Exact Solutions to the Symmetric and Asymmetric Vehicle Routing Problem with Simultaneous Delivery and Pick-Up

In reverse logistics networks, products (e.g., bottles or containers) have to be transported from a depot to customer locations and, after use, from customer locations back to the depot. In order to operate economically beneficial, companies prefer a simultaneous delivery and pick-up service. The resulting Vehicle Routing Problem with Simultaneous Delivery and Pick-up (VRPSDP) is an operational problem, which has to be solved daily by many companies. We present two mixed-integer linear model formulations for the VRPSDP, namely a vehicle-flow and a commodity-flow model. In order to strengthen the models, domain-reducing preprocessing techniques, and effective cutting planes are outlined. Symmetric benchmark instances known from the literature as well as new asymmetric instances derived from real-world problems are solved to optimality using CPLEX 12.1.

Particle placement and the case for “allostructions”

As a reaction against derivational frameworks, Construction Grammar accords no place to regular alternations between two surface patterns. This paper argues for a more tolerant position towards alternations. With respect to the well-known placement variability of verbal particles (pick up the book / pick the book up), the author grants that there is little reason for analysing one ordering as underlying the other but goes on to show that it is equally problematic to claim that the two orderings code two different meanings (or serve two different functions) and therefore cannot be linked in the grammar as variants of a single category. The alternative offered here is to consider the two orderings as two “allostructions” of a more general transitive verb-particle construction underspecified for word order.