An Order Rank Method for Multi-Objective Linear Programming


  • Rabiu Bashir Yunus Universiti Sultan Zainal Abidin (UniSZA), Kuala Terengganu, Malaysia.
  • Abdulhadi Aminu
  • Umar Tasi’u Mustapha


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.

Author Biography

Rabiu Bashir Yunus, Universiti Sultan Zainal Abidin (UniSZA), Kuala Terengganu, Malaysia.

Faculty of Informatics and Computing.


Arsham H., Adlakha V. and Lev B., “A Simplified Algebraic Method for System of Linear Inequalitieswith LP

Applicationsâ€, Omega, vol. 37: pp. 876-882, 2005.

Dantzig G., “Making Process During a Stall in the Simplex Algorithm Linear Algebraand its Applicationsâ€, 144: pp.251-259, 1989.

Demirtas EA., and Ustun O., “An Integrated Multi-objective Decision Making Process for Supplier Selectionand Order Allocation,†Omega, vol.36: pp.76-90, 2008.

Eiselt H.A., and Sandblom C.L., “Linear Programming and its Applicationsâ€, Springer-Verlag,Berlin, 2007.

Hillier FS., and Lieberman GJ., “Introduction to Operations Researchâ€, Six Edition,, Mc Graw- Hill Series.

Ishibuchi H., and Tanaka H., “Multi-objective Programming Optimization of the Interval ObjectiveFunction,†European Journal Operation Research, vol.48:pp.219-225, 1990.

Kim, I.Y., and de Weck, O., “Adaptive weighted-sum method for bi-objective optimization: Paretofront generation,†Structural and Multidisciplinary Optimization, 2004(in press).

Koski J., “Multicriteria truss optimization, “Multi- Criteria Optimization in Engineering and Sciences,edited by Stadler, New York, Plenum Press, 1988.

Marglin S., “Public Investment Criteriaâ€, MIT Press, Cambridge, Massachusetts, 1967.

Suprajitno H., and Mohd I.B, “Linear Programming with Interval Arithmeticâ€, Int. J. Contemp.Math. Sciences, vol.5, no. 7: pp.323-332, 2010.

Zadeh L., “Optimality and Non-Scalar-Valued Performance Criteria,†IEEE Transactionson Automatic Control,AC-

, 59, 1963.




How to Cite

Yunus, R. B., Aminu, A., & Mustapha, U. T. (2015). An Order Rank Method for Multi-Objective Linear Programming. Asian Journal of Applied Sciences, 3(3). Retrieved from




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