Coordinating Supply and Demand on an On-demand Service Platform with Impatient Customers 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 1
Content • Definition • Research Questions • Literature Review • Model Setup • Analytical Results • Numerical illustration: Didi Data • Summary 2
On-demand Service Platform 3
On-demand Service Platform • (1) Customers desire quick service • (2) Many of the platforms use Independent providers Independent Uber Customers Drivers • (3) Use of technology 4
On-demand Service Platform Delivery Transportation Home Services Food & Beverage Health & Beauty Dining & Drinks 5
Some Operating Challenges 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 6
On-demand Service Platform Platform Maximize profit Price p Wage w Demand l Supply k Waiting time Independent Customers Providers Utilization Maximize earnings Maximize utility 7
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”? 8
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 9 (2004), Zhou et al. (2014 ), …
Modeling Framework • Customer demand l depends on price p , and waiting time W q Price p Independent Uber/Didi Customers Drivers Demand l Supply k Waiting time Wq 10
ҧ Customer Demand Consumer utility: 𝑽 𝒘 = 𝒘 − 𝒒 𝒆 − 𝒅𝑿 𝒓 • 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 − 𝒅𝑿 𝒓 ≥ 𝟏 𝒅 Equilibrium price: 𝒒 = 𝟐 − 𝒕 − 𝒆 𝑿 𝒓 • 𝜇 : Maximum (potential) customer demand rate (parameter) • l : Realized customer demand rate; 𝜇 ≤ ҧ 𝜇 (endogenously determined) 𝜇 𝑑 𝑑 • 𝑡 : service level = 𝜇 = 𝑄𝑠𝑝𝑐 𝑤 > 𝑞 + 𝑒 𝑋 = 1 − 𝑞 − 𝑒 𝑋 11 𝑟 𝑟 ഥ
Modeling Framework • Supply of independent service providers k depends on earnings, which depend on wage w , utilization r Wage w Independent Uber/Didi Customers Drivers Supply k Demand l Utilization r 12
Supply of Service Providers Provider’s earning rate: 𝝁𝒆 = 𝒙 𝝁𝒆 𝑭 = 𝒙𝝂 𝝇 = (𝒙𝝂) 𝒍𝝂 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 𝝁𝒆 Provider will participate if 𝑭 = 𝒙 𝒍 ≥ 𝒔 • 𝑠 : Reservation wage per unit time with distribution 𝑉[0,1] (parameter) 𝒍 𝟑 𝒍 Equilibrium wage: 𝒙 = 𝜸 𝝁𝒆 = 𝑳𝝁𝒆 • K : Maximum number of service providers; 𝑙 ≤ 𝐿 (parameter) 𝑙 𝜇𝑒 𝜇𝑒 • b : Participation ratio = 𝐿 = 𝑄𝑠𝑝𝑐 𝑠 ≤ 𝑥 = 𝑥 13 𝑙 𝑙
Modeling Framework • Platform: How to set price p and wage w ? Price p Wage w Independent Uber/Didi Customers Drivers Demand l Supply k 14
Platform’s Decision Problem • Profit function 𝒆 𝑿 𝒓 − 𝒍 𝟑 𝝆 = 𝝁 𝒒 − 𝒙 𝒆 = 𝝁 𝟐 − 𝒕 − 𝒅 𝝁𝒆𝑳 𝒆 = 𝝆(𝒍, 𝒕) Average profit Equilibrium price Equilibrium per request wage rate 𝑥 rate 𝑞 Maximize 𝝆 𝒍, 𝒕 𝜇𝑒 Decision variables: 𝑙𝜗 𝜈 , 𝐿 , 𝑡𝜗[0,1] • One-to-one correspondence between ( p, w ) and ( k, s ) 15
Modeling Framework • Waiting time W q and utilization r both depend on supply k and demand l Price p Wage w Independent Uber/Didi Customers Drivers Demand l Supply k Utilization r= 𝜇𝑒 Waiting time Wq 𝑙𝜈 16
