Benders Decomposition with Delayed Disaggregation for the Active Passive Vehicle Routing Problem

We investigate a new exact solution approach for the Active Passive Vehicle Routing Problem, a vehicle routing problem with complicated temporal synchronisation requirements between vehicles. A key contribution is the introduction of a new principle, Delayed Disaggregation, for Benders Decomposition to produce disaggregated optimality cuts when traditional block-diagonality fails. The technique is applied to a new Mixed Integer Programming formulation of the Active Passive Vehicle Routing Problem. The formulation is built on coupled movements between active and passive vehicles, and solved using Combinatorial Benders Decomposition. The synchronisation constraints result in an interesting subproblem for which we present a tailored algorithm. The new method outperformed the existing Branch-and-Price method by two orders of magnitude and solves 74 instances to optimality for the first time. We investigate the performance impact of route enumeration, a heuristic and valid inequalities on the base Benders algorithm.