  We consider a profit maximization problem in an urban mobility on-demand
service, of which the operator owns a fleet, provides both exclusive and shared
trip services, and dynamically determines prices of offers. With knowledge of
the traveler preference and the distribution of future trip requests, the
operator wants to find the pricing strategy that optimizes the total operating
profit of multiple trips during a specific period, namely, a day in this paper.
This problem is first formulated and analyzed within the dynamic programming
framework, where a general approach combining parametric rollout policy and
stochastic optimization is proposed. A discrete-choice-based price optimization
model is then used for the request level optimal decision problem and leads to
a practical and computationally tractable algorithm for the problem.
  Our algorithm is evaluated with a simulated experiment in the urban traffic
network in Langfang, China, and it is shown to generate considerably higher
profit than naive strategies. Further analysis shows that this method also
leads to higher congestion level and lower service capacity in the urban
traffic system, which highlights a need for policy interventions that balance
the private profit making and the system level optimality.
