1. 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

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

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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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

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

14. 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

15. 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

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

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

18. 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

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