Column generation for the truck and trailer routing problem with time windows

Motivated by the field sta routing and scheduling problem of an Austrian infrastructure service provider, which involves the planning of subroutes, we study the truck and trailer routing problem (TTRP) [2]. In the TTRP, two types of customers are considered: customers that can be visited by a truck pulling a trailer (denoted as vehicle customers) and customers that can only be visited by a truck alone (denoted as truck customers). Each customer has a given demand. In order to serve the customers, three di erent kinds of routes can be planned: routes that are carried out by a single truck (denoted as truck routes); routes that are carried out by a truck pulling a trailer (denoted as vehicle routes) without any intermediate decoupling; and routes carried out by a truck pulling a trailer involving truck-only subroutes. Each such subroute starts and ends at a vehicle customer. At this customer the trailer is decoupled and then re-coupled again at the end of the subroute. The truck has a capacity of Qtruck and the trailer a capacity of Qtrailer. Shifting loads from the trailer to the truck before departing on the next truck-only subroute is possible. The objective is to minimize the total routing cost which corresponds to the total distance traveled by the available vehicle fleet. An important aspect is that a trailer may not be picked up by a truck di erent from the one which decoupled it. Furthermore, each customer may only be visited once. This implies that a decoupling point cannot be used more than once: whenever a vehicle customer is used to park the trailer, it has to be served. However, several consecutive subroutes may start and end at the same vehicle customer.