Mathematical formulation of a deterministic parking reservation system (PRS) with fixed costs

A problem faced in major metropolitan areas, is the search for parking spaces that results in a tremendous loss in productivity time, excess pollution, and driver frustration. The most traditional methods utilized to alleviate the search for parking are fixed signs to parking lots, variable message signs that continuously update the number of available parking spaces at specific parking lots, route planning algorithms from an origin to a specific parking lot, as well as disincentives to the use of personal automobiles through parking pricing and strict enforcement of parking violations. An innovative methodology to address at least partially the search for parking is through a parking reservation system. In this paper, a mathematical formulation is presented for performing parking space assignment to the users based on the minimization of the system wide parking cost subject to the assignment constraints and the parking lot capacity constraints, The problem can be solved with any commercially available solver and it can be shown to yield binary integer solutions.