Coordinating Supply and Demand on an On-demand Service Platformwith Impatient Customers

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Speaker: Jiaru Bai, UC Irvine, The Paul Merage School of Business

Co-authors: Rick So, UC Irvine, Chris Tang, UCLA , Xiqun Chen, Zhejiang University, Hai Wang, Singapore Management University

Content

• Definition

• Research Questions

• Literature Review

• Model Setup

• Analytical Results

• Numerical illustration: Didi Data

• Summary

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On-demand Service Platform

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On-demand Service Platform

• (1) Customers desire quick service

• (2) Many of the platforms use Independent providers

• (3) Use of technology

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Independent Drivers

Customers Uber

On-demand Service Platform

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Transportation Delivery

Home Services

Food & BeverageDining & Drinks

Health & Beauty

Some Operating Challenges

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Quick delivery

• Customers are getting increasingly impatient Choices and competition

Mobile apps

• High degree of variability in both supply and demand

Intricate relationship between endogenous supply and demand

• Set wage and price rates to affect supply and demand

Wage w

Platform

Supply k

Price p

Demand l

CustomersIndependent

Providers

Maximize profit

Maximize earningsMaximize utility

On-demand Service Platform

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Waiting time

Utilization

Research Questions

1. How to model demand and supply in equilibrium?• Customers are time sensitive

• Service providers are earnings sensitive

2. How should an on-demand service platform set its price p and wage w?

a) When payout ratio = wage/price = w/p is fixed? (e.g., 80%)

b) When payout ratio = w/p is dynamic?

c) What is the benefit of “dynamic payout ratio”?

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Literature Review

• Sharing economy• Benjaafar et al. (2015), Fraiberger and Sundarajan (2015), and Jiang

and Tian (2015), Li et al. (2015), …

• On-demand service platforms

• Kokalitcheva (2015), Wirtz and Tang (2016), and Shoot (2015), Chen and Sheldon (2015), Moreno and Terwiesch (2014), Terwiesch (2014), Allon et al. (2012), Taylor (2016), …

• Dynamic Pricing

• Riquelme et al. (2015) and Cachon et al. (2015), Hu and Zhou (2016), Gurvich et al. (2015), …

• Two-sided markets in industrial economics

• Rochet and Tirole (2003, 2006), Anderson (2006), …

• Service Pricing with delay costs in operations management

• Naor (1969), Armony and Haviv (2003), Afeche and Mendelson (2004), Zhou et al. (2014), …

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Modeling Framework

• Customer demand l depends on price p, and waiting time Wq

Independent Drivers

Customers Uber/Didi

Price p

Waiting time Wq

Demand l Supply k

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Customer Demand Consumer utility: 𝑼 𝒗 = 𝒗 − 𝒑 𝒅 − 𝒄𝑾𝒒

• 𝑣 : Value per service unit with distribution 𝑈[0,1] (parameter)

• 𝑝 : Price per service unit (decision variable)

• 𝑑 : Amount of service units per request (parameter − assumed constant)

• 𝑐 : Unit waiting time cost (parameter)

• 𝑊𝑞: Waiting time (endogenously determined)

Consumer will request if 𝑼 𝒗 = 𝒗 − 𝒑 𝒅 − 𝒄𝑾𝒒 ≥ 𝟎

Equilibrium price: 𝒑 = 𝟏 − 𝒔 −𝒄

𝒅𝑾𝒒

• ҧ𝜆 : Maximum (potential) customer demand rate (parameter)

• l : Realized customer demand rate; 𝜆 ≤ ҧ𝜆 (endogenously determined)

• 𝑠 : service level =𝜆

ഥ𝜆= 𝑃𝑟𝑜𝑏 𝑣 > 𝑝 +

𝑐

𝑑𝑊𝑞 = 1 − 𝑝 −

𝑐

𝑑𝑊𝑞 11

Modeling Framework

• Supply of independent service providers k depends on earnings, which depend on wage w, utilization r

Independent Drivers

Customers Uber/Didi

Wage w

Utilization r

Demand l Supply k

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Supply of Service Providers Provider’s earning rate:

𝑬 = 𝒘𝝁 𝝆 = (𝒘𝝁)𝝀𝒅

𝒌𝝁= 𝒘

𝝀𝒅

𝒌

• 𝑤 : Wage per service unit (decision variable)

• 𝜇 ∶ Average service speed of providers (parameter)

• k : Number of participating providers (endogenously determined)

• r : Utilization =𝜆𝑑

𝑘𝜇

Provider will participate if 𝑬 = 𝒘𝝀𝒅

𝒌≥ 𝒓

• 𝑟 : Reservation wage per unit time with distribution 𝑈[0,1] (parameter)

Equilibrium wage: 𝒘 = 𝜷𝒌

𝝀𝒅=

𝒌𝟐

𝑲𝝀𝒅

• K : Maximum number of service providers; 𝑘 ≤ 𝐾 (parameter)

• b : Participation ratio =𝑘

𝐾= 𝑃𝑟𝑜𝑏 𝑟 ≤ 𝑤

𝜆𝑑

𝑘= 𝑤

𝜆𝑑

𝑘 13

Modeling Framework

• Platform: How to set price p and wage w?

