Demand control management for one-way
car sharing system focus on theimbalance between demand and supply
11th Aug. 2015
the 5th International BinN research seminar

M2 NODOKA Kasahara

The University of Tokyokasahara@bin.t.u-Tokyo.ac.jp

Index• Research background• Introduction of one-way car sharing service in Yokohama• Data analysis• Numerical example : Paradox of station distribution• Calculation of profit maximization method in simple
network• Micro simulation in real network• Conclusion

2

Background3• Car sharing service was introduced to Japan as new convenient mobility inrecent years .

The number of registrant
The number of caryear
http://business.nikkeibp.co.jp/article/topics/20140728/269323/?P=3&mds• One-way car sharing : does not require its users to return the vehicle to thesame location from which it was accessed.
• In 2014, the one-way car sharing was approved by law.
→”in the case that we can access the situation of car by utilizing the IT”

Background

4

Round trip Car Sharing
IT information
centerMovement of vehicle
Information of situation ofeach vehicle

One-way Car Sharing
IT information
center

The development of IT technology enable toon-demand transportation system

Car sharing service in Yokohama city5

• October in 2013, Nissan and Yokohama City Launch Choimobi
Yokohama, Japan's First One-way Car Sharing Service with aLarge Number of Ultra-compact EVs• The number of station : 60 (for 110vihicle)• The number of vehicle : 50
• The number of registrant : 14,000• Price : 30 yen / min (basic plan)

Data property

6Probe person data
• activity diary for each monitor and trajectory data by GPS• to describe the learning effect by long-term data
• to grasp the dot base trajectory
surveySurvey period

Number of Monitor

Count of trip

Number of GPS data

Choimobi PP2013

2013/10/01

2014/03/31

11819944

21553929

Choimobi PP2014

2014/09/01

2014/09/30

1610251180192

Choimobi PP2014

2014/10/01 2014/10/31

15902

1038377

8 month123

21,862Total

Use result data
• Record of use• OD, time, the number of vehicle at each station
Survey period

Number of station

Count of use

Number of user

2013/10/11 2014/09/24

54451905910

2014/11/1~2015/6/30

60

17666

Over 10000

What is problem?

7• Uneven distribution of vehicle cause the risk of unavailable
serviceData collected period :2013/10/11-2013/12/20

Full vehicle rate : over 1/3
No vehicle rate : over ½
otherWhat is problem?

High availability
low availability
other

8

8:00-10:00

11:00-13:00

14:00-16:00

17:00-19:00• Imbalance between demand and supply cause the loss ofopportunity cost frequently happens on the operation side when
there is no reservation available for users during their required hours.

What is problem?

9

Paradox of station distribution
When new station establishedin demand concentrated area,profit may rather decrease.

Research Question
How we can reduce this imbalance and then minimize the loss ofopportunity cost

Numerical example :Paradox of station distribution

10

station1

profitExpectedvalue

station43 station

station24 station (no control)

station3

Probability of trip demand
𝑃 𝑑𝑖𝑗 𝑡=𝜆𝑖𝑗 𝑡

𝑑𝑖𝑗 𝑡exp(−𝜆𝑖𝑗 𝑡 )𝑑𝑖𝑗 𝑡!

Expectation value parameter of Poisson distribution

exp(𝛼𝑖𝑗 + 𝛽𝑝𝑖𝑗 𝑡 )𝜆𝑖𝑗 (𝑡) = 𝜆𝑖𝑗 (𝑡) ∙𝐴𝑖𝑗 + exp(𝛼𝑖𝑗 + 𝛽𝑝𝑖𝑗 𝑡 )𝑑𝑖𝑗 : demand of trip between station 𝑖 𝑎𝑛𝑑 𝑗
𝜆𝑖𝑗 (𝑡) : all trip between station 𝑖 𝑎𝑛𝑑 𝑗𝑝𝑖𝑗 : price (controlled variable)
𝐴𝑖𝑗 , 𝛼𝑖𝑗 , 𝛽𝑖𝑗 : parameter (constant)

Method of demand control
1.

Reduce the number of station
 Easy to manage
 Decrease the advantage of one-way car sharing service that allow us tomove short distance.

2.

Relocation by operator
 Surely get lid of the uneven vehicle distribution
 Large operation cost3.

Demand incentive control by changing price Trip to the high demand station : higher price Trip to the low demand station : lower price Demand changes by stochastic

Objective
To Formulate of the stochastic control
system by the pricing strategy and propose
the algorithm.

