An aspect of bilevel interval linear fractional transportation problem with disparate flows: a fuzzy programming approach

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.