Measuring the Effect of Waiting Time on Customer Purchases

Andrés Musalem Duke University

2

Agenda

• Background• My research• Measuring the effect of waiting

time on customer purchases

Background:

Santiago, Chile

Ph.D., Wharton

Ind. Engineering MBA, U. of Chile

Teaching Interests:

• Market Research (U. Chile) • Pricing (Wharton)• Marketing Management (WEMBA, CCMBA, MEM)• GATE: Global academic travel experience (Daytime MBA)

– South America• Product Management (WEMBA, CCMBA)• Marketing Practicum (Daytime MBA):

My research: Quantitative Marketing

• Mathematical models to study:– How consumers react to coupon promotions?

• Implications for targeting– How consumers react to out of stocks?

• Implications for inventory planning– How consumers react to waiting time?

• Implications for customer service– How to estimate demand for products not yet introduced in a market?

• Implications for assortment/product line decisions– How should firms make efforts to attract or retain customers?– How should firms manage customer expectations?

• underpromise and overdeliver?

Data driven

Game Theory

Measuring the Effect of Waiting Time on Customer Purchases

Andrés Musalem Duke University

Joint work with Marcelo Olivares, Yina Lu (Decisions Risk and Operations, Columbia Business School), and Ariel Schilkrut (SCOPIX).

8

RETAIL DECISIONS & INFORMATION

Point of Sales Data Loyalty Card / Customer Panel Data Competitive Information (IRI, Nielsen) Cost data (wholesale prices, accounting)

Customer Experience, Service

Assortment Pricing Promotions

Lack of objective data Surveys:

Subjective measures Sample selection

9

Operations Management Literature

• Research usually focuses on managing resources to attain a customer service level– Staff required so that 90% of the customers wait less than 1 minute– Number of cashiers open so that less than 4 customers are waiting in

line.– Inventory needed to attain a 95% demand fill rate.

• How would you choose an appropriate level of service?– Trade-off: operating costs vs service levels– Link between service levels and customer purchase behavior

Research Goal

10

Real-Time Store Operational Data: Number of Customers in Line

• Snapshots every 30 minutes (6 months)

• Image recognition to identify: number of people

waiting number of servers

+• Loyalty card data

UPCs purchased prices paid Time stamp

Visit Store

Join Deli

Deli Ham

Ham SKU 1

Ham SKU 2

…

Ham SKU nDeli Turkey

Deli Olive

Deli Ci

Purchase prepackaged

Prepackaged Ham

Ham SKU n+1

Ham SKU n+2

…Prepackaged Turkey

Prepackaged Olive

Prepackaged Ci

Outside good

Modeling Customer Choice

11

Require waiting (W)

No waiting

Visit Store

Join Deli

Deli Ham

Ham SKU 1

Ham SKU 2

…

Ham SKU nDeli Turkey

Deli Olive

Deli Ci

Purchase prepackaged

Prepackaged Ham

Ham SKU n+1

Ham SKU n+2

…Prepackaged Turkey

Prepackaged Olive

Prepackaged Ci

Outside good

Modeling Customer Choice

12

Require waiting (W)

No waiting

Waiting cost for products in W

Consumption rate & inventoryPrice sensitivity

PRICE INV

+1[ ] ( , ) T

price CR INVijv j i jv i iv

q Ti iv iv v ijv

U CR

j W f Q E

consumerproductvisit

Seasonality

13

Matching Operational Data with Customer Transactions• Issue: do not know what the queue looked like (Q,E) when a

customer visited the deli section

• Use marketing and operations management tools to model the evolution of the queue between snapshots (e.g., 4:45 and 5:15):– Choice Models: how likely is a customer to join the line if Q customers

are waiting?– Queuing theory: how many customers will remain in the queue by the

time a new customer arrives?

4:15 4:45 5:15 5:45

ts: cashier time stamp

QL2(t), EL2(t)

QL(t), EL(t) QF(t), EF(t)

ts

Queue length

Number of employees

14

RESULTS

15

Results: What drives purchases?

• Customer behavior is better predicted by queue length (Q) than expected waiting time (W, which is proportional to Q/E)

16

Question:

• Consider two hypothetical scenarios:– What if we double the number of employees behind the counter?– What if the length of the line is reduced from 10 to 5 customers?