11lowhighFormulation of profit maximization

12• Maximize the profit by user’s use of Car sharing service
max 𝑅 𝑠 𝑡 , 𝑂 𝑇=𝑟(𝑡|𝑠 𝑡 , 𝑜(𝑡))𝑡Profit of time 𝑡=𝑉𝑖𝑗 𝑡 𝑠 𝑡 , 𝑜 𝑡 𝑝𝑖𝑗 (𝑡|𝑜(𝑡))𝑡𝑖,𝑗The number of trip
between station 𝑖 and 𝑗

The price between station𝑖 and 𝑗𝑁 = {1, … , 𝑖, 𝑗, … , 𝑁}

Set of station𝑑𝑖𝑗 (𝑡)Trip demand at time 𝑡

𝑇 = {1, … , 𝑡, … , 𝑇}

Set of time𝑣𝑖𝑗 (𝑡)The number of real trip at time 𝑡𝑐𝑖

Max of parking space𝑜(𝑡)demand control at time 𝑡

𝑥𝑖 𝑡

The number of vehicle at time 𝑡𝑠 𝑡 = {𝑥1 𝑡 , … , 𝑥𝑁 (𝑡)} Distribution of vehicle at time 𝑡𝑝𝑖𝑗 (𝑡) ∈ 𝑜(𝑡)Price between 𝑖 𝑎𝑛𝑑 𝑗 at time 𝑡

Formulation of profit maximization

13s.t.
𝑥𝑖 = 𝑋

Law of the conservation of the number of vehicle𝑖𝑥𝑖 −𝑣𝑖𝑗 𝑡 +𝑗𝑥𝑖 −𝑣𝑘𝑖 (𝑡) ≥ 0

Constrain of departure𝑣𝑘𝑖 (𝑡) ≥ 𝑐𝑖

Constrain of arrival

𝑘𝑣𝑖𝑗 𝑡 +𝑗𝑘𝑥𝑖 𝑡 + 1 = 𝑥𝑖 −𝑣𝑖𝑗 𝑡 +
𝑗𝑣𝑘𝑖 (𝑡)The movement of vehicle

𝑘𝑁 = {1, … , 𝑖, 𝑗, … , 𝑁}

Set of station𝑑𝑖𝑗 (𝑡)Trip demand at time 𝑡

𝑇 = {1, … , 𝑡, … , 𝑇}

Set of time𝑣𝑖𝑗 (𝑡)The number of real trip at time 𝑡𝑐𝑖

Max of parking space𝑜(𝑡)demand control at time 𝑡

𝑥𝑖 𝑡

The number of vehicle at time 𝑡𝑠 𝑡 = {𝑥1 𝑡 , … , 𝑥𝑁 (𝑡)} Distribution of vehicle at time 𝑡𝑝𝑖𝑗 (𝑡) ∈ 𝑜(𝑡)Price between 𝑖 𝑎𝑛𝑑 𝑗 at time 𝑡Algorithm by using dynamic programming method

14

Dynamic programming method

Calculate an optimum control by considering a state transition of next period=Finite Markov Decision Process(Bellmann, 1957; Howard, 1960)
optimality function
Expected at the time 𝑡 + 1

Profit at the time 𝑡
𝑚𝑎𝑥 𝑟 𝑡 𝑠 𝑡 , 𝑜 𝑡 +𝑢𝑡 (𝑠 𝑡 ) =𝑜 𝑡

𝑃 𝑠 𝑡 +1 𝑠 𝑡 ,𝑜 𝑡

𝑢𝑡+1 (𝑠(𝑡 + 1))

𝑠(𝑡+1)

𝑚𝑎𝑥 𝑟(𝑇|𝑠 𝑇 , 𝑜(𝑇)𝑜 𝑇

(0 < 𝑡 ≤ 𝑇 − 1)
(𝑡 = 𝑇)→calculation is start from last period T towards beforehand

Step1: calculate 𝑢 𝑇 𝑠 𝑇

for state 𝑠 𝑇

Step2 : calculate 𝑢 𝑇−1 𝑠 𝑇 − 1

for state 𝑠 𝑇 − 1

Step3 : repeat towards the former period

Numerical example :Verify the price control effect15

 Calculate double or half price for each OD

profitstation1

Expected value

station4

station2

station3

𝑟 𝑡 is stochastic function⇒result of calculation
are variable

4 station(no control)

4 station(maximize theexpected value)

Solution algorithm
 Maximize the expected value type⇒profit might decrease extreme

