Bilevel transportation problem in neutrosophic environment

Abstract

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.

Solar Power Plant Location Selection Problem by using ELECTRE-III Method in Pythagorean Neutrosophic Programming Approach (A case study on Green Energy in India)

“…Neutrosophic set theory [NST]as an extension of the traditional crisp, fuzzy, and intuitionistic fuzzy set theories introduced by Smarandache F., in 1998 (Smarandache 1998) (Smarandache, Ali, and Khan 2019;Ali and Smarandache 2017;Ye 2018;Abdel-Baset et al, n.d.;Akram, Shumaiza, and Smarandache 2018;Singh, Arora, and Arora 2022;Khatter 2020;Smarandache, n.d.;Rizk-Allah, Hassanien, and Elhoseny 2018;Dat et al 2019;.…”

Transport Task Models with Variable Supplier Availabilities

“…As a criterion for optimality in the transport task, minimization of total transport costs is usually considered [7][8][9], i.e., at certain transport costs from all points of departure [10,11] to all reception points, it is necessary to define a transport plan [12] that satisfies the stated needs of the receiving points with the available quantities of stocks at the points of departure at minimum total transport costs [13][14][15]. This model is known as the transport problem by criterion value [16][17][18]. Some modifications of the transport task by criterion value are also well known [7,19], taking into account the specifics of transport activities.…”

Fully Bipolar Single-Valued Neutrosophic Transportation Problems

“…Kumar [43] presented the cut of single-valued pentagonal neutrosophic numbers and also introduced the arithmetic operation of single-valued pentagonal neutrosophic numbers. By using two different objective functions, Singh et al [44] formulated the journey of a vaccine from its manufacture to its delivery using bilevel transportation problems in a neutrosophic environment. Veeranani et al [45] solved the multiobjective fractional transportation problem by using the neutrosophic goal programming approach [46][47][48].…”