Independent Drivers

Customers Uber/Didi

Price p Wage w

Demand l Supply k

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Platform’s Decision Problem• Profit function

𝝅 = 𝝀 𝒑 − 𝒘 𝒅 = 𝝀 𝟏 − 𝒔 −𝒄

𝒅𝑾𝒒 −

𝒌𝟐

𝝀𝒅𝑲𝒅 = 𝝅(𝒌, 𝒔)

Average profit per request Equilibrium price

rate 𝑝Equilibrium wage rate 𝑤

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Maximize 𝝅 𝒌, 𝒔

Decision variables: 𝑘𝜖𝜆𝑑

𝜇, 𝐾 , 𝑠𝜖[0,1]

• One-to-one correspondence between (p, w) and (k, s)

Modeling Framework• Waiting time Wq and utilization r both depend on supply k and

demand l

Independent Drivers

Customers Uber/Didi

Price p

Waiting time Wq

Demand l

Utilization r=𝜆𝑑

𝑘𝜇

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Wage w

Supply k

Waiting time 𝑊𝑞

Use M/M/k queueing model

Exact formula too complicated

𝑊𝑞 =1

1 +𝑘! (1 − 𝜌)

𝑘𝑘𝜌𝑘 σ0𝑘−1 𝑘𝑖𝜌𝑖

𝑖!

𝜌

𝜆 1 − 𝜌

Numerical results:

𝑊𝑞 =𝜌 2(𝑘+1)

𝜆 1 − 𝜌𝑤ℎ𝑒𝑟𝑒 𝜌 =

𝜆𝑑

𝑘𝜇

Exact when 𝑘 = 1

Very good estimate for 𝑘 > 1; See Sakasegawa (1977)

Analytical results:

𝑊𝑞 =𝜌 2(𝑛+1)

𝜆 1 − 𝜌𝑤ℎ𝑒𝑟𝑒 𝜌 =

𝜆𝑑

𝑘𝜇𝑎𝑛𝑑 𝑎𝑛𝑦 𝑓𝑖𝑥𝑒𝑑 𝑛

Provide analytical support for our numerical results

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Waiting time 𝑊𝑞

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Use M/M/k queueing model

Exact formula too complicated

𝑊𝑞 =1

1 +𝑘! (1 − 𝜌)

𝑘𝑘𝜌𝑘 σ0𝑘−1 𝑘𝑖𝜌𝑖

𝑖!

𝜌

𝜆 1 − 𝜌

Numerical results:

𝑊𝑞 =𝜌 2(𝑘+1)

𝜆 1 − 𝜌𝑤ℎ𝑒𝑟𝑒 𝜌 =

𝜆𝑑

𝑘𝜇

Exact when 𝑘 = 1

Very good estimate for 𝑘 > 1; See Sakasegawa (1977)

Analytical results:

𝑊𝑞 =𝜌 2(𝑛+1)

𝜆 1 − 𝜌𝑤ℎ𝑒𝑟𝑒 𝜌 =

𝜆𝑑

𝑘𝜇𝑎𝑛𝑑 𝑎𝑛𝑦 𝑓𝑖𝑥𝑒𝑑 𝑛

Provide analytical support for our numerical results

Waiting time 𝑊𝑞

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Use M/M/k queueing model

Exact formula too complicated

𝑊𝑞 =1

1 +𝑘! (1 − 𝜌)

𝑘𝑘𝜌𝑘 σ0𝑘−1 𝑘𝑖𝜌𝑖

𝑖!

𝜌

𝜆 1 − 𝜌

Numerical results:

𝑊𝑞 =𝜌 2(𝑘+1)

𝜆 1 − 𝜌𝑤ℎ𝑒𝑟𝑒 𝜌 =

𝜆𝑑

𝑘𝜇

Exact when 𝑘 = 1

Very good estimate for 𝑘 > 1; See Sakasegawa (1977)

Analytical results:

𝑊𝑞 =𝜌 2(𝑛+1)

𝜆 1 − 𝜌𝑤ℎ𝑒𝑟𝑒 𝜌 =

𝜆𝑑

𝑘𝜇𝑎𝑛𝑑 𝑎𝑛𝑦 𝑓𝑖𝑥𝑒𝑑 𝑛

Provide analytical support for our numerical results

Models and Results

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1. Base model with a fixed payout ratio

•𝑤

𝑝= 𝛼, 0 < 𝛼 < 1

2. General model with a dynamic payout ratio

• Free w and p

Base Model: Fixed Payout Ratio

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• Under additional constraint: 𝛼 =𝑤

𝑝, 0 < 𝛼 < 1 (fixed

payout ratio)

• Analytical Result:

• Both the optimal wage rate 𝑤∗ and the optimal price rate 𝑝∗ increase in the maximum demand rate ҧ𝜆 and average service unit 𝑑.

