Online Routing Optimization at a Very Large Scale Patrick Jaillet EECS/LIDS/ORC Joint work with Dimitris Bertsimas, Sloan ORC, and Sébastien Martin, ORC Massachusetts Institute of Technology Online Taxi Routing, Bertsimas, Jaillet, Martin

The taxi routing problem Customer 1 Customer 2 Taxi 2 Online Taxi Routing, Bertsimas, Jaillet, Martin

The taxi routing problem Taxi Routing, Bertsimas, Jaillet, Martin

Online Taxi Routing, Bertsimas, Jaillet, Martin Motivation “Wisdom” has been that such taxi routing problems leave very little room for the use of optimization (e.g., Pillac et al., 2011): Online problem. Not enough control. Simple heuristics are good enough. Real world applications are untractable. But with the growing on-demand ride matching platforms: Smartphone-based, more information is available Centralized: more “control” on vehicle actions In high-demand situations, simple heuristics are not enough (“price surge”...), and with optimization solvers ever more powerful, we may revisit this …. Online Taxi Routing, Bertsimas, Jaillet, Martin

Online Taxi Routing, Bertsimas, Jaillet, Martin Setting Formally, we consider here a variant of the so-called dynamic pick-up and delivery problem with time-windows, as first described in (Savelsbergh, 95) Online setting: customers origin and destination information is made available when they request the ride. The customers have to be picked-up within a time-window. We control which taxi will pick-up which customer. We study how we can use optimization to leverage prior information, and improve the efficiency of the system (more customers served, more revenue…). Online Taxi Routing, Bertsimas, Jaillet, Martin

Online Taxi Routing, Bertsimas, Jaillet, Martin Roadmap A network-flow formulation Scaling to real-world problems Application: NYC Yellow Cabs Online Taxi Routing, Bertsimas, Jaillet, Martin

Re-optimization and offline problem Rolling-horizon with re-optimization strategies have worked well in practice when applied to online routing problems (Yang et al., 2004). Known future customers OFFLINE SOLUTION Current Time Time horizon Cite Patrick’s paper here, reformulate, take more for granted, start with online and go to offline Time OFFLINE SOLUTION update 30s Online Taxi Routing, Bertsimas, Jaillet, Martin

The offline taxi-routing problem Revenue Travel–time Customer c’ Customer c Pick-up time and time-window Feasibility Maximize Revenue Pick-up Decision Online Taxi Routing, Bertsimas, Jaillet, Martin 8

Network flow formulation No cycles (pick-up time-windows are typically smaller than the duration of a ride) Taxi 1 origin Taxi 2 origin Time Online Taxi Routing, Bertsimas, Jaillet, Martin

Network flow formulation We add flow constraints to obtain the optimal solution: Taxi 1 origin Taxi 2 origin Time Online Taxi Routing, Bertsimas, Jaillet, Martin

What makes the problem hard Large Time-windows Combinatorial Optimization Easy to solve: most taxis are free, closest taxi gets customer No time window = TSP, NP-complete High demand/supply Low demand/supply “Simple” Optimization No Optimization Fixed-Pickup time = network max-flow problem (Polynomial) Small Time-Windows Online Taxi Routing, Bertsimas, Jaillet, Martin

Optimization local heuristics (2-OPT…) Max-Flow Formulation (LP) What solver ? Large Time-windows Optimal solvers (MIP) Optimization local heuristics (2-OPT…) High demand/supply Low demand/supply Simple heuristics Max-Flow Formulation (LP) Small Time-Windows Online Taxi Routing, Bertsimas, Jaillet, Martin

New York City yellow cabs NYC Taxi & Limousine commission 2010-2016 : 1.4 billion rides. Pick-up and drop-off time/coordinates, fares, timings, # passengers… Instance of taxi – routing: 5000 cabs Demand on 04/15/16 12-1:30pm in Manhattan: 26,109 customers. LP (without time windows) MIP (with time windows) Online Taxi Routing, Bertsimas, Jaillet, Martin

Trimming the flow graph Trimming the graph using time and distance between customers Taxi 1 origin Taxi 2 origin Time LP (without time windows) MIP (with time windows) Online Taxi Routing, Bertsimas, Jaillet, Martin

Finding the backbone LP MIP We use the tractable LP solver with random pick-up times within the time window to provide “good solutions” and find the edges that are likely to be in optimal solutions (backbone). Taxi 1 origin Taxi 2 origin Time LP (without time windows) MIP (with time windows) Online Taxi Routing, Bertsimas, Jaillet, Martin

Online Taxi Routing, Bertsimas, Jaillet, Martin Manhattan experiment Talk about all simulations difficulties and what we built Online Taxi Routing, Bertsimas, Jaillet, Martin

Online Taxi Routing, Bertsimas, Jaillet, Martin Results Online Taxi Routing, Bertsimas, Jaillet, Martin

Technical challenges that needed to be solved Creating the road network from map data. Getting the real demand data and format it. Estimating travel-times from taxi data. Writing a fast large-scale online routing simulation tool. Using state-of-the-art MIP solvers to re- optimize the fleet actions. Making everything communicate and run in real-time. Online Taxi Routing, Bertsimas, Jaillet, Martin

Online Taxi Routing, Bertsimas, Jaillet, Martin The end …. Thank you! Online Taxi Routing, Bertsimas, Jaillet, Martin