A Novel Scheduling Method for Missile VRP

The two-echelon vehicle routing problem (2E-VRP) has become the key issue in the large scale transportation. One of its variants, the two-echelon vehicle routing problem with satellites synchronization (2E-VRP-SS), considers an additional constraint that the concerned satellites have no capacity and the actions of two kinds of vehicles in the satellites are restrained. Based on 2E-VRP-SS, this paper investigates a new problem of Missile Vehicle routing problem (Missile VRP), which considers some challenging constraints, e.g., the same customer may have to be served by multiple vehicles at the same time, vehicles are allowed to serve multiple customers without returning to satellites, more types of places, including base, launching position, depots and hidden reloading positions, are taken into account. To fulfill the launching demands, e.g., some given numbers of missiles should be launched at launching positions, we propose a new method to schedule the trajectories and actions of all concerned vehicles. The optimization cost of our method is measured by the total travelling distance of all vehicles, which is roughly proportional to the total gasoline consumption. In order to minimize the concerned cost, our method introduces an atomic mission decomposition (AMD) strategy, which considers one unscheduled missile at one time and formulates a list of candidate vehicle trajectory solutions. For each candidate solution, its total estimated cost is the sum of both the real cost of all scheduled missiles and the predicted cost of unscheduled missiles. All candidate solutions are sorted according to their estimated cost and inserted into a solution queue. Each time step, the first one in the solution queue, whose estimated cost is the minimal, is processed by AMD. As AMD may explosively increase the solution queue and exceeds the computer memory’s capacity, our method introduce a strategy to adaptively adjust (increase) a scaling parameter (SP) which is proportional to the predicted cost of unscheduled missiles. When the current computer memory cannot accommodate more candidate solutions, SP is increased to reduce the solution queue length at the cost of potential deviation from the optimal performance. The proposed scheduling method with AMD and SP is verified through some CMT4 instances and demonstrates good performance, which is quite close to that by the exhaustive method, at fast speed.