This paper presents the first full-fledged branch-and-price (bap) algorithm for the capacitated arc-routing problem (CARP). Prior exact solution techniques either rely on cutting planes or the transformation of the CARP into a node-routing problem. The drawbacks are either models with inherent...

In many branch-and-price algorithms, the column generation subproblem consists of computing feasible constrained paths. In the capacitated arc-routing problem (CARP), elementarity constraints concerning the edges to be serviced and additional constraints resulting from the branch-and-bound...

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...