An L1-norm method for generating all of efficient solutions of multi-objective integer linear programming problem

This paper extends the proposed method by Jahanshahloo et al. (2004) (a method for generating all the efficient solutions of a 0-1 multi-objective linear programming problem, Asia-Pacific Journal of Operational Research). This paper considers the recession direction for a multi-objective integer lin...

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Vydané v:Journal of industrial engineering international Ročník 8; číslo 1; s. 1 - 8
Hlavní autori: Tohidi, Ghasem, Razavyan, Shabnam
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Heidelberg Springer 01.12.2012
Springer Berlin Heidelberg
Islamic Azad University, South Tehran Branch
Predmet:
efficient solution
Engineering
Engineering Economics
Facility Management
Industrial and Production Engineering
L1-norm
Logistics
Marketing
Mathematical and Computational Engineering
multi-objective integer linear programming
Organization
Original Research
Quality Control
recession direction
Reliability
Safety and Risk
single objective integer linear programming
L1-norm
Recession direction
Efficient solution
Multi-objective integer linear programming
Single objective integer linear programming
ISSN:2251-712X, 1735-5702, 2251-712X
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Shrnutí:This paper extends the proposed method by Jahanshahloo et al. (2004) (a method for generating all the efficient solutions of a 0-1 multi-objective linear programming problem, Asia-Pacific Journal of Operational Research). This paper considers the recession direction for a multi-objective integer linear programming (MOILP) problem and presents necessary and sufficient conditions to have unbounded feasible region and infinite optimal values for objective functions of MOILP problems. If the number of efficient solution is finite, the proposed method finds all of them without generating all feasible solutions of MOILP or concluding that there is no efficient solution. In any iteration of the proposed algorithm, a single objective integer linear programming problem, constrained problem, is solved. We will show that the optimal solutions of these single objective integer linear programming problems are efficient solutions of an MOILP problem. The algorithm can also give subsets of efficient solutions that can be useful for designing interactive procedures for large, real-life problems. The applicability of the proposed method is illustrated by using some numerical examples.
Bibliografia:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:2251-712X
1735-5702
2251-712X
DOI:10.1186/2251-712X-8-17