Multi-choice fractional stochastic multi-objective transportation problem

Uncertainty in real-world fractional transportation problem is the major issue. In this paper, a multi-choice fractional stochastic multi-objective transportation problem (MCFS-MOTP) is investigated. Due to the uncertainty, in the introduced model, the coefficients of the fractional objective functions are a multi-choice type also, the parameters of the constraints are treated as multi-choice independent normally distributed random variables. Firstly, an interpolating polynomial is detailed utilizing practical qualities at nonnegative integer nodes to deal with any multi-choice parameters based on Newton divided difference method. Secondly, stochastic programming approach is applied to transform the probabilistic constraints into crisp ones. Moreover, we introduced a linearization methodology to work out the linear form of the problem. Finally, a fuzzy goal programming approach and the \(\epsilon \)-constrain method were utilized to think through the issue. Applicability of the proposed model was verified through a numerical example.