Four-dimensional uncertain multi-objective multi-item transportation problem

Abstract

This paper considers a four-dimensional multi-objective multi-item transportation problem (4DMOMITP), where all the parameters are regarded as uncertain variables. In this paper, three mathematical models, namely expected value model (EVM), optimistic value model (OVM) and dependent optimistic-constrained model (DOCM), are discussed for the uncertain model of 4DMOMITP.Thesemodels are converted into their corresponding deterministic forms using different ranking criteria from uncertainty theory. These deterministic models are then solved by using the Lingo 18.0 software, utilizing three different classical approaches for obtaining a solution. A numerical example is given to illustrate the application of the model and the solution algorithm. A sensitivity analysis for the OVM and DOCM models has also been performed with respect to the confidence levels.