Multi-objective solid transportation problem under stochastic environment
- 34 Downloads
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.
KeywordsSolid transportation problem multi-objective decision making stochastic programming chance-constraint programming gamma distribution
The authors are thankful to the reviewers for their thoughtful comments and suggestions, which improved the quality and presentation of the article.
- 2.Schell E D 1955 Distribution of a product by several properties. In: Proceedings of the Second Symposium in Linear Programming, DCS/Comptroller HQ, US Air Force, Washington, DC, vol. 2, pp. 615–642Google Scholar
- 14.Roy S, Mahapatra D and Biswal M P 2012 Multi-choice stochastic transportation problem with exponential distribution. Journal of Uncertain Systems 6: 200–213Google Scholar
- 15.Cui Q and Sheng Y 2012 Uncertain programming model for solid transportation problem. Information 15: 342–348Google Scholar
- 23.Deb K 1999 Solving goal programming problems using multi-objective genetic algorithms. In: Proceedings of the 1999 Congress on Evolutionary Computation, IEEE, Washington, DC, pp. 77–84Google Scholar