Uncertain programming model for multi-item solid transportation problem

TL;DR

This paper introduces an uncertain multi-objective transportation model for multiple items, converting it into deterministic problems using uncertainty theory, and demonstrates its application with a numerical example.

Contribution

It presents a novel uncertain programming model for multi-item transportation problems and converts it into solvable deterministic problems using uncertainty theory techniques.

Findings

Model successfully converts uncertain parameters into deterministic equivalents.

The approach effectively solves multi-item transportation problems with constraints.

Numerical example demonstrates the model's practical applicability.

Abstract

In this paper, an uncertain Multi-objective Multi-item Solid Transportation Problem (MMSTP) based on uncertainty theory is presented. In the model, transportation costs, supplies, demands and conveyances parameters are taken to be uncertain parameters. There are restrictions on some items and conveyances of the model. Therefore, some particular items cannot be transported by some exceptional conveyances. Using the advantage of uncertainty theory, the MMSTP is first converted into an equivalent deterministic MMSTP. By applying convex combination method and minimizing distance function method, the deterministic MMSTP is reduced into single objective programming problems. Thus, both single objective programming problems are solved using Maple 18.02 optimization toolbox. Finally, a numerical example is given to illustrate the performance of the models.