Optimal time-differentiated pricing for a competitive mixed traditional and crowdsourced event parking market

Abstract

An event-based parking pricing problem, the Crowdsourced Event Parking Market Pricing Problem, is proposed wherein parking lot owners and others who are willing to rent out privately owned spaces compete to attract drivers who are looking for available parking spaces. Each parking location owner’s problem is modeled as a bi-level program, where the upper-level parking garages, individuals and consolidators (the players) compete for customers, setting their prices to maximize revenue given the response of the lower-level followers. The lower-level followers choose their parking locations based on the utilities they derive from the spaces, which is a function of the proximity of the spaces to their destinations, parking fees and crowdedness. Prices are set as a function of the time of reservation. Reservation-time based pricing enables price differentiation for late comers either in the form of lower prices to attract last-minute customers when excess spaces are anticipated or higher-pricing if few spaces are expected to remain empty. A multi-period, stochastic Equilibrium Problem with Equilibrium Constraints (EPEC) formulation of the Crowdsourced Event Parking Market Pricing Problem is presented, and a diagonalization method with embedded gradient ascent approach for solution of individual player Mathematical Programs with Equilibrium Constraints (MPECs) is proposed for its solution. Both supply- and demand-side uncertainties are explicitly modeled. Solutions provide competitive parking prices set by reservation time for each parking facility, whether the facility involves a large parking garage or single parking space owner. Numerical experiments were conducted to illustrate the proposed concepts and assess the potential impact of crowdsourced parking spaces on the parking market. The results show that social welfare increases by more than 5% when crowdsourced parking locations account for 7% of the parking market. Results from additional numerical experiments show that ignoring stochasticity results in revenue loss for all parking owners. The developed techniques aim to facilitate existing and new parking facility owners to participate in crowdsourced event-parking markets.