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 setup 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.
An intuitive way to handle optimization problems with random parameters is to undergo stochastic optimization. The aim of this paper is to reduce the complexity of the transportation problem where the parameters of the problem are characterized by the random uncertainty. In this study, we consider a transportation problem with stochastic uncertainty. We propose an alternative method of chance constraint based on Essen inequality to eradicate the stochastic uncertainty and obtain the computationally tractable formulation of the stochastic problem.In addition, we have established computationally tractable formulations of the problem with various kinds of random distributions, namely uniform distribution, exponential distribution, and gamma distribution. Finally, we present some numerical examples and compare the results with two current models, namely the E-model and the V-model.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.