Waiting time 𝑋 𝑟 Use M/M/k queueing model Exact formula too complicated 1 𝜍 𝑋 𝑟 = 𝑙−1 𝑙 𝑗 𝜍 𝑗 1 + 𝑙! (1 − 𝜍) 𝜇 1 − 𝜍 σ 0 𝑙 𝑙 𝜍 𝑙 𝑗! Numerical results: 𝑟 = 𝜍 2(𝑙+1) 𝑥ℎ𝑓𝑠𝑓 𝜍 = 𝜇𝑒 𝑋 𝜇 1 − 𝜍 𝑙𝜈 Exact when 𝑙 = 1 Very good estimate for 𝑙 > 1 ; See Sakasegawa (1977) Analytical results: 𝑟 = 𝜍 2(𝑜+1) 𝑥ℎ𝑓𝑠𝑓 𝜍 = 𝜇𝑒 𝑋 𝑙𝜈 𝑏𝑜𝑒 𝑏𝑜𝑧 𝑔𝑗𝑦𝑓𝑒 𝑜 17 𝜇 1 − 𝜍 Provide analytical support for our numerical results
Waiting time 𝑋 𝑟 Use M/M/k queueing model Exact formula too complicated 1 𝜍 𝑋 𝑟 = 𝑙−1 𝑙 𝑗 𝜍 𝑗 1 + 𝑙! (1 − 𝜍) 𝜇 1 − 𝜍 σ 0 𝑙 𝑙 𝜍 𝑙 𝑗! Numerical results: 𝑟 = 𝜍 2(𝑙+1) 𝑥ℎ𝑓𝑠𝑓 𝜍 = 𝜇𝑒 𝑋 𝜇 1 − 𝜍 𝑙𝜈 Exact when 𝑙 = 1 Very good estimate for 𝑙 > 1 ; See Sakasegawa (1977) Analytical results: 𝑟 = 𝜍 2(𝑜+1) 𝑥ℎ𝑓𝑠𝑓 𝜍 = 𝜇𝑒 𝑋 𝑙𝜈 𝑏𝑜𝑒 𝑏𝑜𝑧 𝑔𝑗𝑦𝑓𝑒 𝑜 18 𝜇 1 − 𝜍 Provide analytical support for our numerical results
Waiting time 𝑋 𝑟 Use M/M/k queueing model Exact formula too complicated 1 𝜍 𝑋 𝑟 = 𝑙−1 𝑙 𝑗 𝜍 𝑗 1 + 𝑙! (1 − 𝜍) 𝜇 1 − 𝜍 σ 0 𝑙 𝑙 𝜍 𝑙 𝑗! Numerical results: 𝑟 = 𝜍 2(𝑙+1) 𝑥ℎ𝑓𝑠𝑓 𝜍 = 𝜇𝑒 𝑋 𝜇 1 − 𝜍 𝑙𝜈 Exact when 𝑙 = 1 Very good estimate for 𝑙 > 1 ; See Sakasegawa (1977) Analytical results: 𝑟 = 𝜍 2(𝑜+1) 𝑥ℎ𝑓𝑠𝑓 𝜍 = 𝜇𝑒 𝑋 𝑙𝜈 𝑏𝑜𝑒 𝑏𝑜𝑧 𝑔𝑗𝑦𝑓𝑒 𝑜 19 𝜇 1 − 𝜍 Provide analytical support for our numerical results
Models and Results 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 20
Base Model: Fixed Payout Ratio 𝑥 • Under additional constraint: 𝛽 = 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 . 21
General Model: Dynamic Payout Ratio Price p* Wage w* Payout Ratio Profit 𝝆 ∗ w*/p* Not monotone Max. # providers ↓ ↓ ↑ K Not monotone Service rate ↓ ↓ ↑ μ Unit waiting cost c Max. demand rate ത 𝛍 Avg. units requested d 22
General Model: Dynamic Payout Ratio Price p* Wage w* Payout Ratio Profit 𝝆 ∗ w*/p* Not monotone Max. # providers ↓ ↓ ↑ K Not monotone Service rate ↓ ↓ ↑ μ Unit waiting cost Not monotone ↑ ↑ ↓ c Max. demand rate ത 𝛍 Avg. units requested d 23
General Model: Dynamic Payout Ratio Price p* Wage w* Payout Ratio Profit 𝝆 ∗ w*/p* Not monotone Max. # providers ↓ ↓ ↑ K Not monotone Service rate ↓ ↓ ↑ μ Unit waiting cost Not monotone ↑ ↑ ↓ c Max. demand rate ↑ ↑ ↑ ↑ ത 𝛍 Avg. units requested ↑ ↑ ↑ ↑ d 24
Extension: Total Welfare Equitable payoff parameter, • Total welfare function: 0 ≤ γ ≤ 1 Π 𝑙, 𝑡 = (1 − γ)π 𝑙, 𝑡 + γ(𝐷 𝑡 + 𝑄 𝑡 ) Total welfare Platform’s Consumer and profit Provider surplus • 𝛿 = 0 , basic model (platform profit) • 𝛿 = 1/2 , equal weights on profit and consumer/provider welfare • ℎ𝑗ℎ𝑓𝑠 𝛿 = higher weight on consumer/provider welfare 25
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 𝑥 ∗ increases But the optimal price rate 𝑞 ∗ is not necessarily monotonic. Optimal payout ratio ( w */ p *) increases Platform profit p * decreases 26 Social welfare ( C s +P s ) increases
Didi Company • Founded in June 2012 • China equivalent of Uber • The largest on-demand ride-hailing service platform operating in over 360 Chinese cities 27
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