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Route-cost-assignment with joint user and operator behavior as a many-to-one stable matching assignment game
Saeid Rasulkhani*, Joseph Chow*
*C2SMART University Transportation Center, Department of Civil & Urban Engineering, New York University, New York, NY, USA
ma𝑥𝑋𝑣 𝑋
s.t.
where,
Research Problem
ma𝑥𝑋𝑣 𝑋
Proposed Methodology
Case Study Results
ma𝑥𝑋𝑣 𝑋
s.t.
where,
• Increase in options of travelers
• We need to have better
understanding of their behavior
• Traveler choices depend on
decisions of system provider
Using assignment game we try to
take into account the behaviors of
both travelers and operators
Using assignment game we
try to take into account the
behaviors of both travelers
and operators
Classic Assignment Game Problem (A Cooperative game):
How the cost allocation works
max 𝑖∈𝑃 𝑗∈𝑄 𝑎𝑖𝑗𝑥𝑖𝑗
s.t.
𝑖∈𝑃 𝑥𝑖𝑗 ≤ 𝑞𝑗 ∀𝑗 ∈ 𝑄
𝑗∈𝑄
𝑥𝑖𝑗 ≤ 𝑤𝑖 ∀𝑖 ∈ 𝑃
𝑥𝑖𝑗 ∈ 0,1 ∀𝑗 ∈ 𝑄& ∀𝑖 ∈ 𝑃
Assignment Game In Transportation Studies
Travelers and operators as two sides of game
max
𝑠∈𝑆
𝑟∈𝑅
𝑎𝑠𝑟𝑥𝑠𝑟
s.t.
𝑟∈𝑅
𝑥𝑠𝑟 ≤ 𝑞𝑠 ∀𝑠 ∈ 𝑆/{𝑘}
𝑠∈𝑆/{𝑘}
𝛿𝑎𝑠𝑟𝑥𝑠𝑟 ≤ 𝑤𝑎 ∀𝑎 ∈ 𝐴𝑟 , 𝑟 ∈ R
𝑠∈𝑆/{𝑘}
𝑥𝑠𝑟 ≤ 𝑀 1 − 𝑥𝑘𝑟 ∀𝑟 ∈ 𝑅
𝑥𝑠𝑟 ∈ ℤ+ ∀𝑠 ∈ 𝑆/{𝑘}, 𝑟 ∈ 𝑅𝑥𝑘𝑟 ∈ 0,1 𝑟 ∈ 𝑅
NYC taxi example
passenger path Taxi
passenger Taxi pathTicket price percentage of users pay in three different scenario:
0
10
20
30
40
50
60
70
80
90
100
0 5 10 15 20 25
Perc
ent
Ticket Price ($)
Single Riding Ticket Price Operator Optimal Ticket Price user optimal ticket price
Sorted gap between user- and operator-optimal pricing undershared taxi policy
0
1
2
3
4
5
6
11
93
75
57
39
11
09
12
71
45
16
31
81
19
92
17
23
52
53
27
12
89
30
73
25
34
33
61
37
93
97
41
54
33
45
14
69
48
75
05
52
35
41
55
95
77
59
56
13
63
16
49
66
76
85
70
37
21
73
9
Gap
bet
wee
n u
ser-
and
op
erat
or-
op
tim
al (
$)
Users
Conclusion and future works
• It is generalized and can be used in several applications. In fact in most of the cases that two sets of supply and demand are working together can be formulated in the proposed model.
• Unlike most of the studies that have strict cost allocation policy ormechanism, in this proposed model any cost allocation policy can beconsidered.
• This proposed model is very powerful tool for pricing and evaluatingcost allocation policies. Unlike conventional studies that just look atone side of supply or demand, this model takes in to account the jointbehavior of both users and operators.
Conclusion
Future Work
• Taking into account the effect of congestion, In such a model, the payoff table (𝑎𝑠𝑟 = 𝑈𝑠𝑟 − 𝑡𝑠𝑟) would need to treat 𝑡𝑠𝑟 as a function of flow.
• Consideration of dynamic ridesharing assignment• stochastic scenarios for risk pooling (cost allocations between
operators) in the case of such an events
Sharing NYC taxi rides
Affiliation
Saeid RasulkhaniDepartment of Civil & Urban EngineeringTandon School of EngineeringNew York UniversityEmail: [email protected]
Joseph Y. J. ChowDeputy Director, C2SMART University Transportation CenterAssistant Professor, Department of Civil & Urban EngineeringTandon School of EngineeringNew York UniversityEmail: [email protected]
