Charnes and Cooper’s Transformations for Solving Uncertain Multi-Item Fixed Charge Solid Transportation Problem

Abstract

This paper focusses on the multi-item fixed charge solid transportation problem (MIFCSTP) with parameters like transportation cost, fixed charge, conveyance capacities, and supply and demand values taken as uncertain variables. The model representing MIFCSTP with uncertain variables is known as an uncertain model which cannot be solved directly by standard techniques. So, to deal with uncertain MIFCSTP, the expected value model (EVM) and dependent chance-constrained model (DCCM) are formulated. Later, using the theory of uncertainty, these two models are converted into their corresponding deterministic forms. This crisp formulation of the EVM is solved directly by LINGO 18.0 software whereas the Charnes and Cooper’s transformation is applied on the deterministic form of the DCCM for converting it into linear form. Then, the optimal solution of the transformed linear form of the DCCM is obtained using LINGO 18.0 software. At the end, the application of the formulated models is demonstrated with the help of a numerical illustration.