Computation of Some Stochastic Transportation Problems Using Essen Inequality

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.