We consider the logistics capacity planning problem arising in the context of supply-chain management. We address the tactical-planning problem of determining the quantity of capacity units, hereafter called bins, of different types to secure for the next period of activity, given the uncertainty on future needs in terms of demand for loads (items) to be moved or stored, and the availability and costs of capacity for these movements or storage activities. We propose a modeling framework introducing a new class of bin packing problems, the Stochastic Variable Cost and Size Bin Packing Problem. The resulting two-stage stochastic formulation with recourse assigns to the first stage the tactical capacity-planning decisions of selecting bins, while the second stage models the subsequent adjustments to the plan, securing extra bins and packing the items into the selected bins, performed each time the plan is applied and new information becomes known. We propose a new meta-heuristic based on progressive hedging ideas that includes advanced strategies to accelerate the search and efficiently address the symmetry strongly present in the problem considered due to the presence of several equivalent bins of each type. Extensive computational results for a large set of instances support the claim of validity for the model, efficiency for the solution method proposed, and quality and robustness for the solutions obtained. The method is also used to explore the impact on the capacity plan and the recourse to spot-market capacity of a quite wide range of variations in the uncertain parameters and the economic environment of the firm. 
Logistics capacity planning: A stochastic bin packing formulation and a progressive hedging meta-heuristic