Abstract
In present times, the e-commerce industry has become a crucial platform between the manufacturers and the common man. There might arise some situations in the market due to which manufacturers are not able to estimate the exact demand for their products, which may result in excess production. Moreover, the demand for the products in the market depends on the purchasing power of the common man. The decrease in purchasing power results in the low sale of the products. This uncertain situation of the market has been depicted by Bilevel Interval Linear Fractional Transportation Problem with distinct flows. The supply, demand, and cost coefficients in the objective functions at two levels are interval parameters. The two-level problem comprises of delivery of products from manufacturers to e-warehouses at the upper level and then to customers at the lower level. At upper level, flow is enhanced since the goods which are manufactured by the industries in large quantities need to be sold out. At lower level, flow is restricted while transporting the goods from e-warehouses to customers. Further, in order to promote the sale of the products, e-websites offer the customers free delivery of the products at their doorsteps. At the same time, they also pick the goods from them if the products are damaged or not of their choice or for any other reason. This in turn incurs the additional cost to the e-websites. The constraints in this defined problem are mixed. The interval parameters in the defined problem are tackled using the concept of centre and width of the interval. This converts the bilevel problem into a bilevel multi-objective transportation problem. A satisfactory solution to the problem is obtained by the fuzzy programming and goal programming approaches. A numerical is illustrated explaining the methodology. Further, the solutions are compared through these two techniques.
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Acknowledgements
The authors would like to thank the Institution of Eminence (IOE), University of Delhi for supporting this research. (Vide Grant No. IOE/2021/12/FRP). The authors are also grateful to the reviewers for their valuable suggestions, incorporating which has helped us in improving the quality of the paper to a great extent.
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This study was supported by the Institution of Eminence (IOE), University of Delhi (Vide Grant No. IOE/2021/12/FRP).
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Both the authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by [CKJ] and [RA]. The first draft of the manuscript was written by [RA] and both the authors commented on previous versions of the manuscript. Both the authors read and approved the final manuscript.
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Arora, R., Jaggi, C.K. An aspect of bilevel interval linear fractional transportation problem with disparate flows: a fuzzy programming approach. Int J Syst Assur Eng Manag 14, 2276–2288 (2023). https://doi.org/10.1007/s13198-023-02069-x
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DOI: https://doi.org/10.1007/s13198-023-02069-x
Keywords
- Interval uncertainty
- Enhanced flow
- Restricted flow
- Linear fractional transportation problem
- Bilevel programming
- Fuzzy programming
- Goal programming