Multimodal Capacity Planning with Uncertainty on Contract Fulfilment

Contracting with carriers or third-party logistics firms is a way to secure transportation or warehousing capacity for the next planning period. However, contracts are concluded under uncertainty regarding the demand of loads to be transported, the availability of contracted capacity and of the extra one if needed. The question is how much to contract of each type of capacity to minimize the costs of the contract and of ad-hoc future actions to redress an unfavorable situation. We model this planning problem by extending the Stochastic Variable Cost and Size Bin Packing Problem. Extensive numerical experiments are conducted considering the case of an express courier in a City Logistics environment.