Coordinating Supply and Demand on an On-demand Service Platform - - PowerPoint PPT Presentation

Coordinating Supply and Demand

• n an On-demand Service Platform

with 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

4 Independent Drivers Customers Uber

On-demand Service Platform

5 Transportation Delivery Home Services Food & Beverage Dining & 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

Customers

Independent Providers

Maximize profit Maximize earnings Maximize 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: 𝑽 𝒘 = 𝒘 − 𝒒 𝒆 − 𝒅𝑿𝒓
• 𝑤 : Value per service unit with distribution 𝑉[0,1] (parameter)
• 𝑞 : Price per service unit (decision variable)
• 𝑒 : Amount of service units per request (parameter − assumed constant)
• 𝑑 : Unit waiting time cost (parameter)
• 𝑋

𝑟: Waiting time (endogenously determined)

• Consumer will request if 𝑽 𝒘 = 𝒘 − 𝒒 𝒆 − 𝒅𝑿𝒓 ≥ 𝟏
• Equilibrium price: 𝒒 = 𝟐 − 𝒕 −

𝒅 𝒆 𝑿𝒓

• ҧ

𝜇 : Maximum (potential) customer demand rate (parameter)

• l : Realized customer demand rate; 𝜇 ≤ ҧ

𝜇 (endogenously determined)

• 𝑡 : service level =

𝜇 ഥ 𝜇 = 𝑄𝑠𝑝𝑐 𝑤 > 𝑞 + 𝑑 𝑒 𝑋 𝑟

= 1 − 𝑞 −

𝑑 𝑒 𝑋 𝑟

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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:

𝑭 = 𝒙𝝂 𝝇 = (𝒙𝝂) 𝝁𝒆 𝒍𝝂 = 𝒙 𝝁𝒆 𝒍

• 𝑥 : Wage per service unit (decision variable)
• 𝜈 ∶ Average service speed of providers (parameter)
• k : Number of participating providers (endogenously determined)
• r : Utilization = 𝜇𝑒

𝑙𝜈

• Provider will participate if 𝑭 = 𝒙

𝝁𝒆 𝒍 ≥ 𝒔

• 𝑠 : Reservation wage per unit time with distribution 𝑉[0,1] (parameter)
• Equilibrium wage: 𝒙 = 𝜸

𝒍 𝝁𝒆 = 𝒍𝟑 𝑳𝝁𝒆

• K : Maximum number of service providers; 𝑙 ≤ 𝐿 (parameter)
• b : Participation ratio =

𝑙 𝐿 = 𝑄𝑠𝑝𝑐 𝑠 ≤ 𝑥 𝜇𝑒 𝑙

= 𝑥

𝜇𝑒 𝑙

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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

𝝆 = 𝝁 𝒒 − 𝒙 𝒆 = 𝝁 𝟐 − 𝒕 − 𝒅 𝒆 𝑿𝒓 − 𝒍𝟑 𝝁𝒆𝑳 𝒆 = 𝝆(𝒍, 𝒕)

Average profit per request Equilibrium price rate 𝑞 Equilibrium wage rate 𝑥

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• Maximize 𝝆 𝒍, 𝒕
• Decision variables: 𝑙𝜗

𝜇𝑒 𝜈 , 𝐿 , 𝑡𝜗[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= 𝜇𝑒

𝑙𝜈

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Wage w Supply k

Waiting time 𝑋

𝑟

Use M/M/k queueing model

• Exact formula too complicated

𝑋

𝑟 =

1 1 + 𝑙! (1 − 𝜍) 𝑙𝑙𝜍𝑙 σ0

𝑙−1 𝑙𝑗𝜍𝑗

𝑗! 𝜍 𝜇 1 − 𝜍

• Numerical results:

𝑋

𝑟 = 𝜍 2(𝑙+1)

𝜇 1 − 𝜍 𝑥ℎ𝑓𝑠𝑓 𝜍 = 𝜇𝑒 𝑙𝜈

• Exact when 𝑙 = 1
• Very good estimate for 𝑙 > 1; See Sakasegawa (1977)
• Analytical results:

𝑋

𝑟 = 𝜍 2(𝑜+1)

𝜇 1 − 𝜍 𝑥ℎ𝑓𝑠𝑓 𝜍 = 𝜇𝑒 𝑙𝜈 𝑏𝑜𝑒 𝑏𝑜𝑧 𝑔𝑗𝑦𝑓𝑒 𝑜

• Provide analytical support for our numerical results

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Waiting time 𝑋

𝑟

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Use M/M/k queueing model

• Exact formula too complicated

𝑋

𝑟 =

1 1 + 𝑙! (1 − 𝜍) 𝑙𝑙𝜍𝑙 σ0

𝑙−1 𝑙𝑗𝜍𝑗

𝑗! 𝜍 𝜇 1 − 𝜍

• Numerical results:

𝑋

𝑟 = 𝜍 2(𝑙+1)

𝜇 1 − 𝜍 𝑥ℎ𝑓𝑠𝑓 𝜍 = 𝜇𝑒 𝑙𝜈

• Exact when 𝑙 = 1
• Very good estimate for 𝑙 > 1; See Sakasegawa (1977)
• Analytical results:

