Constructive and blocking power in collaborative transportation

We empirically investigate constructive and blocking power concepts in transportation planning. Our main question is what do these concepts represent in collaborative transportation. We address it by studying cost allocation and coalition structure problems in a real-world case on forest transportation involving eight companies. The potential savings of collaboration in this case account for about 9 %. We find that players more centrally located tend to benefit from the nucleolus allocation, which takes into account only the constructive power. Other methods, which take into account the blocking power, namely the modiclus and the SM-nucleolus, correct the relative importance of the central players with respect to those in more peripheral areas. The blocking power acknowledges that the more peripheral companies, as a block, are still crucial to the collaboration, despite among themselves they have little opportunities for collaboration. Our main conclusion is that incorporating the blocking power as a criterion in a cost sharing rule for collaborative planning in transportation is important specially in the case where the coalition consists of one or few centrally located companies and several peripheral companies. A method based merely on the constructive power might extremely benefit the central companies, hurting the possibilities of sustaining the coalition.