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
Assortment




Pricing
Customer
Experience,
Service
Promotions
Point of Sales Data
Customer Panel Data
Competitive Information (IRI, Nielsen)
Cost data (wholesale prices, accounting)


Lack of objective data
Surveys:
 Subjective measures
 Sample selection
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
3
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
4
Modeling Customer Choice
Outside good
Ham SKU 1
Ham SKU 2
Deli Ham
…
Deli Turkey
Ham SKU n
Join Deli
Require
waiting
(W)
Deli Olive
Deli Ci
Ham SKU n+1
Visit Store
Purchase
prepackaged
Prepackaged
Ham
Prepackaged
Turkey
Prepackaged
Olive
Ham SKU n+2
…
No
waiting
Prepackaged Ci
Price sensitivity
U ijv
consumer
upc
visit
Consumption rate & inventory
  j  i price PRICE jv   CR CRi   INV INViv
+1[j  W ]  iq f (Qiv , Eiv )   T Tv   ijv
Waiting cost for
products in W
5
Matching Operational Data with Customer Transactions
• Issue: do not know the exact state of the queue (Q,E)
observed by a customer
ts: cashier time stamp
4:15
QL2(t),
EL2(t)
ts
4:45
QL(t),
EL(t)
5:15
QF(t),
EF(t)
5:45
• Use choice models & queueing theory to model the evolution
of the queue between snapshots (e.g., 4:45 and 5:15)
Erlang model (M/M/c) with joining probability d k  [0,1]
 d1
 d0
0
1

 d2
2
2
 dc
…
c
c
 d c 1
c+1
…
(c  1) 
6
Results: What drives purchases?
• Customer behavior is better predicted by queue length (Q)
than expected waiting time (W=Q/E)
7
> Single line checkout for faster shopping
8
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)
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?
congestion
congestion
– 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%)
11/5/2010
11
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
12
Waiting & Price Sensitivity Heterogeneity
0.30
Purchase probability
0.25
0.20
0.15
Mean price
sensitivity
0.10
0.05
0.00
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Queue length
13
Waiting & Price Sensitivity Heterogeneity
0.30
Low price
sensitivity
Purchase probability
0.25
0.20
0.15
Mean price
sensitivity
0.10
0.05
High price
sensitivity
0.00
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Queue length
14
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
Cross-price elasticity of demand: % change in demand of H product
after 1% price reduction on L product
Correlation between price and waiting sensitivity
Waiting
Sensitivity
Heterogeneity
None
Medium
High
-0.9
-0.5
0
0.5
0.9
-0.34
-0.74
-0.23
-0.45
-0.04
-0.12
-0.21
-0.05
-0.07
-0.01
-0.01
15
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
16
QUESTIONS?
11/5/2010
17
Queues and Traffic: Congestion Effects
Queue length and transaction volume are positively correlated
due to congestion
18
Stochastic Process of the Queue
Erlang model (M/M/c) with abandonment:
¸ d0
0
¸ d2
¸ d1
1
2
2¹
¸ dc+ 1
¸ dc
…
c
c¹
c+1
…
c¹
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.
19
Estimating the Observed Queue Length
12
11
10
Qt + 1 = 8
9
~¿
Q
8
7
P(¢ ¡ ¿) Q ¿ Q t + 1
6
5
P(¿) Q t Q ¿
4
3
Qt = 2
2
1
0
t
0
¿
0.05
0.1
0.15
t+1
P(Q)
Time customer
approaches queue
20
Estimating the Observed Queue Length
12
11
10
9
Qt + 1 = 8
8
7
Q
6
5
4
3
Qt = 2
2
1
0
t
0
¿
0.05
0.1
0.15
t+1
P(Q)
Time customer
approaches queue
21
Estimating the Observed Queue Length
12
11
10
9
Qt + 1 = 8
8
7
Q
6
5
4
3
Qt = 2
2
1
0
t
0
0.05
¿
0.1
0.15
t+1
P(Q)
~¿ = k) = P
Pr( Q
P (¿) Q t k ¢P (¢ ¡ ¿) k Q t + 1
1
k= 0
P (¿) Q t k ¢P (¢ ¡ ¿) k Q t + 1
Time customer
approaches queue
22
Estimating the Observed Queue Length
20
¿= 5
18
¿ = 15
¿ = 25
16
Queue length
14
12
10
8
6
4
2
0
0
5
10
15
20
25
30
t (min)
•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.
23
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
24
Matching Operational Data with Customer
Transactions
• Issue: do not know the exact state of the queue observed by a
customer
ts: cashier time stamp
4:15
QL2(t),
EL2(t)
4:45
QL(t),
EL(t)
ts
5:15
QF(t),
EF(t)
Continuous
time data
5:45
Periodic data
• 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
25
Consumer Utility
• Utility of customer i of purchasing product j during visit v:
Price sensitivity
U ijv
Consumption rate and
household inventory
  j  i price PRICE jv   CR CRi   INV INViv
+1[j  W ]  iq f (Qiv , Eiv )   T Tv   ijv
Waiting cost for
products in W
•
•
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)
26
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
27
Planning



Labor Budget
Product
Assortments by
Category/Store
Pricing &
Promotions
Archival Data
Store
Execution


Staffing
(Part/Full-Time)
Allocation of
Front/BackOffice Work
Service
Performance



Assistance by
Sales Associates
Product
Availability
Waiting time
Profit



?
What can we learn from store
operational data?
Traffic
Basket Size
Conversion
Rates
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
29
11/5/2010
30