VRP with Minimum Delivery Latency Using Linear Programming

Vehicle Routing Problems (VRPs) concern allocating multiple vehicles to service requests with routes that start and end at a depot, visit all requests, and minimize some operational cost. Many UAV situations can be modeled in a manner that represents tasks to be accomplished by service requests and UAVs as agents that fulfill these requests. Often, communications are restricted by available power, data rate, noise margins, and cost. These constraints cause information gathered at request locations to be delivered only when the UAV returns to the “depot.” In other words, UAVs must be allocated to services requests and then deliver information gathered at the request location to a communication range to be able to transmit information back to a command and control HQ. Because of limited communication ranges which result from limited power onboard small UAVs, information is not delivered until the UAV returns to the depot. Research on similar problems show some related work on minimizing the latency of the pickup of requests but not the delivery. This work attempts to study the VRP with minimum delivery latency and formulate a Linear Programming (LP) solution. The objective function is shown to be nonlinear, but it can be linearized at a cost: many new variables are added to linearize it. This in turn, makes the problem intractable, and only solutions to small problems are obtained.