Layout Design of Parking Lots with Mathematical Programming

There is a vivid debate in cities all over the world on how to distribute the restricted space in urban areas among stakeholders. Urban design movements such as new pedestrianism or Copenhagenization advocate that too much space is attributed to cars. In this context, our research investigates the optimization of parking lots with the help of mathematical programming. For the given ground plot of a parking lot, we maximize the number of parking spaces each reachable via a driving lane, so that the urban space attributed to the parking of cars is efficiently used. Based on a grid of squares in which we rasterize the ground plot, this paper presents mixed-integer programs based on three different resolutions for orthogonal parking. Our computational study explores the tradeoff between the additional parking spaces promised by a higher resolution and the increased computational effort because of the larger solution space (and vice versa). We compare our optimization approaches with a sample of 177 real-world parking lots and show that optimization can be a serviceable car park design tool with the help of a case study.