Measuring the effect of queues on customer purchases
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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.

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Measuring the Effect of Queues on Customer Purchases

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Measuring the effect of queues on customer purchases

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.

TexPoint fonts used in EMF.

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Retail decisions information

Retail Decisions & INFORMATION

Assortment

Pricing

Promotions

Customer Experience, Service

  • Lack of objective data

  • Surveys:

    • Subjective measures

    • Sample selection

  • Point of Sales Data

  • Customer Panel Data

  • Competitive Information (IRI, Nielsen)

  • Cost data (wholesale prices, accounting)


Operations management literature

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


Real time store operational data number of customers in line

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


Modeling customer choice

Modeling Customer Choice

Require waiting (W)

No waiting


Modeling customer choice1

Modeling Customer Choice

Require waiting (W)

No waiting

Price sensitivity

Consumption rate & inventory

consumer

visit

upc

Waiting cost for products in W

Seasonality


Matching operational data with customer transactions

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

ts

4:15

4:45

5:15

5:45

QL2(t), EL2(t)

QL(t), EL(t)

QF(t), EF(t)


Matching operational data with customer transactions1

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)

ts: cashier time stamp

ts

4:15

4:45

5:15

5:45

QL2(t), EL2(t)

QL(t), EL(t)

QF(t), EF(t)

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

0

1

c

c+1

2


Results what drives purchases

Results: What drives purchases?

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


Measuring the effect of queues on customer purchases

> Single line checkout for faster shopping


Managerial implications combine or split queues

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)


Managerial implications combine or split queues1

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)


Measuring the effect of queues on customer purchases

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%)


Estimated parameters

Estimated Parameters

  • Effect is non-linear

    • 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-monotone


Waiting price sensitivity heterogeneity

Waiting & Price Sensitivity Heterogeneity

Mean price sensitivity


Waiting price sensitivity heterogeneity1

Waiting & Price Sensitivity Heterogeneity

Low price sensitivity

Mean price sensitivity

High price sensitivity


Managerial implications category pricing

Managerial Implications: Category Pricing

  • Example:

    • Two products H andL 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


Conclusions

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


Questions

Questions?


Queues and traffic congestion effects

Queues and Traffic: Congestion Effects

Queue length and transaction volume are positively correlated due to congestion


Stochastic process of the queue

Stochastic Process of the Queue

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

0

1

c

c+1

2

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.


Estimating the observed queue length

Estimating the Observed Queue Length

t

t+1

¿

Time customer approaches queue


Estimating the observed queue length1

Estimating the Observed Queue Length

t

t+1

¿

Time customer approaches queue


Estimating the observed queue length2

Estimating the Observed Queue Length

t

t+1

¿

Time customer approaches queue


Estimating the observed queue length3

Estimating the Observed Queue Length

  • 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.


Measuring the effect of queues on customer purchases

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