Towards Dynamic Pricing for Shared Mobility on Demand using Markov Decision Processes and Dynamic Programming

TL;DR

This paper develops a Markov Decision Process framework with a Dynamic Programming algorithm to optimize dynamic pricing in shared mobility services, aiming to balance demand and supply by regulating estimated waiting times.

Contribution

It introduces a novel MDP formulation and DP solution for real-time dynamic pricing in SMoDS, integrating demand-supply balance with passenger behavior modeling.

Findings

EWT regulation effectively balances demand and supply.

The proposed method demonstrates promising results in offline simulations.

Framework can be extended for online pricing with behavioral models.

Abstract

In a Shared Mobility on Demand Service (SMoDS), dynamic pricing plays an important role in the form of an incentive for the decision of the empowered passenger on the ride offer. Strategies for determining the dynamic tariff should be suitably designed so that the incurred demand and supply are balanced and therefore economic efficiency is achieved. In this manuscript, we formulate a discrete time Markov Decision Process (MDP) to determine the probability desired by the SMoDS platform corresponding to the acceptance rate of each empowered passenger at each state of the system. We use Estimated Waiting Time (EWT) as the metric for the balance between demand and supply, with the goal that EWT be regulated around a target value. We then develop a Dynamic Programming (DP) algorithm to derive the optimal policy of the MDP that regulates EWT around the target value. Computational experiments are conducted that demonstrate the regulation of EWT is effective, through various scenarios. The overall demonstration is carried out offline. The MDP formulation together with the DP algorithm can be utilized to an online determination of the dynamic tariff by integrating with our earlier works on Cumulative Prospect Theory based passenger behavioral modeling and the AltMin dynamic routing algorithm, and form the subject of future works.