𝑋

𝑟 = 𝜍 2(𝑜+1)

𝜇 1 − 𝜍 𝑥ℎ𝑓𝑠𝑓 𝜍 = 𝜇𝑒 𝑙𝜈 𝑏𝑜𝑒 𝑏𝑜𝑧 𝑔𝑗𝑦𝑓𝑒 𝑜

• Provide analytical support for our numerical results

Waiting time 𝑋

𝑟

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Use M/M/k queueing model

• Exact formula too complicated

𝑋

𝑟 =

1 1 + 𝑙! (1 − 𝜍) 𝑙𝑙𝜍𝑙 σ0

𝑙−1 𝑙𝑗𝜍𝑗

𝑗! 𝜍 𝜇 1 − 𝜍

• Numerical results:

𝑋

𝑟 = 𝜍 2(𝑙+1)

𝜇 1 − 𝜍 𝑥ℎ𝑓𝑠𝑓 𝜍 = 𝜇𝑒 𝑙𝜈

• Exact when 𝑙 = 1
• Very good estimate for 𝑙 > 1; See Sakasegawa (1977)
• Analytical results:

𝑋

𝑟 = 𝜍 2(𝑜+1)

𝜇 1 − 𝜍 𝑥ℎ𝑓𝑠𝑓 𝜍 = 𝜇𝑒 𝑙𝜈 𝑏𝑜𝑒 𝑏𝑜𝑧 𝑔𝑗𝑦𝑓𝑒 𝑜

• Provide analytical support for our numerical results

Models and Results

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• 1. Base model with a fixed payout ratio
• 𝑥

𝑞 = 𝛽, 0 < 𝛽 < 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: 𝛽 =

𝑥 𝑞 , 0 < 𝛽 < 1 (fixed

payout ratio)

• Analytical Result:
• Both the optimal wage rate 𝑥∗ and the optimal price

rate 𝑞∗ increase in the maximum demand rate ҧ 𝜇 and average service unit 𝑒.

General Model: Dynamic Payout Ratio

Price p* Wage w* Payout Ratio w*/p* Profit 𝝆∗

• Max. # providers

K

Not monotone

↓ ↓ ↑ Service rate μ

Not monotone

↓ ↓ ↑ Unit waiting cost c

• Max. demand rate

ത 𝛍

• Avg. units requested

d 22

23 Price p* Wage w* Payout Ratio w*/p* Profit 𝝆∗

• Max. # providers

K

Not monotone

↓ ↓ ↑ Service rate μ

Not monotone

↓ ↓ ↑ Unit waiting cost c

Not monotone

↑ ↑ ↓

• Max. demand rate

ത 𝛍

• Avg. units requested

d

General Model: Dynamic Payout Ratio

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General Model: Dynamic Payout Ratio

Price p* Wage w* Payout Ratio w*/p* Profit 𝝆∗

• Max. # providers

K

Not monotone

↓ ↓ ↑ Service rate μ

Not monotone

↓ ↓ ↑ Unit waiting cost c

Not monotone

↑ ↑ ↓

• Max. demand rate

ത 𝛍 ↑ ↑ ↑ ↑

• Avg. units requested

d ↑ ↑ ↑ ↑

Extension: Total Welfare

• Total welfare function:

Π 𝑙, 𝑡 = (1 − γ)π 𝑙, 𝑡 + γ(𝐷𝑡 + 𝑄

𝑡)

• 𝛿 = 0, basic model (platform profit)
• 𝛿 = 1/2, equal weights on profit and consumer/provider welfare
• ℎ𝑗𝑕ℎ𝑓𝑠 𝛿 = higher weight on consumer/provider welfare

25 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

• n consumer/provider welfare)
• The optimal wage rate 𝑥∗ increases
• But the optimal price rate 𝑞∗ is not necessarily

monotonic.

• Optimal payout ratio (w*/p*) increases
• Platform profit p* decreases
• Social welfare (Cs+Ps) increases

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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/hour

Non-peak hour (11pm):

• l=1000
• m=26 km/hour

28 Non-peak Hours Peak 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 0.81 29

• Focus on Exp

xpress/Private services

• Maximum number of available drivers 𝑳≈390
• The fix

fixed pa payout rati tio α ≈ 80%

• Reservati

tion wage 𝒔 ~ RMB 30 - 40

• Value pe

per km 𝒘 ~ RMB 2 – 4

• Fi

Fixed d = 6km

• Two sce

scenario ios:

• Peak hour: ത

𝝁 = 200/ℎ𝑠, 𝝂 = 19 km/hour

• Non

Non-pea eak hour: ത 𝝁 = 100/ℎ𝑠, 𝝂 = 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 31

General Model: Optimal PayoutRatio

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

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Optimal Profit: Fixed vs. Dynamic PayoutRatios

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 ҧ 𝜇

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

demand ҧ 𝜇

• Using Didi data, we illustrate that the firm can earn significantly more by

using a dynamic payout ratio

• Limitations/Future research
• Dynamic pricing
• Platform competition

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Thank you!

Questions?

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