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Multi-objective capacitated transportation problem with mixed constraint: a case study of certain and uncertain environment

Author

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  • Srikant Gupta

    (Aligarh Muslim University)

  • Irfan Ali

    (Aligarh Muslim University)

  • Aquil Ahmed

    (Aligarh Muslim University)

Abstract

In this paper, we have formulated a new model of multi-objective capacitated transportation problem (MOCTP) with mixed constraints. In this model, some objective functions are linear and some are fractional and are of conflicting in nature with each other. The main objective of this paper is to decide the optimum order of the product quantity which is to be shipped from source to the destination subject to the capacitated restriction on each route. Here the two situations have been discussed for the MOCTP model. In the first situation, we have considered that all the input information of the MOCTP model is exactly known and therefore a fuzzy goal programming approach have been directly used for obtaining the optimum order quantity of the product. While in the second situation the input information of the MOCTP model are uncertain in nature and this uncertainty have been studied and handled by the suitable approaches like trapezoidal fuzzy numbers, multi-choices, and probabilistic random variables respectively. Due to the presence of all these uncertainties and conflicting natures of objectives functions, we cannot solve this MOCTP directly. Therefore firstly we converted all these uncertainties into deterministic forms by using the appropriate transformation techniques. For this, the vagueness in MOCTP defined by trapezoidal fuzzy numbers has been converted into its crisp form by using the ranking function approach. Multichoices in input information parameters have been converted into its exact form by the binary variable transformation technique. Randomness in input information is defined by the Pareto probability distribution, and for conversion into deterministic form chance constrained programming has been used. After doing all these transformations, we have applied fuzzy goal programming approach for solving this resultant MOCTP model for obtaining the optimum order quantity. A case study has been done to illustrate the computational procedure.

Suggested Citation

  • Srikant Gupta & Irfan Ali & Aquil Ahmed, 2018. "Multi-objective capacitated transportation problem with mixed constraint: a case study of certain and uncertain environment," OPSEARCH, Springer;Operational Research Society of India, vol. 55(2), pages 447-477, June.
    • Handle: RePEc:spr:opsear:v:55:y:2018:i:2:d:10.1007_s12597-018-0330-4
    DOI: 10.1007/s12597-018-0330-4
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    References listed on IDEAS

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    1. Sankar Kumar Roy, 2014. "Multi-choice stochastic transportation problem involving Weibull distribution," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 21(1), pages 38-58.
    2. S. Acharya & M.P. Biswal, 2016. "Solving multi-choice multi-objective transportation problem," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 8(4), pages 509-527.
    3. Liu, Shiang-Tai & Kao, Chiang, 2004. "Solving fuzzy transportation problems based on extension principle," European Journal of Operational Research, Elsevier, vol. 153(3), pages 661-674, March.
    4. Chang, Ching-Ter, 2007. "Multi-choice goal programming," Omega, Elsevier, vol. 35(4), pages 389-396, August.
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    Cited by:

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    2. P. Senthil Kumar, 2020. "Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 11(1), pages 189-222, February.
    3. Pravash Kumar Giri & Manas Kumar Maiti & Manoranjan Maiti, 2023. "Profit maximization fuzzy 4D-TP with budget constraint for breakable substitute items: a swarm based optimization approach," OPSEARCH, Springer;Operational Research Society of India, vol. 60(2), pages 571-615, June.
    4. Md. Ashraful Babu & M. A. Hoque & Md. Sharif Uddin, 2020. "A heuristic for obtaining better initial feasible solution to the transportation problem," OPSEARCH, Springer;Operational Research Society of India, vol. 57(1), pages 221-245, March.
    5. Shalabh Singh & Sonia Singh, 2022. "Shipment in a multi-choice environment: a case study of shipping carriers in US," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 30(4), pages 1195-1219, December.

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