In real-world logistics and supply chain operations, decision-makers are often required to allocate resources before full information about demand is revealed, forcing them to make refined decisions once that data becomes fully available. This thesis addresses this challenge by proposing a two-stage stochastic model for a variant of the Variable Cost and Size Bin Packing Problem with Stochastic Items. The model reflects a realistic setting in which bins differ in cost and size, and aims to minimize total costs while ensuring feasible and efficient packing. The algorithm developed captures the trade-offs between early commitments and later adjustments under uncertainty, incorporating key constraints such as heterogeneous costs, item incompatibility, and multiple capacity dimensions.