# Multi-objective solid transportation problem under stochastic environment

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## Abstract

In real life, three-dimensional (solid) transportation problem is an uncertain multi-objective decision-making (MODM) problem. In particular, it involves searching for the best transportation set-up that meets the decision maker’s preferences by considering the conflicting objectives/criteria such as transportation cost, transportation time, environmental and social issues. To tackle such complex situations, this paper proposes a general formulation of the multi-objective solid transportation problem (STP) with some random parameters. The paper makes the following contributions: (i) proposes a solution methodology based on chance-constraint programming technique to solve an STP with the uncertainty characterized by gamma distribution, (ii) proposes the initial feasibility conditions for the problem and (iii) extends fuzzy programming approach for solving the multi-objective stochastic problems. A numerical example is presented to illustrate the model and methodology.

## Keywords

Solid transportation problem multi-objective decision making stochastic programming chance-constraint programming gamma distribution## Notes

### Acknowledgements

The authors are thankful to the reviewers for their thoughtful comments and suggestions, which improved the quality and presentation of the article.

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