Pricing for a last-mile transportation system

The Last-Mile Problem refers to the provision of travel service from the nearest public transportation node to a home or other destination. Last-Mile Transportation System (LMTS), which has recently emerged, provide on-demand shared transportation. We consider an LMTS with multiple passenger types—adults, senior citizens, children, and students. The LMTS designer determines the price for the passengers, last-mile service vehicle capacity, and service fleet size (number of vehicles) for each last-mile region to maximize the social welfare generated by the LMTS. The level of last-mile service (in terms of passenger waiting time) is approximated by using a batch arrival, batch service, multi-server queueing model. The LMTS designer's optimal decisions and optimal social welfare are obtained by solving a constrained nonlinear optimization problem. Our model is implemented in numerical experiments by using real data from Singapore. We show the optimal annual social welfare gained is large. We also analyze a counterpart LMTS in which the LMTS designer sets an identical price for all passenger types. We find that in the absence of price discounts for special groups of passengers, social welfare undergoes almost no change, but the consumer surplus of passengers in special groups suffers significantly.