TY - JOUR ID - 119248 TI - Computation of three-stage stochastic transportation planning under an uncertain environment JO - Annals of Optimization Theory and Practice JA - AOTP LA - en SN - 2588-3666 AU - Singh, Shubham AU - Nigam, Ritu AU - Chakraborty, Debjani AD - iit kharagpur AD - IIT Kharagpur AD - Department of Mathematics IIT Kharagpur Y1 - 2020 PY - 2020 VL - 3 IS - 3 SP - 93 EP - 115 KW - stochastic optimization KW - Chance constraints programming KW - Essen inequality DO - 10.22121/aotp.2020.252845.1047 N2 - 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. UR - https://aotp.fabad-ihe.ac.ir/article_119248.html L1 - https://aotp.fabad-ihe.ac.ir/article_119248_3f54634045711497ac70b96bb5d15e54.pdf ER -