Conic scalarization approach to solve multi-choice multi-objective transportation problem with interval goal
- 223 Downloads
This paper explores the study of multi-choice multi-objective transportation problem (MCMTP) under the light of conic scalarizing function. MCMTP is a multi-objective transportation problem (MOTP) where the parameters such as cost, demand and supply are treated as multi-choice parameters. A general transformation procedure using binary variables is illustrated to reduce MCMTP into MOTP. Most of the MOTPs are solved by goal programming (GP) approach, but the solution of MOTP may not be satisfied all times by the decision maker when the objective functions of the proposed problem contains interval-valued aspiration levels. To overcome this difficulty, here we propose the approaches of revised multi-choice goal programming (RMCGP) and conic scalarizing function into the MOTP, and then we compare among the solutions. Two numerical examples are presented to show the feasibility and usefulness of our paper. The paper ends with a conclusion and an outlook on future studies.
KeywordsTransportation problem Multi-objective decision making Multi-choice programming Goal programming Conic scalarization Interval uncertainty
The second author is very much thankful to University Grants Commission (UGC) of India for providing financial support to continue this research work under [JRF(UGC)] scheme: Sanctioned letter number [F.17-130/1998(SA-I)] dated 26/06/2014. The authors are also very much thankful to the anonymous reviewers for their comments to improve the quality of the paper.
- Gasimov, R. N. (2001). Characterization of the Benson proper efficiency and scalarization in nonconvex vector optimization, Multiple Criteria Decision Making in the New Millennium. Book Series: Lecture Notes in Economics and Mathematical Systems, 507, 189–198.Google Scholar
- Ignizio, J. P. (1976). Goal programming and extensions. Lexington, MA: Lexington Books.Google Scholar
- Lee, S.M., & Olson, D. (2000). Goal programming, In: Gal T., Stewart T. J., Hanne T. (Eds.), Multi-criteria decision making: Advances in MCDM models, algorithms, theory, and applications. Boston: Kluwer, Chapter 8, pp. 569–581.Google Scholar
- Miettinen, K. (1999). Nonlinear multi-objective Optimization. Boston: Kluwer.Google Scholar
- Roy, S. K., & Mahapatra, D. R. (2011). Multi-objective interval-valued transportation probabilistic problem involving log-normal. International Journal of Computing Science and Mathematics, 1(2), 14–21.Google Scholar
- Roy, S. K., Mahaparta, D. R., & Biswal, M. P. (2012). Multi-choice stochastic transportation problem with exponential distribution. Journal of Uncertain Systems, 6(3), 200–213.Google Scholar
- Tamiz M., Jones D.F., & Mirrazavi S.K. (1997). Intelligent solution and analysis of goal programmes: The GPSYS System, Technical Report, School of computer science and mathematics, University of Portsmouth, UK.Google Scholar