Capacity Planning with Uncertainty on Contract Fulfillment

This paper focuses on the tactical planning problem faced by a shipper which seeks to secure transportation and warehousing capacity, such as containers, vehicles or space in a warehouse, of different sizes, costs, and characteristics, from a carrier or logistics provider, while facing different sources of uncertainty. The uncertainty can be related to the loads to be transported or stored, the cost and availability of ad-hoc capacity on the spot market in the future, and the availability of the contracted capacity in the future when the shipper needs it. This last source of uncertainty on the capacity loss on the contracted capacity is particularly important in both long-haul transportation and urban distribution applications, but no optimization methodology has been proposed so far. We introduce the Stochastic Variable Cost and Size Bin Packing with Capacity Loss problem and model that directly address this issue, together with a metaheuristic to efficiently address it. We perform a set of extensive numerical experiments on instances related to long-haul transportation and urban distribution contexts and derive managerial insights on how such capacity planning should be performed.