Fuzzy programming for multi-choice bilevel transportation problem

• Authors: ARORA Ritu , GUPTA Kavita
• Languages of publication: EN

Abstracts

Multi-choice programming problems arise due to the diverse needs of people. In this paper, multi-choice optimization has been applied to the bilevel transportation problem. This problem deals with transportation at both the levels, upper as well as lower. There are multiple choices for demand and supply parameters. The multi-choice parameters at the respective levels are converted into polynomials which transmute the defined problem into a mixed integer programming problem. The objective of the paper is to determine a solution methodology for the transformed problem. The significance of the formulated model is exhibited through an example by applying it to the hotel industry. The fuzzy programming approach is employed to obtain a satisfactory solution for the decision-makers at the two levels. A comparative analysis is presented in the paper by solving the bilevel multi-choice transportation problem with goal programming mode as well as by the linear transformation technique. The example is solved using computing software.

Keywords

EN

bilevel programming; transportation problem; fuzzy programming; goal programming; tolerance limits; satisfactory solution

• Publisher: Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
• Journal: Operations Research and Decisions
• Year: 2021
• Volume: 31
• Issue: 3
• Pages: 5-21

Contributors

author

ARORA Ritu

• Department of Mathematics, Keshav Mahavidyalaya, University of Delhi, H-4-5 Zone, Pitampura Near Sainik Vihar, Delhi 110034, India

author

GUPTA Kavita

• Department of Mathematics, Kirori Mal College, University of Delhi, Delhi 110007, India

References

• ABOUNACER R., REKIK M., RENAUD J., An exact solution approach for multi-objective location-transportation problem for disaster response, Comp. Oper. Res., 2014, 41, 83–93.
• AGHABABAEI B., PISHVAEE M.S., BARZINPOUR F., A fuzzy bi-level programming approach to scarce drugs supply and ration planning problem under risk , Fuzzy Sets Syst., 2021, DOI: 10.1016/j. fss.2021.02.021.
• BASTIAANSSEN J., JOHNSON D., LUCAS K., Does transport help people to gain employment? A systematic review and meta-analysis of the empirical evidence, Transp. Rev., 2020, 40 (5), 607–628.
• CAO C., LIU Y., TANG O., GAO X., A fuzzy bi-level optimization mode l for multi-period post-disaster relief distribution in sustainable humanitarian supply chains, Int. J. Prod. Econ., 2021, 235, 108081.
• CHAKRABORTY D., JANA D.K., ROY T.K., A new approach to solve multi-objective multi-choice multi-item Atanassov’s intuitionistic fuzzy transportation problem using chance operator, J. Int. Fuzzy Syst., 2015, 28 (2), 843–865.
• CLEGG J., SMITH M., XIANG Y., YARROW R., Bilevel programming applied to optimizing urban transportation, Transp. Res. Part B: Meth., 2001, 35 (1), 41–70.
• DU J., LI X., YU L., DAN R., ZHOU J., Multi-depot vehicle routing problem for hazardous materials transportation: A fuzzy bilevel programming, Inf. Sci., 2017, 399, 201–218.
• GOSWAMI S., PANDA A., DAS C.B., Multi-objective cost varying transportation problem using fuzzy programming, Ann. Pure Appl. Math., 2014, 7 (1), 47–52.
• HO H.P., CHANG C.T., KU C.Y., On the location selection problem using analytic hierarchy proces and multi-choice goal programming, Int. J. Syst. Sci., 2013, 44 (1), 94–108.
• JACOBS G.D., GREAVES N., Transport in developing and emerging nations, Transp. Rev., 2003, 23 (2), 133–138.
• JALIL S.A., JAVAID S., MOHD MUNEEB S., A decentralized multi-level decision making model for solid transportation problem with uncertainty, Int. J. Syst. Assur. Eng. Manage., 2018, 9 (5), 1022–1033.
• JEFFREYS H., JEFFREYS B.S., Lagrange’s Interpolation Formula, Methods of Mathematical Physics 3rd Ed., Cambridge University Press, Cambridge 1988, 260.
• JI P., CHU K.F., A dual-matrix approach to the transportation problem , Asia Pacific J. Oper. Res., 2002, 19, 35–45.
• KAUR A., KUMAR A., A new method for solving fuzzy transportation problems using ranking function, Appl. Math. Model., 2011, 35 (12), 5652–5661.
• KAUR D., MUKHERJEE S., BASU K., Solution of a multi-objective and multi-index real-life transportation problem using different fuzzy membership functions, J. Opt. Theory Appl., 2015, 164, 666–678.
• KHALIL T.A., RAGHAV Y.S., BADRA N., Optimal solution of multi-choice mathematical programming problem using a new technique, Am. J. Oper. Res., 2016, 6, 167–172.
• KUMAR R., EDALATPANAH S.A., JHA S., SINGH R., A Pythagorean fuzzy approach to the transportation problem, Comp. Int. Syst., 2019, 5 (2), 255–263.
• LIANG T.F., Interactive multi-objective transportation planning decisions using fuzzy linear programming, Asia Pacific J. Oper. Res., 2008, 25 (1), 11–31.
• LIU G.S., ZHANG J.Z., Decision making of transportation plan, a bilevel transpor tation problem approach, J. Ind. Manage. Opt., 2005, 1 (3), 305–314.
• MAHAPATRA D.R., PANDA S., SANA S.S., Multi-choice and stochastic programming for transportation problem involved in supply of foods and medicines to hospitals with consideration of logistic distribution, RAIRO Oper. Res., 2020, 54 (4), 1119–1132.
• MAITI S.K., ROY S.K., Analysing interval and multi-choice bi-level programming for Stackelberg game using intuitionistic fuzzy programming, Int. J. Math. Oper. Res., 2020, 16 (3), 354–375.
• MARDANI A., ZAVADSKAS E.K., KHALIFAH Z., JUSOH A., MD NOR K., Multiple criteria decision-making techniques in transportation systems: a systematic review of the state of the art literature, Transport, 2016, 31 (3), 359–385.
• MIDYA S., ROY S.K., YU V.F., Intuitionistic fuzzy multi-stage multi-objective fixed charge solid transportation problem in a green supply chain, Int. J. Mach. Lear. Cyber., 2021, 12 (3), 699–717.
• MSIGWA R.E., LU Y., GE Y., ZHANG L., A smoothing approach for solving transportation problem with road-toll pricing and capacity expansions, J. Ineq. Appl., 2015, Art. No. 237.
• PRATIHAR J., KUMAR R., EDALATPANAH S.A., DEY A., Modified Vogel’s approximation method for transportation problem under uncertain environment, Compl. Int. Syst., 2001, 7 (1), 29–40.
• RANARAHU N., DASH J.K., ACHARYA S., Computation of multi-choice multi-objective fuzzy probabilistic transportation problem, Oper. Res.. Dev. Sect., 2018, 81–95.
• SCOTT R.A., GEORGE B.T., PRYBUTOK V.R., A public transportation decision-making model within a metropolitan area, Dec. Sci., 2016, 47 (6), 1048–1072.
• SINGH P., KUMARI S., SINGH P., Fuzzy efficient interactive goal programming approach for multi-objective transportation problems, Int. J. Appl. Comp. Math., 2017, 3, 505–525.
• SPERANZA M.G., Trends in transportation and logistics, European J. Oper. Res., 2018, 264 (3), 830–836.
• ZHANG H., GAO Z., Bilevel programming model and solution method for mixed transportation network design problem, J. Syst. Sci. Compl., 2009, 22, 446–459.

Identifiers

DOI

10.37190/ord210301