Optimal Vehicle Dispatching Schemes via Dynamic Pricing

TL;DR

This paper develops a convex optimization framework using Markov decision processes to compute revenue-optimal dynamic pricing and dispatching schemes for ride-sharing, demonstrating significant improvements over existing methods.

Contribution

It introduces an efficient algorithm for exact computation of optimal randomized pricing schemes via a convex MDP formulation, advancing ride-sharing revenue management.

Findings

The proposed scheme outperforms fixed and surge pricing in empirical tests.

The convex MDP approach enables exact solutions for complex pricing problems.

Empirical results show increased revenue and efficiency in real-world data.

Abstract

Over the past few years, ride-sharing has emerged as an effective way to relieve traffic congestion. A key problem for these platforms is to come up with a revenue-optimal (or GMV-optimal) pricing scheme and an induced vehicle dispatching policy that incorporate geographic and temporal information. In this paper, we aim to tackle this problem via an economic approach. Modeled naively, the underlying optimization problem may be non-convex and thus hard to compute. To this end, we use a so-called "ironing" technique to convert the problem into an equivalent convex optimization one via a clean Markov decision process (MDP) formulation, where the states are the driver distributions and the decision variables are the prices for each pair of locations. Our main finding is an efficient algorithm that computes the exact revenue-optimal (or GMV-optimal) randomized pricing schemes. We characterize the optimal solution of the MDP by a primal-dual analysis of a corresponding convex program. We also conduct empirical evaluations of our solution through real data of a major ride-sharing platform and show its advantages over fixed pricing schemes as well as several prevalent surge-based pricing schemes.