This paper presents the study of a multichoice multiobjective transportation problem (MCMOTP) when at least one of the objectives has multiple aspiration levels to achieve, and the parameters of supply and demand are random variables which are not predetermined. The random variables shall be assumed to follow extreme value distribution, and the demand and supply constraints will be converted from a probabilistic case to a deterministic one using a stochastic approach. A transformation method using binary variables reduces the MCMOTP into a multiobjective transportation problem (MOTP), selecting one aspiration level for each objective from multiple levels. The reduced problem can then be solved with goal programming. The novel adapted approach is significant because it enables the decision maker to handle the many objectives and complexities of real-world transportation problem in one model and find an optimal solution. Ultimately, a mixed-integer mathematical model has been formulated by utilizing GAMS software, and the optimal solution of the proposed model is obtained. A numerical example is presented to demonstrate the solution in detail.