Measuring the Effect of Queues 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).

2011 Marketing Science Conference, Houston, TX.

RETAIL DECISIONS & INFORMATION

Point of Sales Data 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

3

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

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

Research Goal

4

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

5

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

consumerupc visit

6

Matching Operational Data with Customer Transactions• Issue: do not know the exact state of the queue (Q,E)

observed by a customer

• Use choice models & queueing theory to model the evolution of the queue between snapshots (e.g., 4:45 and 5:15)

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

Erlang model (M/M/c) with joining probability

0 1 2 c c+1… …

[0,1]kd

1d 2d0d cd 1cd

2 c ( 1)c

7

Results: What drives purchases?

• Customer behavior is better predicted by queue length (Q) than expected waiting time (W=Q/E)

8

> Single line checkout for faster shopping

9

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)

10

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)

1111/5/2010

– 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

12

Estimated Parameters

•Increase from Q=5 to 10 customers in line => equivalent to 3.2% price increase

•Increase from Q=10 to 15 customers in line => equivalent to 8.3% price increase

•Negative correlation between price & waiting sensitivity

•Effect is non-linear

13

0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Queue length

Purc

hase

pro

babi

lity

Waiting & Price Sensitivity Heterogeneity

Mean price sensitivity

14

0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 200.00

0.05

0.10

0.15

0.20

0.25

0.30

Queue length

Purc

hase

pro

babi

lity

Waiting & Price Sensitivity Heterogeneity

Mean price sensitivity

Low price sensitivity

High price sensitivity

15

Managerial Implications: Category Pricing

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

– Customers are heterogeneous in their price and waiting sensitivity– Discount on the price of the L product increases demand, but generates more congestion– 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

16

Conclusions

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

• Estimation challenge: partial observability of the queue– Combine choice models with queueing theory to estimate the

transition between each snapshot of information

• 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

– Consumers exhibit a non-monotone reaction to queue length

17

QUESTIONS?

11/5/2010

18

Queues and Traffic: Congestion Effects

Queue length and transaction volume are positively correlated due to congestion

19

Stochastic Process of the Queue

0 1 2

¸d0 ¸d1 ¸d2

c c+1

¸dc

…

c¹

…

¸dc+1

Erlang model (M/M/c) with abandonment:

dk 2 [0;1] : probability customer joins queue of length k

Given ¸, ¹, dk, we can calculate probability transition matrix P(¿):

P(¿)ij = probability that during time ¿ queue moves from length i to j.

Parameters (¸, ¹, d) are estimated using the periodic queue data.

2¹ c¹

20

Estimating the Observed Queue Length

t

¿

~Q¿

Qt = 2

Qt+1 = 8

Time customer approaches queue

t+1

0

1

2

3

4

5

6

7

8

9

10

11

12

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

P(Q)

P (¿)Q t Q ¿

P (¢ ¡ ¿)Q ¿ Q t + 1

21

Estimating the Observed Queue Length

t

¿

Qt = 2

Qt+1 = 8

Time customer approaches queue

t+1

0

1

2

3

4

5

6

7

8

9

10

11

12

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14

P(Q)

Q

22

Estimating the Observed Queue Length

t

¿

Qt = 2

Qt+1 = 8

Time customer approaches queue

t+1

Pr( ~Q¿ = k) =P (¿)Q t k ¢P (¢ ¡ ¿)k Q t + 1P 1

k = 0P (¿)Q t k ¢P (¢ ¡ ¿)k Q t + 1

0

1

2

3

4

5

6

7

8

9

10

11

12

0 0.020.040.060.08 0.1 0.120.140.16

P(Q)

Q

23

Estimating the Observed Queue Length

0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

18

20

t (min)

Que

ue le

ngth

¿ = 5 ¿ = 15 ¿ = 25

•Obtain a distribution of Qv for each transaction by integrating over possible values of ¿.•Use E(Qv) as a point estimate of the observed Q value.

24

Managing Service Levels in Retail Operations

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

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

• How to choose an appropriate level of service?– Trade-off between operating costs and value for the customer.– Customer experience are subjective and hard to measure

25

Matching Operational Data with Customer Transactions• Issue: do not know the exact state of the queue observed by a

customer

• Periodic data could be used to estimate the (Q,E) corresponding to a transaction– E.g. weighted average of periodic observations around the time stamp

of visit– Idea: use information about the stochastic process driving the

evolution of the queue

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

Continuous time data

Periodic data

26

Consumer Utility

• Utility of customer i of purchasing product j during visit v:

• Customer heterogeneity: random coefficients for price and waiting effect, potentially correlated

• Alternative specifications of f(Q,E) to test for non-linear effects and alternative measures that affect choice (e.g Q/E)

Waiting cost for products in W

Consumption rate and household 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

27

Measuring the Effect of Waiting Time on Customer Purchases

• Data– Deli section of large supermarket chain – Store operational data during 6 months,

every 30 minutes– Large number of products: more than 30

deli-related categories, 135 SKUs– Loyalty card data, including time-stamp

of each transaction

Archival Data ?

Labor Budget Product

Assortments by Category/Store

Pricing & Promotions

ProfitPlanning StoreExecution

Service Performance

Staffing (Part/Full-Time)

Allocation of Front/Back-Office Work

Assistance by Sales Associates

Product Availability

Waiting time

Traffic Basket Size Conversion

Rates

What can we learn from store operational data?

29

Discussion

• Use of store operational data to capture actual objective measures of service– methodology to match periodic operational information with

customer transactions– Estimate effect of queues on customer purchases

• Identify interesting features on how customers react to waiting time:– Affected by queue length, not necessarily expected wait– Non-linear effect, high heterogeneity– Waiting sensitivity is negatively correlated with price sensitivity

• Managerial implications on queuing design and segmentation

3011/5/2010