A KKM approach for inverse capacitated transportation problem in neutrosophic environment

Inverse optimization is one of the interesting areas in both fundamental and applied research. This paper introduces a new approach, named as Khalifa, Kumar, and Mirjalili (KKM) approach, for solving the inverse capacitated transportation problem (ICTP) in a neutrosophic environment. The problem is considered with unit transportation cost associated with the single-valued trapezoidal neutrosophic numbers. Using the proposed KKM approach, the objective of the research work is to make the transportation cost as low as possible, which can lead to an optimal feasible solution. Based on the score function, the neutrosophic problem is first converted into an equivalent deterministic problem and then into a linear programming (LP) problem. Afterwards, by applying the dual and optimality conditions the inverse problem is obtained. In the end, an illustrative example is given to support the proposed approach and to gain more insights.