A novel robust fuzzy stochastic programming for closed loop supply chain network design under hybrid uncertainty.

In today's business environments, the high importance of economic benefits and environmental impacts of using scrapped products has caused most companies to move to designing the closed loop supply chain network. This paper considers the closed loop supply chain network design problem under hybrid uncertainty, while there are two sources of uncertainty for most parameters, thus require fortifying of the robustness of the decision. The first source is that some uncertain parameters may be based on the future scenarios which are considered according to the probability of their occurrence. The second source is that the values of these parameters in each scenario are usually imprecise and can be specified by possibilistic distributions. In this case, the best robust decision has some additional properties in terms of mean value and variability of the objective function. We introduced two types of the variability named scenario variability and possibilistic variability. Possibility theory is used to choose a solution in such a problem and a novel robust fuzzy stochastic programming approach is proposed that has significant advantages. The performance of the proposed model is also compared with that of other models in term of the mean cost and variability by simulation.