General Model: Dynamic Payout Ratio

Price p* Wage w* Payout Ratiow*/p*

Profit𝝅∗

Max. # providersK

Not monotone ↓ ↓ ↑

Service rateμ

Not monotone ↓ ↓ ↑

Unit waiting costc

Max. demand rateത𝛌

Avg. units requestedd

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Price p* Wage w* Payout Ratiow*/p*

Profit𝝅∗

Max. # providersK

Not monotone ↓ ↓ ↑

Service rateμ

Not monotone ↓ ↓ ↑

Unit waiting costc

Not monotone ↑ ↑ ↓

Max. demand rateത𝛌

Avg. units requestedd

General Model: Dynamic Payout Ratio

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General Model: Dynamic Payout Ratio

Price p* Wage w* Payout Ratiow*/p*

Profit𝝅∗

Max. # providersK

Not monotone ↓ ↓ ↑

Service rateμ

Not monotone ↓ ↓ ↑

Unit waiting costc

Not monotone ↑ ↑ ↓

Max. demand rateത𝛌

↑ ↑ ↑ ↑

Avg. units requestedd

↑ ↑ ↑ ↑

Extension: Total Welfare

• Total welfare function:

Π 𝑘, 𝑠 = (1 − γ)π 𝑘, 𝑠 + γ(𝐶𝑠 + 𝑃𝑠)

• 𝛾 = 0, basic model (platform profit)

• 𝛾 = 1/2, equal weights on profit and consumer/provider welfare

• ℎ𝑖𝑔ℎ𝑒𝑟 𝛾 = higher weight on consumer/provider welfare25

Platform’s profit

Equitable payoff parameter,0 ≤ γ ≤ 1

Consumer and Provider surplus

Total welfare

Extension: Total Welfare

Main Results:1) For any γ ≤ 2/3, the results in the basic model continue to hold.

2) When the “equitable payoff” γ increases (higher weight on consumer/provider welfare)

The optimal wage rate 𝑤∗ increases

But the optimal price rate 𝑝∗ is not necessarily monotonic.

Optimal payout ratio (w*/p*) increases

Platform profit p* decreases

Social welfare (Cs+Ps) increases26

Didi Company

• Founded in June 2012

• China equivalent of Uber

• The largest on-demand ride-hailing service platform operating in over 360 Chinese cities

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Didi Data• Hangzhou, capital city of Zhejiang province with over 7 million people

• Sep. 7-13 and Nov. 1-30 in 2015

Peak hour (9am, 7pm):• l=2000• m=19 km/hourNon-peak hour (11pm):• l=1000• m=26 km/hour

28Non-peak HoursPeak Hours

Didi Data• Hangzhou, capital city of Zhejiang province with over 7 million people

• Sep. 7-13 and Nov. 1-30 in 2015

Average travel distance fairly constant during peak and non-peak hours:• d ~ 6-7 km

• Price rate is higher during peak hours

and lower during non-peak hours

• Price rate and demand has a

correlation coefficient of 0.8129

Focus on Express/Private services

Maximum number of available drivers 𝑲≈390

The fixed payout ratio α ≈ 80%

Reservation wage 𝒓 ~ RMB 30 - 40

Value per km 𝒗 ~ RMB 2 – 4

Fixed d = 6km

Two scenarios:Peak hour: ത𝝀 = 200/ℎ𝑟, 𝝁 = 19 km/hour

Non-peak hour: ത𝝀 = 100/ℎ𝑟, 𝝁 = 26 km/hour

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Model Illustration Based on Didi data

General Model: Optimal price and wage rates

Peak Hour Scenario Non-peak Hour Scenario

c : unit waiting cost

p* : optimal price rate

w* : optimal wage rate

k* : optimal realized number of drivers

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General Model: Optimal Payout Ratio

Optimal payout ratio a* increases as unit waiting cost c increases

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Optimal Profit: Fixed vs. Dynamic Payout Ratios

Substantial profit increases when the optimal payout ratio is significantly

different from the fixed ratio!

Optimal a*=0.6

Optimal a*=0.8

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Summary• A modeling framework for optimal price and wage decisions for an on-

demand service platforms

• Price- and time-sensitive customers

• Independent (wage-sensitive) service providers

• Queueing model to incorporate customer waiting cost

• Some key findings

• Optimal price p* and wage w* are increasing in the max potential demand ҧ𝜆

• Optimal payout ratio w*/p* is also increasing in the max potential demand ҧ𝜆

• Using Didi data, we illustrate that the firm can earn significantly more by using a dynamic payout ratio

• Limitations/Future research

• Dynamic pricing

• Platform competition34

Thank you!

Questions?

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