Dynamic Vehicle Routing Problem with Prompt Confirmation of Advance Requests

TL;DR

A novel computational approach is proposed for this vehicle routing problem, which integrates a quick insertion search for prompt confirmation with an anytime algorithm for continual optimization, and which guides both the insertion and the anytime algorithms towards optimal, non-myopic solutions.

Abstract

Transit agencies that operate on-demand transportation services have to respond to trip requests from passengers in real time, which involves solving dynamic vehicle routing problems with pick-up and drop-off constraints. Based on discussions with public transit agencies, we observe a real-world problem that is not addressed by prior work: when trips are booked in advance (e.g., trip requests arrive a few hours in advance of their requested pick-up times), the agency needs to promptly confirm whether a request can be accepted or not, and ensure that accepted requests are served as promised. State-of-the-art computational approaches either provide prompt confirmation but lack the ability to continually optimize and improve routes for accepted requests, or they provide continual optimization but cannot guarantee serving all accepted requests. To address this gap, we introduce a novel problem formulation of dynamic vehicle routing with prompt confirmation and continual optimization. We propose a novel computational approach for this vehicle routing problem, which integrates a quick insertion search for prompt confirmation with an anytime algorithm for continual optimization. To maximize the number requests served, we train a non-myopic objective function using reinforcement learning, which guides both the insertion and the anytime algorithms towards optimal, non-myopic solutions. We evaluate our computational approach on a real-world microtransit dataset from a public transit agency in the U.S., demonstrating that our proposed approach provides prompt confirmation while significantly increasing the number of requests served compared to existing approaches.

Figures (14)

• Figure 1: During service, (1) requests arrive following a known distribution (e.g., based on historical data); (2) upon the arrival of each request, we decide whether to accept or reject the request given the current state of the service; (3) we promptly notify the passenger of our decision; (4) until the next request arrives, we continuously optimize route plans to better accommodate future requests. Symbols $p_k$ and $d_k$ represent the pickup and dropoff of request $k$, respectively.
• Figure 2: Distribution of request rejection rates across 5 different episodes from the real-world microtransit data.
• Figure 3: Distribution of request rejection rates across 5 different episodes from the NYC taxi data.
• Figure 4: Distribution of rejection rates across 5 different episodes from the real-world microtransit data, with various running-time limits for the anytime algorithm (in seconds).
• Figure 5: Distribution of rejection rates for the trained policy $\pi^*$ with neural-network architectures based on MLP ($\blacksquare$), KAN ($\blacksquare$), and CNN ($\blacksquare$), across 5 different episodes from the microtransit data.