The Synchronized Vehicle Dispatching Problem

The synchronized Vehicle Dispatching Problem (SVDP) is a transportation problem that arises in many real world situations. One that illustrates well this problem is special version of the Dial-a-Ride problem, in which some disabled persons require assistance in order to prepare for transportation. In this case, a special team is sent to the residence of the special customer a few minutes before the vehicle to insure that the transfer is made safely and efficiently. The help can vary from dressing for winter conditions to providing wheelchair assistance and is not usually required at all times or by all customers. This means the schedule of the special assistance teams needs to be synchronized with the schedules of the rest of the fleet. To our knowledge this problem has not yet been presented in the literature, however there are many variants of the Vehicle Dispatching Problem covering many real life applications. Gendreau and Potvin [1], Qiu and Hsu [6] and Psaraftis [5] have published detailed surveys describing the different problems and solution approaches. Most efficient algorithms address this problem with local search techniques (like Tabu search for instances). Ichoua [3] has later introduced a taxonomy to further categorize the problems of this class. The synchronization constraints make this problem quite hard to solve using traditional local search methods. For instance, if the insertion of a special customer delays the route of a special vehicle then all regular visits associated with that route must also be delayed, independently of the vehicle that serviced them. But delaying a regular vehicle means delaying also the visits associated with other special customers and so on. This high number of interconnections means that to insert one customer one might have to recompute the visit time of every customer already inserted. Constraint Programming thus seems well suited for this kind of problem since it not only provides an easy way to express the synchronization constraints but, by representing visit times as domain variables and by propagating the synchronization constraints only when needed, it allows an efficient implementation of those constraints.