Comparison of IP and CNF Models for Control of Automated Valet Parking Systems

In automated valet parking system, a central computer controls a number of robots which have the capability to move in two directions, under cars, lift a car up, carry it to another parking slot, and drop it. We study the theoretical throughput limitations of these systems: Given a car park layout, an initial configuration of a car park (location of cars, robots), into a desired, terminal configuration, what is the optimal set of control instructions for the robots to reorganize the initial into the terminal configuration. We propose a discretization, and compare an Integer Programming model and a CNF-model on realworld and random test data.