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A decentralized multi-level decision making model for solid transportation problem with uncertainty

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Abstract

In this paper, a multi-level model for the solid transportation problem having uncertain variables is presented. Multi-level programming deals with the situation where more than one decision maker is available to model decentralized planning problem in any hierarchical system. In the model presented in this paper, all the parameters involved viz. transportation costs, supply availabilities, demands and conveyance capacities are considered as uncertain parameters. As the problem is based on uncertainty theory, the idea of minimizing (or maximizing) the expectation of objective functions under the set of chance constraints is followed to formulate the problem. A crisp model equivalent to the multi-level uncertain solid transportation problem is also given. A fuzzy based solution approach for solving multi-level programming problems is discussed to solve the presented model. Further, a numerical example of a three-level uncertain solid transportation problem with two conveyance options is given in order to understand the model more clearly.

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Acknowledgements

Authors are thankful to the reviewers and the editor for the insightful revision suggestions. The second author is also thankful to the University Grants Commission, New Delhi, India for providing financial assistance under the UGC-BSR Research start-up grant, (No. F.30-90/2015(BSR), FD Diary No. 11767, dated: 02-03-2015), to carry out this research work.

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Authors and Affiliations

  1. Department of Statistics and Operations Research, Aligarh Muslim University, Aligarh, India

    Syed Aqib Jalil, Shakeel Javaid & Syed Mohd Muneeb

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  1. Syed Aqib Jalil
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  2. Shakeel Javaid
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  3. Syed Mohd Muneeb
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Correspondence to Syed Aqib Jalil.

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Jalil, S.A., Javaid, S. & Muneeb, S.M. A decentralized multi-level decision making model for solid transportation problem with uncertainty. Int J Syst Assur Eng Manag 9, 1022–1033 (2018). https://doi.org/10.1007/s13198-018-0720-2

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  • DOI: https://doi.org/10.1007/s13198-018-0720-2

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