In many practical cases one has to choose an arrangement of different objects so that they are compatible. Whenever the compatibility of the objects can be checked by a pair-wise comparison the problem can be moddeled using the graph-theoretic notion of cliques.

This paper introduces a special kind of multi-depot pickup and delivery problem. In contrast to the general pickup and delivery problem (GPDP, see e.g. [19,31]) all requests have to be picked up at or delivered to one central location which has the function of a hub or consolidation point. In...