A branch and price algorithm for the combined vehicle routing and scheduling problem with synchronization constraints

In this paper we present a branch and price algorithm for the combined vehicle routing and scheduling problem with synchronization constraints. The synchronization constraints are used to model situations when two or more customers need simultaneous service. The synchronization constraints impose a temporal dependency between vehicles, and it follows that a classical decomposition of the vehicle routing and scheduling problem is not directly applicable. With our algorithm, we have solved 44 problems to optimality from the 60 problems used for numerical experiments. The algorithm performs time window branching, and the number of subproblem calls is kept low by adjustment of the columns service times.