Optimal Supply Control for Shared Mobility with Logit Mode-Choice Dynamics

In this paper, we discuss the evolution of mode shares over time in a stylised single origin-destination setting with fixed demand and linear non-separable latency functions. One of the modes is assumed to resemble a ride-hailing service whose operator can control its supply over time. The operator is assumed to be interested in reducing costs while trying to achieve a target market share and the problem is formulated as a finite-horizon continuous optimal control problem. We derive the conditions on supply that ensure a unique stochastic user equilibrium and present a necessary condition that achieves the operator's targets. The framework is demonstrated using simulation.