Transcript [Business Communication]

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).
RETAIL DECISIONS & INFORMATION
Assortment




Pricing
Customer
Experience,
Service
Promotions
Point of Sales Data
Loyalty Card / Customer Panel Data
Competitive Information (IRI, Nielsen)
Cost data (wholesale prices, accounting)


Lack of objective data
Surveys:
 Subjective measures
 Sample selection
2
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
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
Customer Choice Set
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
5
Matching Operational Data with Customer Transactions
• Issue: do not know what the queue looked like (Q,E) when a
customer visited the deli section
ts: cashier time stamp
4:15
QL2(t),
EL2(t)
4:45
QL(t),
EL(t)
ts
5:15
QF(t),
EF(t)
Queue
length
Number of
employees
5:45
• 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?
6
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
productvisit
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
7
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]
8
If we knew all model parameters and visit time:
estimating the Observed Queue Length
𝑄𝜏
𝑃(𝜏)𝑄𝑡 𝑄𝜏
Qt = 2
t
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
0
0.1
0.2
t+1
¿
Time customer
approaches queue
9
But, visit time is unobserved!
Conditional Queue Distribution
20
18
t=15
t=5
t=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.
10
Model Estimation Details
Store traffic data
=> Arrival Rate ¸
Initial guess of
choice model dk
freq.
queue length
Queue length faced by
the customer and
loyalty card data =>
Choice Model dk
Empirical distribution of
Q, dk , ¸ , queuing
model => Service Rate ¹
Previous snapshot , dk ,
¸, ¹ and queuing model
=> Queue Length faced
by the customer
11
Simulation
12
RESULTS
13
Results: What drives purchases?
• Customer behavior is better predicted by queue length (Q)
than expected waiting time (W, which is proportional to Q/E)
14
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?
15
> Single line checkout for faster shopping
16
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)
17
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)
18
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%)
19
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
•Pre-packaged products don’t help much.
• Attract only 7% of deli lost sales when Q=5 -> Q=10
•Correlation between price & waiting sensitivity
20
Waiting & Price Sensitivity
21
Waiting & Price Sensitivity
22
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?
23
Congestion & Demand Externalities
$ $$ $$
$ $$
$
Price Discount on Product L
$$
$ $
$
$$
$
$ $$
$
$
24
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
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
25
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
26
QUESTIONS?
27
Summary Statistics
28
Queues and Traffic: Congestion Effects
Queue length and transaction volume are positively correlated
due to congestion
29
Empirical vs Theoretical Queue distributions:
30
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 joining the queue: dk.
5. Go to step 2 until dk converges.
31