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 Waiting cost for products in W Consumption rate & inventoryPrice sensitivity consumer upc visit

6. 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) 6 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 ……

7. Results: What drives purchases? Customer behavior is better predicted by queue length (Q) than expected waiting time (W=Q/E) 7

8. 8 > Single line checkout for faster shopping

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) 9

10. 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

11. 11/5/201011 – 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

12. Estimated Parameters 12 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 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

13. Waiting & Price Sensitivity Heterogeneity 13 Mean price sensitivity

14. Waiting & Price Sensitivity Heterogeneity 14 Mean price sensitivity Low price sensitivity High price sensitivity

15. 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 15 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

16. 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

17. QUESTIONS? 11/5/201017

18. Queues and Traffic: Congestion Effects 18 Queue length and transaction volume are positively correlated due to congestion

19. Stochastic Process of the Queue 19 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.

20. Estimating the Observed Queue Length 20 t ¿ Time customer approaches queue t+1

21. Estimating the Observed Queue Length 21 t ¿ Time customer approaches queue t+1

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

23. Estimating the Observed Queue Length 23 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.

24. 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

25. Matching Operational Data with Customer Transactions Issue: do not know the exact state of the queue observed by a customer 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 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 Continuous time data Periodic data

26. Consumer Utility Utility of customer i of purchasing product j during visit v : 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 Waiting cost for products in W Consumption rate and household inventory Price sensitivity

27. 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

28. Archival Data ?  Labor Budget  Product Assortments by Category/Store  Pricing & Promotions Profit Planning Store Execution Store Execution Service Performance  Staffing (Part/Full-Time)  Allocation of Front/Back- Office Work  Assistance by Sales Associates  Product Availability  Waiting time  Traffic  Basket Size  Conversion Rates What can we learn from store operational data?

29. 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

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