Multi-objective solid transportation problem under stochastic environment

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.