An Order Rank Method for Multi-Objective Linear Programming
Keywords:MOLPP, Pareto-Optimal, Order Rank Method
Inthis paper, a method is proposed to solve the Multi- objective linear programming problem (MOLPP);the method uses the idea of an order relation to rank the interval numbers.It checks the dominance of the optimal objective values,which are assumed to be an interval numbers by comparing order relations based on their mid-points and radius.Moreover, we demonstrate some numerical examples which show that,the proposed method could be a worthy alternative.
Arsham H., Adlakha V. and Lev B., â€œA Simplified Algebraic Method for System of Linear Inequalitieswith LP
Applicationsâ€, Omega, vol. 37: pp. 876-882, 2005.
Dantzig G., â€œMaking Process During a Stall in the Simplex Algorithm Linear Algebraand its Applicationsâ€, 144: pp.251-259, 1989.
Demirtas EA., and Ustun O., â€œAn Integrated Multi-objective Decision Making Process for Supplier Selectionand Order Allocation,â€ Omega, vol.36: pp.76-90, 2008.
Eiselt H.A., and Sandblom C.L., â€œLinear Programming and its Applicationsâ€, Springer-Verlag,Berlin, 2007.
Hillier FS., and Lieberman GJ., â€œIntroduction to Operations Researchâ€, Six Edition,, Mc Graw- Hill Series.
Ishibuchi H., and Tanaka H., â€œMulti-objective Programming Optimization of the Interval ObjectiveFunction,â€ European Journal Operation Research, vol.48:pp.219-225, 1990.
Kim, I.Y., and de Weck, O., â€œAdaptive weighted-sum method for bi-objective optimization: Paretofront generation,â€ Structural and Multidisciplinary Optimization, 2004(in press).
Koski J., â€œMulticriteria truss optimization, â€œMulti- Criteria Optimization in Engineering and Sciences,edited by Stadler, New York, Plenum Press, 1988.
Marglin S., â€œPublic Investment Criteriaâ€, MIT Press, Cambridge, Massachusetts, 1967.
Suprajitno H., and Mohd I.B, â€œLinear Programming with Interval Arithmeticâ€, Int. J. Contemp.Math. Sciences, vol.5, no. 7: pp.323-332, 2010.
Zadeh L., â€œOptimality and Non-Scalar-Valued Performance Criteria,â€ IEEE Transactionson Automatic Control,AC-
, 59, 1963.
How to Cite
- Papers must be submitted on the understanding that they have not been published elsewhere (except in the form of an abstract or as part of a published lecture, review, or thesis) and are not currently under consideration by another journal published by any other publisher.
- It is also the authors responsibility to ensure that the articles emanating from a particular source are submitted with the necessary approval.
- The authors warrant that the paper is original and that he/she is the author of the paper, except for material that is clearly identified as to its original source, with permission notices from the copyright owners where required.
- The authors ensure that all the references carefully and they are accurate in the text as well as in the list of references (and vice versa).
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Attribution-NonCommercial 4.0 International that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
- The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.