• Both half the expected waiting time, but which one would have a stronger impact on customer purchase behavior?

• What’s the implication?

17

> Single line checkout for faster shopping

18

Managerial Implications: Combine or Split Queues?• Pooled system: single queue with c servers

• Split system: c parallel single server queues, customers join the shortest queue (JSQ)

19

Managerial Implications: Combine or Split Queues?• Pooled system: single queue with c servers

• Split system: c parallel single server queues, customers join the shortest queue (JSQ)

20

– Pooled system is more efficient in terms of average waiting time– In split system, individual queues are shorter => If customers react to

length of queue, this can help to reduce lost sales (by as much as 30%)

Managerial Implications: Combine or Split Queues?

congestion congestion

21

Estimated Parameters

•Effect is non-linear• Increase from Q=5 to 10 customers in line

=> equivalent to 1.7% price increase• Increase from Q=10 to 15 customers in line

=> equivalent to 5.5% price increase

•Negative correlation between price & waiting sensitivity

•Pre-packaged products don’t help much.• Attract only 7% of deli lost sales when Q=5 -> Q=10

22

Waiting & Price Sensitivity

23

Waiting & Price Sensitivity

24

Managerial Implications: Category Pricing• Example:

– Two products H and L with different qualities and prices: pH > pL

– Customers sensitive to price are insensitive to waiting and vice versa.– What if we offer a discount on the price of the L product?

25

Congestion & Demand Externalities

$$$$$$ $

$ $$$$ $$

$$

$$$$ $

Price Discount on Product L

$

26

Managerial Implications: Category Pricing• Example:

– Two products H and L with different prices: pH > pL

– Customers sensitive to price are insensitive to waiting and vice versa.– What if we offer a discount on the price of the L product?– If price and waiting sensitivity are negatively correlated, a significant fraction of H customers

may decide not to purchase

Correlation between price and waiting sensitivity -0.9 -0.5 0 0.5 0.9

Waiting None - - -0.04 - -Sensitivity Medium -0.34 -0.23 -0.12 -0.05 -0.01

Heterogeneity High -0.74 -0.45 -0.21 -0.07 -0.01

Cross-price elasticity of demand: % change in demand of H product after 1% price reduction on L product

27

Conclusions

• New technology enables us to better understand the link between service performance and customer behavior

• Estimation challenge: limited information about the queue– Combine choice models with queuing theory

• Results & implications:– Consumers act as if they consider queue length, but not speed of service >

Consider splitting lines or making speed more salient– Price sensitivity negatively correlated with waiting sensitivity > Price

reductions on low priced products may generate negative demand externalities on higher price products

28

QUESTIONS?

29

Queues and Traffic: Congestion Effects

Queue length and transaction volume are positively correlated due to congestion

30

Summary Statistics

31

Model Estimation Details

1. Customer arrival rate (¸): store traffic data2. Service rate (¹): given ¸ and an initial guess of utility model

we estimate ¹ by matching the observed distribution of queue lengths with that implied by the Erlang model.

3. Queue length: Given ¹ and ¸, and the initial guess of utility model we estimate the queue length that customers faced (integrating the uncertainty about the time when they visited the deli).

4. The estimated queue lengths is used to estimate the probability of a customer joining the queue.

5. The process can be repeated until utility converges.

32

Empirical vs Theoretical Queue distributions:

Marketing and other disciplines

MarketingEconomics

Psychology

Engineering

Sociology

Statistics

Ethnography

competition

sales force allocation

consumer decisions

demand forecast

in-depth consumer research

word of mouth

34

Help Vinay & Sameer

Marketing Management

35

3C’s STP+4P’s Angiomax

:What price

would you charge?Why Teams Vinay

and Sameer’s social media

approach was successful?

Would you improve

Starbucks’ service?

Unilever: Should

Unilever introduce

a new product in

Brazil?

Hulu: Ads vs No Ads?

How would you promote the Ford Ka?

Molson: Why the social

media campaign was

not successful?

36

Purchase probability versus queue length and number of employees