In the current times of the predominance of COVID-19, almost all the countries are conducting inoculation drives. Given the market’s inability to compute how much to manufacture, how to transport and the frequently changing demand, the cost of safely and timely transporting the vaccines from factory to syringe is currently indeterminate. In this paper, we formulate this situation using a bilevel transportation problem with neutrosophic numbers (BLTP-NN). The problem comes from a vaccine manufacturing company where the vaccine is produced and then transported to different distribution centres from where it is further transported to various health centres for the conduction of their vaccination drive. The authors have tried to perceive this situation from two perspectives by formulating two different problems. The first problem is a bilevel linear fractional transportation problem which aims at minimizing the transportation cost in proportion to per unit maximization of quantity transported. The second problem is a bilevel indefinite quadratic transportation problem which aims at minimizing the transportation cost and depreciation cost. In both problems, cost coefficients are neutrosophic numbers along with availabilities and demands in the constraint set. These formulated bilevel transportation problems in neutrosophic environment are solved using goal programming strategy to arrive at a satisfactory solution. The relevance of this work is to help the decision makers in budgeting their finances related to the transportation by strategic disbursement leading to a smooth administration of vaccination program.

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In this paper, a bilevel problem is exhibited wherein both the manufacturers and e-traders want to minimize the cost of transportation as well as deterioration cost. In todays world, reliability on online ordering has increased manifold. The “app culture” has lured the common man to prefer virtual shopping over the physical one. The consumers can order the necessities or the goods of their choice through electronic delivery apps. The manufacturers have tied up with e-traders who in turn satisfy the consumers demand. With this aim, a bilevel indefinite quadratic transportation problem is dened. Sometimes it is difcult to estimate the daily demand of perishable products on a regular basis. Therefore, demand and supply parameters become uctuating in nature. To tackle this situation, bilevel indefinite quadratic transportation problem with intuitionistic fuzzy demand and supply parameters is formulated. This problem is dealt by converting fuzzy parameters into crisp ones. The transformed problem is then solved by two methods, intuitionistic fuzzy programming and fuzzy goal programming approach. To support the results, an example is also illustrated numerically representing the practical application of the problem. A comparative analysis of the solutions obtained from the two techniques is also presented. The problem is solved by computing software.