4 station(max-min)Micro simulation

16

start

noSTEP1:
trip generation
yes
STEP2:
availablelimit
yes

noAvailable station
Next trip

yes
STEP3:
mode choiceyesDO

no Unavailable station

noSTEP4:
Processing of departure

STEP5:
Processing of returnavailability

Probability of service available changes
dynamic and discrete⇒ necessary to consider availability for mode choice

Next time
nofinishyes

Mode choice model by using PP data

17

Probe Person data : activity diary for each monitor and trajectory data by GPSsurvey
Choimibi PP2013
Choimobi PP2014

Survey period

Number of Monitor

Count of trip

Number of registrant

118
1619944
1927

21553929
2218469

2013/10/01 2014/3/31
2014/9/1-2014/10/31

Use result data
Survey period

Number of station

2013/10/11 2014/09/24Mode choice model by using MNL𝛿𝑐𝑠 exp(𝑉𝑐𝑠 )𝑃𝑐𝑠 =𝑚 𝛿𝑚 exp(𝑉𝑚 )𝑐𝑠 : car sharing
𝑃𝑐𝑠 : probability of car sharing
𝑉𝑚 : constant term of mode 𝑚
𝛿𝑚 : availability of mode 𝑚Considering availability of CS

Count of use
54

Number of user

45190

variables

5910
parametert-valuespecific constants(publictransportation)

1.010

7.23 **

Time [*10min]-0.203-2.06 *

Cost [*100 yen]

-0.239-8.52 **

Access/egress time [min]-0.028-5.43 **

Under 1km(walk)-1.240-9.56**

number of sample

688

LL(0)

-1232.731

LL(β)-716.47𝜌𝜌20.40

Application to the real network
Simulation Scenario
Scenario

Station interval

Pricing control

A500m

Without

B

500m

WithC

100m

Without

D100mwith

18

Pricing rule(a) Set half price(10yen/min) whenvehicle ahead to the empty
station or depart from fullstation(b) Set double price(40yen/min)when vehicle make origin station
full or depart station empty

Distribution of station (left : 500m interval, right : 100m interval)

Result of simulation

19

Result of Simulation

Simulation Scenario

Scenario

Profit (yen)Count of user

Station interval

Pricing control

A

347,260

1,709

500m

WithoutB

401,390

1,862500m

WithC

272,580

2,279100m

Without

D

303,900

2,391100m

withB

The number of Station

ACtimeD

Conclusion

20Summary• Propose the algorithm and formulation regarding to the stochastic
control with pricing strategy deal with loss of opportunity caused byuneven station distribution .
→enable to control considering the stochastic transition of system• Evaluate the pricing strategy in the Yokohama network by
constructing the micro simulation based on the Use result data.
→enable to consider availability of CS
Future works• Elaboration and sophistication of Micro simulation and activity model• Verify the profit maximization in the real network.
• Examine the scenario for simulation ….. And so onReference•

Nissan, choimobi•

http://www.nissan-global.com/EN/NEWS/2013/_STORY/131010-02-e.html•Pigou, A. C., The Economics of Welfare., MacMillan, London, 1920.

•Knight, F., Some Fallacies in the Interpretation of Social Costs, Quarterly Journal of Economics, Vol.38, pp.582–606, 1924.

•Downs, A., The Law of Peak-Hour Expressway Cngestion, Traffic Quarterly, Vol.16, pp.393-409.

•

Thomson, J., M., Great Cities and their Traffic, Gollancz, London.

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•Bellmann, R., Dynamic Programming, Princeton Univ. Press, New Jersey, 1957.

•

Howard, A., Dynamic Programming and Markov Processes, The MIT Press, Cambridge, Massachusetts, 1960.

•Ciari, F., Dobler, C., and Axhausen, K., Modeling one-way shared vehicle systems: an agent-based approach, paper presented at 13thInternational Conference on Travel Behaviour Research, Toronto, July 2012.

•Barth, M. and Todd, M. , Simulation model performance analysis of a multiple shared vehicle system, Transportation Research Part C,Vol.7(4), pp.237-259, 1999.

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Nair, R., Miller-Hooks, E., Fleet Management for Vehicle Sharing Operations, Transportation Science, Vol.45, pp.524-540, 2011.

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21

Appendix

22

2013/10/11

2014/11/1

2014/11/1

2014/9/30

20014/10/28

201/10/9

2014/10/4705063(131)60(10001020

2015/9/-21110)

A

1,000-

50-

1112

A

20A
BBB

5130