Dynamic Control of Logistics Queueing Networks for Large-Scale Fleet Management

Dynamic fleet management problems are normally formulated as networks over dynamic networks. Additional realism usually implies the inclusion of complicating constraints, typically producing exceptionally large integer programs. In this paper, we present for the first time the formulation of dynamic fleet management problems in an optimal control setting, using a novel formulation called a Logistics Queueing Network (LQN). This formulation replaces a single, large optimization problem with a series of very small problems that involve little more than solving a single sort at each point in space and time. We show that this approach can produce solutions that are within a few percent of a global optimum but provide for considerably more flexibility than standard linear programs.