Bin Packing Problem with uncertainty on item availability: an application to Capacity Planning in Logistics

Most modern companies are part of international economic networks, where goods are produced under different strategies, then transported over long distances and stored for variable periods of time at different locations along the considered network. These activities are often performed by first consolidating goods in appropriate bins, which are then stored at warehouses and shipped using multiple vehicles through various transportation modes. Companies thus face the problem of planning for sufficient capacity, e.g., negotiating it with third party logistic firms (3PLs) that specify both the capacity to be used and the logistical services to be performed. Given the time lag that usually exists between the capacity-planning decisions and the operational decisions that define how the planned capacity is used, the common assumption that all information concerning the parameters of the model is known is unlikely to be observed. We therefore propose a new stochastic problem, named the Variable Cost and Size Bin Packing Problem with Stochastic Items. The problem considers a company making a tactical capacity plan by choosing a set of appropriate bins, which are defined according to their specific volume and fixed cost. Bins included in the capacity plan are chosen in advance without the exact knowledge of what items will be available for the dispatching. When, during the operational phase, the planned capacity is not sufficient, extra capacity must be purchased. An extensive experimental plan is used to analyze the impact that diversity in instance structure has on the capacity planning and the effect of considering different levels of variability and correlation of the stochastic parameters related to items.