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

Transcription

1 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

2 Content Definition Research Questions Literature Review Model Setup Analytical Results Numerical illustration: Didi Data Summary 2

3 On-demand Service Platform 3

4 On-demand Service Platform (1) Customers desire quick service (2) Many of the platforms use Independent providers Customers Uber Independent Drivers (3) Use of technology 4

5 On-demand Service Platform Transportation Delivery Home Services Food & Beverage Dining & Drinks Health & Beauty 5

6 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

7 On-demand Service Platform Platform Maximize profit Price p Wage w Demand l Supply k Customers Waiting time Utilization Independent Providers Maximize utility Maximize earnings 7

8 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

9 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), 9

10 Modeling Framework Customer demand l depends on price p, and waiting time W q Price p Customers Demand l Uber/Didi Supply k Independent Drivers Waiting time Wq 10

11 Customer Demand Consumer utility: U v = v p d cw q 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) W q : Waiting time (endogenously determined) Consumer will request if U v = v p d cw q 0 Equilibrium price: p = 1 s c d W q λ ҧ : Maximum (potential) customer demand rate (parameter) l : Realized customer demand rate; λ λ ҧ (endogenously determined) s : service level = λ ഥλ = Prob v > p + c d W q = 1 p c d W q 11

12 Modeling Framework Supply of independent service providers k depends on earnings, which depend on wage w, utilization r Wage w Customers Demand l Uber/Didi Supply k Independent Drivers Utilization r 12

13 Supply of Service Providers Provider s earning rate: E = wμ ρ = (wμ) λd kμ w : Wage per service unit (decision variable) λd = w k μ Average service speed of providers (parameter) k : Number of participating providers (endogenously determined) r : Utilization = λd kμ Provider will participate if E = w λd k r r : Reservation wage per unit time with distribution U[0,1] (parameter) Equilibrium wage: w = β k λd = k2 Kλd K : Maximum number of service providers; k K (parameter) b : Participation ratio = k K = Prob λd r w k = w λd k 13

14 Modeling Framework Platform: How to set price p and wage w? Price p Wage w Customers Demand l Uber/Didi Supply k Independent Drivers 14

15 Platform s Decision Problem Profit function π = λ p w d = λ 1 s c d W q k2 λdk d = π(k, s) Average profit per request Equilibrium price rate p Equilibrium wage rate w Maximize π k, s Decision variables: kε λd, K, sε[0,1] μ One-to-one correspondence between (p, w) and (k, s) 15

16 Modeling Framework Waiting time W q and utilization r both depend on supply k and demand l Price p Wage w Customers Demand l Uber/Didi Supply k Independent Drivers Waiting time Wq Utilization r= λd kμ 16

17 Waiting time W q Use M/M/k queueing model Exact formula too complicated 1 W q = k! (1 ρ) 1 + k k ρ k Numerical results: Exact when k = 1 W q = ρ 2(k+1) λ 1 ρ σ 0 k 1 k i ρ i i! ρ λ 1 ρ λd where ρ = kμ Very good estimate for k > 1; See Sakasegawa (1977) Analytical results: ρ 2(n+1) λd W q = where ρ = and any fixed n λ 1 ρ kμ Provide analytical support for our numerical results 17

18 Waiting time W q Use M/M/k queueing model Exact formula too complicated 1 W q = k! (1 ρ) 1 + k k ρ k Numerical results: Exact when k = 1 W q = ρ 2(k+1) λ 1 ρ σ 0 k 1 k i ρ i i! ρ λ 1 ρ λd where ρ = kμ Very good estimate for k > 1; See Sakasegawa (1977) Analytical results: ρ 2(n+1) λd W q = where ρ = and any fixed n λ 1 ρ kμ Provide analytical support for our numerical results 18

19 Waiting time W q Use M/M/k queueing model Exact formula too complicated 1 W q = k! (1 ρ) 1 + k k ρ k Numerical results: Exact when k = 1 W q = ρ 2(k+1) λ 1 ρ σ 0 k 1 k i ρ i i! ρ λ 1 ρ λd where ρ = kμ Very good estimate for k > 1; See Sakasegawa (1977) Analytical results: ρ 2(n+1) λd W q = where ρ = and any fixed n λ 1 ρ kμ Provide analytical support for our numerical results 19

20 Models and Results 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 20

21 ҧ Base Model: Fixed Payout Ratio Under additional constraint: α = w p payout ratio), 0 < α < 1 (fixed Analytical Result: Both the optimal wage rate w and the optimal price rate p increase in the maximum demand rate λ and average service unit d. 21

22 General Model: Dynamic Payout Ratio Max. # providers K Service rate μ Unit waiting cost c Max. demand rate തλ Price p* Wage w* Payout Ratio w*/p* Profit π Not monotone Not monotone Avg. units requested d 22

23 General Model: Dynamic Payout Ratio Max. # providers K Service rate μ Unit waiting cost c Max. demand rate തλ Price p* Wage w* Payout Ratio w*/p* Profit π Not monotone Not monotone Not monotone Avg. units requested d 23

24 General Model: Dynamic Payout Ratio Max. # providers K Service rate μ Unit waiting cost c Max. demand rate തλ Avg. units requested d Price p* Wage w* Payout Ratio w*/p* Profit π Not monotone Not monotone Not monotone 24

25 Extension: Total Welfare Total welfare function: Equitable payoff parameter, 0 γ 1 Π k, s = (1 γ)π k, s + γ(c s + P s ) Total welfare Platform s profit Consumer and Provider surplus γ = 0, basic model (platform profit) γ = 1/2, equal weights on profit and consumer/provider welfare higher γ = higher weight on consumer/provider welfare 25

26 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 (C s +P s ) increases 26

27 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

28 Didi Data Hangzhou, capital city of Zhejiang province with over 7 million people Sep and Nov in 2015 Peak hour (9am, 7pm): l=2000 m=19 km/hour Non-peak hour (11pm): l=1000 m=26 km/hour Peak Hours Non-peak Hours 28

29 Didi Data Hangzhou, capital city of Zhejiang province with over 7 million people Sep and Nov in 2015 Average travel distance fairly constant during peak and nonpeak 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

30 Model Illustration Based on Didi data Focus on Express/Private services Maximum number of available drivers K 390 The fixed payout ratio α 80% Reservation wage r ~ RMB 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 30

31 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

32 General Model: Optimal Payout Ratio Optimal payout ratio a* increases as unit waiting cost c increases 32

33 Optimal Profit: Fixed vs. Dynamic Payout Ratios Optimal a*=0.6 Optimal a*=0.8 Substantial profit increases when the optimal payout ratio is significantly different from the fixed ratio! 33

34 ҧ ҧ Summary A modeling framework for optimal price and wage decisions for an ondemand 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 λ Optimal payout ratio w*/p* is also increasing in the max potential demand λ 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 34

35 Thank you! Questions? 35