Industries growth drives transportation development, leading to diverse methods. This expansion brings challenges, notably the stochastic fuzzy transportation problem (SFTP), a probabilistic chance- constrained programming (CCP) issue. SFTP handles fuzzy objectives amid supply-demand randomness. The transportation problem's (TP) core aim is efficient product movement between customers and producers to meet demand at a lower cost. TP's parameters encompass cost, supply, and demand. Uncertainties in reality include randomness and fuzziness. Randomness reflects potential outcomes and is quantified using random variables (RVs). Real-world scenarios involve multiple objectives, e.g., cost and time minimization. This study addresses the multi- objective transportation problem within a stochastic- fuzzy context, using Weibull distribution. The goal is to optimize transportation quantities considering real-world uncertainties.