1. 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. Read the TexPoint manual before you delete this box.: AAAAAA A A A A A

2. 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 3 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 4

5. Modeling Customer Choice 5 Require waiting (W) No waiting

6. Modeling Customer Choice 6 Require waiting (W) No waiting Waiting cost for products in W Consumption rate & inventoryPrice sensitivity consumer upc visit Seasonality

7. Matching Operational Data with Customer Transactions Issue: do not know the exact state of the queue (Q,E) observed by a customer 7 4:154:455:155:45 ts: cashier time stamp Q L2(t ), E L2(t ) Q L(t ), E L(t ) Q F(t ), E F(t ) ts

8. 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) 8 4:154:455:155:45 ts: cashier time stamp Q L2(t ), E L2(t ) Q L(t ), E L(t ) Q F(t ), E F(t ) ts Erlang model (M/M/c) with joining probability 01 2 cc+1 ……

9. Results: What drives purchases? Customer behavior is better predicted by queue length (Q) than expected waiting time (W=Q/E) 9

10. 10 > Single line checkout for faster shopping

11. 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) 11

12. 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) 12

13. 11/5/201013 – 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

14. Estimated Parameters 14 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 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

15. Waiting & Price Sensitivity Heterogeneity 15 Mean price sensitivity

16. Waiting & Price Sensitivity Heterogeneity 16 Mean price sensitivity Low price sensitivity High price sensitivity

17. Managerial Implications: Category Pricing Example: – Two products H and L with different prices: p H > p L – 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 17 Correlation between price and waiting sensitivity -0.9 -0.500.50.9 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

18. 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 18

19. QUESTIONS? 11/5/201019

20. Queues and Traffic: Congestion Effects 20 Queue length and transaction volume are positively correlated due to congestion

21. Stochastic Process of the Queue 21 01 2 cc+1 …… Erlang model (M/M/c) with abandonment: Given ¸, ¹, d k, 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.

22. Estimating the Observed Queue Length 22 t ¿ Time customer approaches queue t+1

23. Estimating the Observed Queue Length 23 t ¿ Time customer approaches queue t+1

24. Estimating the Observed Queue Length 24 t ¿ Time customer approaches queue t+1

25. Estimating the Observed Queue Length 25 Obtain a distribution of Q v for each transaction by integrating over possible values of ¿. Use E(Q v ) as a point estimate of the observed Q value.

26. 26 Pictures