This document summarizes research on using data analytics and constraint programming to optimize ridesharing systems. The researchers define a "feasible match constraint" to improve the quality of matches between drivers and passengers based on trip histories. They assess current ridesharing schemes using a constraint programming model that maximizes matched riders while satisfying constraints like start/end times and trip durations. Experiments on real trip data show the potential to significantly increase matching and reduce unmatched participants by allowing drivers to also be passengers. The work aims to improve traffic flow and reduce emissions from personal vehicles.

1. Data analytics & optimisation
for assessing ridesharing
systems
Vincent Armant and Nahid Mahbub and Kenneth N. Brown
Centre for
Data Analytics
Rides sharing System
A ridesharing system helps intended drivers and prospective passengers to share
their rides. A ridesharing system aims at:
• improving the traffic flow in smart cities,
• reducing the number of cars and gaz emissions.
Problem:
Mismatches can act as disincentive for deployed ridesharing applications.
<
(a) euclidean distance matches (b) feasible matches
Example of feasible and infeasible ride matches
Contributions:
• (Data Analytics) We improve the quality of returned matches by defining a
Feasible Match Constraint based on histories of advertised trips.
• (Constraint Programming) We assess and improve the potential of current
ride sharing schemes using feasible matches found as input to a CP model.
Feasible match inferred from users’ behaviours
An advertised trip by the user u only describes the user’s intended : start time,
start location, and destination. From histories of successful trip adverts we infer:
• the time window, i.e., earliest and latest time a user is willing to share his trip,
• the max distance a rider will be willing to walk for pick-up and drop-off.
time
tearly
u
start time
earliest
tstart
u
start time
intended
tlatest
u
arrival time
latest
δ−
start delay
negative
δ+
start delay
positive
f1(π∗
)
travel time estimation
(a) inferred time window parameters (b) a rider reachable area
Using the user behaviour parameters, we define the feasible match constraint
between a rider and a driver checking the geographical and time consistency
between the two trip adverts. Given a set of trip adverts, we can then compute
the feasible match graph G = (TSD, TSR, E) where TSD (resp. TSR) is the set
of driver adverts in blue dots, (resp. riders in red dots).
Inferred feasible match graph G of the trip adverts in region 2
Ridesharing Constraints Optimisation Model
To assess the potential of a ride-sharing scheme using a CP model, we associate
each edge (tsd, tsr) ∈ G to a rideshare trip interval variable ytsd,tsr
and
maximize:
Σ
(tsd,tsr)∈E
x,tsr
(1)
subject to:
ytsd,tsr
.start ≥ max(tearly
d , tearly
r ), ∀(tsd, tsr) ∈ E (2)
ytsd,tsr
.end ≤ min(tlatest
d , tlatest
r ), ∀(tsd, tsr) ∈ E (3)
ytsd,tsr
.duration = ytsd,tsr
.end − ytsd,tsr
.start, ∀(tsd, tsr) ∈ E (4)
ytsd,tsr
.duration ≥ π ∗lstart,ldest , ∀(tsd, tsr) ∈ E (5)
CUMULATIVE({ytsd,tsr
}, nbSeatsd, ≤), ∀tsd ∈ TSD (6)
ALTERNATIVE(xtsr
, {ytsd,tsr
|(tsd, tsr) ∈ E}), ∀tsr ∈ TSR (7)
(xtsc
.presence ⇒ ytrc,tsr
.presence), ∀(tsd, tsr) ∈ E (8)
We maximize the total number of rider participants (1) when each rideshare trip
has to start after both the earliest rider and earliest driver start (2) and end before
both the latest rider and latest driver arrivals (3). Each rideshare trip duration (4)
has to be greater than the rider’s shortest path (5). At any time, each driver’ car
occupancy does not exceed the number of available seats (6). A rider can only be
in at most one rideshare trip (7). Shifters, i.e., drivers willing to change role,
cannot be both a rider and driver (8).
Assessing the quality of ridesharing schemes
The experiments have been run on ridesharing trip adverts of 4 regions collected
during a period of 12 months.
Quality of ride matches found by typical search w.r.t. feasible-matches
Typical search T45 # edges # feasible found # feasible # unfeasible found # feasible not found precision recall
region 1 802 647 588 214 59 0.733 0.909
region 2 559 364 326 233 38 0.583 0.896
region 3 1678 1691 1616 62 75 0.963 0.956
region 4 4223 3590 3326 897 264 0.788 0.926
In regions 3 and 4, the typical search performs well while regions 1 and 2 represent
cases where inappropriate match suggestions and missing proposals can act as a
disincentive for users.
Assessing the optimal ride matches scheme with a new hypothesis
FM represents the ride sharing scheme for Feasible Matches. T45FM represents
the feasible matches found by a typical search. After observing an imbalance
among participants (not enough riders cf 2nd column), we also assess the heuristic
where drivers also accept to become riders (i.e., shifters) cf FMDS and T45FMDS.
region 3 # users # riders / # drivers # matched riders matched drivers % unmatched
FM
1871 0.67
656 328 47.41
T45FM 630 332 48.58
FMDS
1871 1.67
1392 321 8.44
T45FMDS 1340 316 11.49
For region 3, the table shows the potential gain to reduce the unmatched
participants by up to 80% by persuading drivers to become passengers. Moreover,
even if the solving time for small instances (<1000 users) (regions 1 and 2) is less
than 10 sec, the solving time drastically increases for the largest instances, regions
2 and 3. We will address this issue in future works.
references
• Data analytics and optimisation for assessing a ride sharing system, V.A.,
J.H., N.M., K.B. in Intelligent Data Analysis 2015
• Cumulative constraint problem for assessing a ride sharing system V.A.,
N.M., K.B. workshop BPPC 15 in Constraint Programming conference 2015
This work is supported by Science Foundation Ireland (SFI) Grant 10/IN.1/I3032 and FP7 FET-Open Grant 284715. The Insight Centre for Data Analytics is supported by SFI Grant SFI/12/RC/2289.