The classical transportation problem (TP), which entails the allocation of a (set of) product (products) from multiple origins to multiple destinations at the minimal feasible expense, encompasses a broad spectrum of significant transportation and industrial problems in reality. Within real-world scenarios, the supply capacities of goods at origins and the demands of goods at destinations are subject to variability and may be influenced by various internal and external factors. In this study, we develop a stochastic optimisation model for the classical TP that accounts for multiple types of products and uncertainty in both supply and demand quantities. This model includes uncertainties located on the right-hand side (RHS), making it a special type of stochastic models. To address this ensuing intricate problem, a matheuristic algorithm is constructed, composed of ideas from variable neighbourhood search (VNS), fixed set search (FSS), and partial mathematical optimisation. This algorithm demonstrates notable efficiency when compared to some alternative methodologies.