#18-04367

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: saeid@nyu.edu

Joseph Y. J. ChowDeputy Director, C2SMART University Transportation CenterAssistant Professor, Department of Civil & Urban EngineeringTandon School of EngineeringNew York UniversityEmail: joseph.chow@nyu.edu