Transcript [Business Communication]

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).
Wharton Empirical Workshop in
Operations Management.
Motivation
• Research in OM 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% fill rate.
• 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
2
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
3
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
4
Modeling Customer Choice
Ham SKU 1
Outside good
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   CRCRi   INV INViv
+1[j W ]  iq f (Qiv , Eiv )   T Tv   ijv
Waiting cost for
products in W
Seasonality
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)
4:45
QL(t),
EL(t)
ts
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)
6
Estimating the Observed Queue Length
12
11
10
𝑄𝜏
9
8
7
6
𝑃(𝜏)𝑄𝑡 𝑄𝜏
5
4
3
Qt = 2
2
1
0
t
0
0.05
¿
0.1
P(Q)
0.15
t+1
Time customer
approaches queue
7
Estimating the Observed Queue Length
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18
17
16
15
14
13
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11
10
9
8
7
6
5
4
3
2
1
0
Qt = 2
t
0
0.1
0.2
t+1
¿
Time customer
approaches queue
8
Estimating the Observed Queue Length
Conditional Queue Distribution
20
18
t=15
t=5
t=25
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Queue length
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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.
9
Simulation
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RESULTS
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Estimated Parameters
•Effect is non-linear
•Increase from Q=5 to 10 customers in line
=> equivalent to 3.5% price increase
•Increase from Q=10 to 15 customers in line
=> equivalent to 10.1% price increase
•Negative correlation between price & waiting sensitivity
•Effect is non-monotone
12
Waiting Sensitivity for the Average Customer
0.30
0.25
Purchase probability
0.20
0.15
Average customer
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
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Average customer
Waiting Sensitivity for the Average Customer
0.30
0.25
Low price
sensitivity
Purchase probability
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
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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
15
Congestion & Demand Externalities
$ $$ $$
$ $$
$
Price Discount on Product L
$$
$ $
$
$$
$
$ $$
$
$
16
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
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> 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)
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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%)
21
Conclusions
• New data collection 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:
– Price sensitivity negatively correlated with waiting sensitivity > Price
reductions on low priced products may generate negative demand
externalities on higher price products
– Consumers exhibit non-linear reaction to queue length
– If consumers consider queue length, but not speed of service, this
may have implications for pooling queues.
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QUESTIONS?
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Queues and Traffic: Congestion Effects
Queue length and transaction volume are positively correlated
due to congestion
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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
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Queueing/Choice Model
Erlang model (M/M/c) with joining probability dk [0,1]
 d1
 d0
0
1

 d2
2
2
 dc
…
c
c
 dc 1
c+1
…
c
dk [0,1]
Parameters (¸, ¹, d) are estimated using the periodic queue data.
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Model Estimation Details
1. Customer arrival rate (¸): store traffic data
2. Service rate (¹): given ¸ and an initial guess of dk 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 dk 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: dk.
5. The process can be repeated until dk converges.
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Empirical vs Theoretical Queue distributions:
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Summary Statistics
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RETAIL DECISIONS & INFORMATION
Planning



Labor Budget
Assortment by
Category/Store
Prices &
Promotion
Strategy
Archival Data
Store
Execution


Staffing
(Part/Full-Time)
Allocation of
Front/BackOffice Work
Service
Performance



Assistance by
Sales Associates
Product
Availability
Waiting at
check-out
Profit



Conversion
Rates
Basket Size
Traffic Growth
?
What can we learn from store
operational data?
30
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 dk [0,1]
 d1
 d0
0
1

 d2
2
2
 dc
…
c
c
 dc 1
c+1
…
c
31
Pictures
32