%0 Journal Article
%T Computation of three-stage stochastic transportation planning under an uncertain environment
%J Annals of Optimization Theory and Practice
%I Firouzabad Institute of Higher Education
%Z 2588-3666
%A Singh, Shubham
%A Nigam, Ritu
%A Chakraborty, Debjani
%D 2020
%\ 12/01/2020
%V 3
%N 3
%P 93-115
%! Computation of three-stage stochastic transportation planning under an uncertain environment
%K stochastic optimization
%K Chance constraints programming
%K Essen inequality
%R 10.22121/aotp.2020.252845.1047
%X Stochastic programming is often used to solve optimization problems where parameters are uncertain. In this article, we have proposed a mathematical model for a three-stage transportation problem, where the parameters, namely transport costs, demand, unload capacity and external purchasing costs are uncertain. In order to remove the uncertainty, we have proposed a new transformation technique to reformulate the uncertain model deterministically with the help of Essen inequality. The obtained equivalent deterministic model is nonlinear. Furthermore, we have provided a theorem to ensure that the deterministic model gives a feasible solution. Finally, a numerical example, following uniform random variables, is presented to illustrate the model and methodology.
%U http://aotp.fabad-ihe.ac.ir/article_119248_3f54634045711497ac70b96bb5d15e54.pdf