A branch-and-price algorithm for the vehicle routing problem with roaming delivery locations

•We study the vehicle routing problem with roaming delivery locations (VRPRDL) motivated by the interest in trunk delivery applications.•We present an efficient branch-and-price algorithm for solving the VRPRDL optimally.•We perform an extensive computational study to test the performance of our algorithm.•We also solve the problem considering a hybrid delivery strategy and analyze the benefits of making optimal use of the trunk delivery option.

We study the vehicle routing problem with roaming delivery locations in which the goal is to find a least-cost set of delivery routes for a fleet of capacitated vehicles and in which a customer order has to be delivered to the trunk of the customer's car during the time that the car is parked at one of the locations in the (known) customer's travel itinerary. We formulate the problem as a set-covering problem and develop a branch-and-price algorithm for its solution. The algorithm can also be used for solving a more general variant in which a hybrid delivery strategy is considered that allows a delivery to either a customer's home or to the trunk of the customer's car. We evaluate the effectiveness of the many algorithmic features incorporated in the algorithm in an extensive computational study and analyze the benefits of these innovative delivery strategies. The computational results show that employing the hybrid delivery strategy results in average cost savings of nearly 20% for the instances in our test set.