Coordinating Supply and Demand on an On-Demand Service Platform with Impatient Customers

We consider an on-demand service platform using earning-sensitive independent providers with heterogeneous reservation price (for work participation) to serve its time and price-sensitive customers with heterogeneous valuation of the service. As such, the supply and demand are "endogenously" dependent on the price the platform charges its customers and the wage the platform pays its independent providers. We present an analytical model with endogenous supply (number of participating agents) and endogenous demand (customer request rate) to study this on-demand service platform. To coordinate endogenous demand with endogenous supply, we include the steady-state waiting time performance based on a queueing model in the customer utility function to characterize the optimal price and wage rates that maximize the profit of the platform. We first analyze a base model that uses a fixed payout ratio (i.e., the ratio of wage over price), and then extend our model to allow the platform to adopt a time-based payout ratio. We find that it is optimal for the platform to charge a higher price when demand increases; however, the optimal price is not necessarily monotonic when the provider capacity or the waiting cost increases. Furthermore, the platform should offer a higher payout ratio as demand increases, capacity decreases or customers become more sensitive to waiting time. We also find that the platform should lower its payout ratio as it grows with the number of providers and customer demand increasing at about the same rate. We use a set of actual data from a large on-demand ride-hailing platform to calibrate our model parameters in numerical experiments to illustrate some of our main insights.