1. Optimization of Surge Price
for Rebalancing the Yellow
Taxis Demand
in Manhattan, New York
Yiyuan Lei
Bilal ThonnamThodi
Bingqing Liu
Dec. 20, 2019
2. * 2
Introduction
● What is Surge Price?
○ Dynamic Pricing Strategy applied to adjust supply-demand
relationship
● Why Surge Price?
○ Sometimes there are more riders in a given area than available
drivers, sometimes the opposite
● How does it work?
○ High prices in areas with redundant demand
○ motivate drivers to come to these areas
○ induce mode shift of the redundant demand
3. * 3
Literature Review
● Impact of surge pricing
○ Supply side: evaluating the impact of dynamic pricing on labor supply from an economic
perspective
○ Impact on the transportation system: making the system healthie
● Peeking into Uber’s black box of surge price algorithm
○ Lack of transparency has led to concerns about whether Uber artificially manipulate prices
● How we should regulate shared-economy companies like Uber to benefit the customers instead
of the incumbents
● Few studies looking into how to effectively make surge price policies to balance the system
healthiness and the benefits of the operators, which is the research gap that we are trying to fill in this
project.
4. * 4
Data
New York City’s Taxi and Limousine Commission open-
source the taxi trips records data
7. * 7
Network Parameterization
● Computation of and
○ compute the numbers of pick-ups in each taxi zone in the
research time interval and take the number as the supply of
the nodes (zones).
○ Trips recorded are only the demand met, potential demand
cannot be seen in the dataset.
○ With the assumption that the total demand is larger than the
total supply, we randomly apply multipliers from 1 to 2 to
the amount of demand that is met (equal to the supply) to
estimate the total potential.
8. * 8
Network Parameterization
● Computation of
○ The expected fares follows (approximately) a log-normal distribution and we take
the expected value of this fare distribution to represent the expected fare per trip.
● Computation of
○ extract the travel-time of the trips whose starting and ending points consistent with
the starting and ending points of all the links we defined, and computed the average
travel time for all the trips corresponding to each link as the initial travel cost of the
link.
10. * 10
Benchmark System Assumptions:
● All the vehicles at a node (zone) is
picking up the passengers at the
same node as a priority
● Since the total demand within the
area is bigger than the total supply,
we are adding a dummy node to help
solving the problem.
To balance the importance of travel time
and revenue,
11. * 11
Alternative System
Surge Price Multiplier:
Fare of a trip:
Demand Function and Elasticity:
Zones with different socio-economic
attributes may react differently to the
change of price, so we clustered all the
zones into 3 different clusters.
E = 0.30
E = 0.49
E = 0.12
13. * 13
Alternative Systems
● is an indicator, indicating if node j
is a demand node, 1 if node j is a
demand node, 0 otherwise
● 1,2,3 → node conservation
● 4 → node conservation of the dummy
node.
● 5,6,7→ track all the demand nodes
● 8 → set the link cost at 0 if the
dummy link is formed with a demand
node, M otherwise.
14. * 14
Alternative Systems
● With Non-convexity problem and
Computationally hard.
● With the purpose of balancing short-
term supply and demand, the
algorithm determining the surge price
multipliers should be computationally
fast to be able to operate in a timely
manner.
● Heuristic approaches
○ profitable for operators
○ time-saving for passengers
○ also computationally easy to be
timely
15. * 15
Alternative Systems
● Policy 1: Demand Based penalty
○ Each zone is preassigned with a based surge price multiplier;
○ When exceeds by 5% of the total, an additional 1.01 multiplier is applied;
○ When exceeds by 15% of the total, an additional 1.05 multiplier is applied;
○ When exceeds by 20% of the total, an additional 1.1 multiplier is applied;
● Policy 2: Price elasticity based penalty
○ Each zone is preassigned with a based surge price multiplier;
○ Cluster 0: Price Elasticity is 0.49, an additional 1.01 multiplier is applied;
○ Cluster 1: Price Elasticity is 0.30, an additional 1.05 multiplier is applied
○ Cluster 2: Price Elasticity is 0.12, an additional 1.1 multiplier is applied
● Policy 3: Mixture factors penalty
○ The surge price multiplier is based on the mixture effects of demand based penalty and price
elasticity based penalty
17. * 17
Benchmark System
● The objective value: -1443
● The optimal total revenue: 2123 ($)
● The optimal assignment time: 1273 (s)
● Revenue by clusters:
Cluster 0 (E= 0.49) Cluster 1 (E = 0.3) Cluster 2 (E =0.12)
Revenue ($) 901 1071 150
Table1. The revenue of each cluster in Benchmark system
18. Table2. The revenue of each cluster in alternative system 1
18
Alternative System: Policy 1
● The optimal base surge price is 1.4
● The objective value: -2055
● The optimal total revenue: 2906
● The optimal assignment time: 1347
● Revenue by clusters
Cluster 0
(E= 0.49)
Cluster 1
(E = 0.3)
Cluster 2
(E =0.12)
Revenue 1127 1562 216 Figue The objective function under policy 1
19. Table3. The revenue of each cluster in alternative system 2
19
Alternative System: Policy 2
● The optimal base surge price is 1.6
● The objective value: -2058
● The optimal total revenue: 1402
● The optimal assignment time: 2923
● Revenue by clusters
Cluster 0
(E= 0.49)
Cluster 1
(E = 0.3)
Cluster 2
(E =0.12)
Revenue 1224 1427 272 Figue The objective function under policy 2
20. Table3. The revenue of each cluster in alternative system 3
20
Alternative System: Policy 3
● The optimal base surge price is 1.6
● The objective value: -2076
● The optimal total revenue: 1402
● The optimal assignment time: 2946
● Revenue by clusters
Cluster 0
(E= 0.49)
Cluster 1
(E = 0.3)
Cluster 2
(E =0.12)
Revenue 1224 1450 272 Figure The objective function under policy 3
21. * 21
Comparison
● The benchmark system has the minimum assignment time
● The optimal solutions in the alternative systems all increased the revenue
● Based on the objective value, policy 3 (mixed factors penalization) is the ideal policy
Time (s) Revenue ($) Time (delayed) Revenue (Increased) Objective value
Benchmark 1273 2123 NA NA -1443
Policy 1 1347 2906 5.8% 36.9% -2055
Policy 2 1402 2923 10.1% 37.7% -2058
Policy 3 1402 2946 10.1% 38.8% -2076
Table4. Systems comparisons
22. * 22
Conclusions
● We propose policy 3 as the optimal policy The base penalty is 1.6
● improves the revenue by 38.8%
● The assignment time is within 11%
Figure. The change of revenue under policy 3Figure. The change of time under policy 3
23. * 23
Conclusions
● Highest surge price multiplier is 1.7776 at zone 15 and zone
56
● Lowest surge price multiplier is 1.616
Table5. Policy 3 surge pricing multiplier at each zones E = 0.49
E = 0.12
E = 0.30
24. *
Conclusions
● The highest link flow under optimal policy 3 is 44;
● Most of the link flows are zero due to we are assigning the
taxies using the smaller travelling time while maintaining
relative high revenue;
● The highest demand under policy 3 is node 8 with 266
riders, the penalty at that zone is 1.616;
● The highest penalty is 1.776 at node 15 with demand 2 and
node 56 with demand 44;
