Business and Management
Decision making
Mathematical optimization
Mathematical research
Methods
Numerical methods
Operations research
Operations Research/Decision Theory
Priorities
Programming
Croatia
Multi objective programming problem
Bilevel programming problem
Efficient solution
Aspiration
Priority
ISSN:1435-246X, 1613-9178
Online Access:Get full text
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Summary:In practical problems, which can be stated in the form of multi objective programming problem, we have usually a large set of efficient solutions. So, which solution from this set should be taken, appears as a natural question here. In the paper we propose some sustainable principles and simple numerical method for such choice. The method respects aspirations and priorities of decision makers and enables iterations for possible improvement of the solution. In this way decision makers can clearly understand why a particular solution is obtained and when and how it can be improved. The features of the method are explained by a practical example. An applications to bilevel programming problems are also presented, where the both side mapping, between the set of efficient solutions and the set of all possible priorities, is shown. It is illustrated in detail through several linear and nonlinear examples.
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ISSN:1435-246X
1613-9178
DOI:10.1007/s10100-020-00718-1