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Multi-objective solid transportation problems with budget constraint in uncertain environment

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  • Pradip Kundu
  • Samarjit Kar
  • Manoranjan Maiti

Abstract

This paper investigates multi-objective solid transportation problems (MOSTP) under various uncertain environments. The unit transportation penalties/costs are taken as random, fuzzy and hybrid variables respectively, in three different uncertain multi-objective solid transportation models and in each case, the supplies, demands and conveyance capacities are fuzzy. Also, apart from source, demand and capacity constraints, an extra constraint on the total budget at each destination is imposed. Chance-constrained programming technique has been used for the first two models to obtain crisp equivalent forms, whereas expected value model is formulated for the last. We provide an another approach using the interval approximation of fuzzy numbers for the first model to obtain its crisp form and compare numerically two approaches for this model. Fuzzy programming technique and a gradient based optimisation - generalised reduced gradient (GRG) method are applied to beget the optimal solutions. Three numerical examples are provided to illustrate the models and programming.

Suggested Citation

  • Pradip Kundu & Samarjit Kar & Manoranjan Maiti, 2014. "Multi-objective solid transportation problems with budget constraint in uncertain environment," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(8), pages 1668-1682, August.
    • Handle: RePEc:taf:tsysxx:v:45:y:2014:i:8:p:1668-1682
    DOI: 10.1080/00207721.2012.748944
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    Cited by:

    1. Hailin Wu & Fengming Tao & Qingqing Qiao & Mengjun Zhang, 2020. "A Chance-Constrained Vehicle Routing Problem for Wet Waste Collection and Transportation Considering Carbon Emissions," IJERPH, MDPI, vol. 17(2), pages 1-21, January.
    2. Totan Garai & Dipankar Chakraborty & Tapan Kumar Roy, 2019. "Multi-objective Inventory Model with Both Stock-Dependent Demand Rate and Holding Cost Rate Under Fuzzy Random Environment," Annals of Data Science, Springer, vol. 6(1), pages 61-81, March.
    3. Deepika Rani & T. R. Gulati & Amit Kumar, 2015. "On Fuzzy Multiobjective Multi-Item Solid Transportation Problem," Journal of Optimization, Hindawi, vol. 2015, pages 1-13, March.
    4. Khurana, Archana & Adlakha, Veena & Lev, Benjamin, 2018. "Multi-index constrained transportation problem with bounds on availabilities, requirements and commodities," Operations Research Perspectives, Elsevier, vol. 5(C), pages 319-333.
    5. Pradip Kundu, 2021. "A multi-objective reliability-redundancy allocation problem with active redundancy and interval type-2 fuzzy parameters," Operational Research, Springer, vol. 21(4), pages 2433-2458, December.
    6. Pradip Kundu & Saibal Majumder & Samarjit Kar & Manoranjan Maiti, 2019. "A method to solve linear programming problem with interval type-2 fuzzy parameters," Fuzzy Optimization and Decision Making, Springer, vol. 18(1), pages 103-130, March.

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