The selective vehicle routing problem in a collaborative environment

We consider a selective vehicle routing problem, in which customers belonging to di?fferent partners in a logistic coalition are served in a single logistic operation with multiple vehicles. Each partner determines a cost of non-delivery (CND) for each of its customers, and a central algorithm creates an operational plan, including the decision on which customers to serve and in which trip. Th?e total transportation cost of the coalition is then divided back to the partners through a cost allocation mechanism. Th?is paper investigates the eff?ect on the cost allocation of a partner’s strategy on nondelivery penalties (high/low) and the properties of its customer locations (distance to the depot, degree of clustering). Th?e eff?ect of the cost allocation method used by the coalition is also investigated. We compare the well-known Shapley value cost allocation method to our novel problem-speci?fic method: the CND-weighted cost allocation method. We prove that an adequate cost allocation method can provide an incentive for each partner to behave in a way that benefi?ts the coalition. Further, we develop a transformation that is able to transform any cost allocation into an individually rational one without losing this incentive.