Measuring the Effect of Queues on Customer Purchases

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.: AAAAAAAAAAA

2. 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)

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 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

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

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

7. 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)

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) 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

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

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)

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)

13. 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%)

14. 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

15. Waiting & Price Sensitivity Heterogeneity Mean price sensitivity

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

17. 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

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

19. Questions?

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

21. 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.

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

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

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

25. 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.

26. Pictures