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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). Wharton Empirical Workshop in Operations Management.

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Measuring the Effect of Queues on Customer Purchases

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  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). Wharton Empirical Workshop in Operations Management. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AAAAAAAAAAA

  2. Motivation • Research in OM 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% fill rate. • 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

  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. Modeling Customer Choice Require waiting (W) No waiting

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

  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) 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)

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

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

  9. 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.

  10. Simulation

  11. Results

  12. Estimated Parameters • Effect is non-linear • Increase from Q=5 to 10 customers in line • => equivalent to 3.5% price increase • Increase from Q=10 to 15 customers in line • => equivalent to 10.1%price increase • Negative correlation between price & waiting sensitivity • Effect is non-monotone

  13. Waiting Sensitivity for the Average Customer Average customer

  14. Average customer Waiting Sensitivity for the Average Customer Low price sensitivity Mean price sensitivity High price sensitivity

  15. 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

  16. Congestion & Demand Externalities $$ $$ $$ $$ $$ $$ $ $ $ $ $ $ $ $ $ $ Price Discount on Product L

  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. > Single line checkout for faster shopping

  19. 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)

  20. 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)

  21. 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%)

  22. Conclusions • New data collection 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: • Price sensitivity negatively correlated with waiting sensitivity > Price reductions on low priced products may generate negative demand externalities on higher price products • Consumers exhibit non-linear reaction to queue length • If consumers consider queue length, but not speed of service, this may have implications for pooling queues.

  23. Questions?

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

  25. 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)

  26. Queueing/Choice Model Erlang model (M/M/c) with joining probability Parameters (¸, ¹, d) are estimated using the periodic queue data. … … 0 1 c c+1 2

  27. Model Estimation Details • Customer arrival rate (¸): store traffic data • 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. • 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). • The estimated queue lengths is used to estimate the probability of a customer joining the queue: dk. • The process can be repeated until dkconverges.

  28. Empirical vs Theoretical Queue distributions:

  29. Summary Statistics

  30. Retail decisions & information Planning Store Execution Service Performance Profit • Labor Budget • Assortment by Category/Store • Prices & Promotion Strategy • Staffing (Part/Full-Time) • Allocation of Front/Back-Office Work • Assistance by Sales Associates • Product Availability • Waiting at check-out • Conversion Rates • Basket Size • Traffic Growth ? Archival Data • What can we learn from store operational data?

  31. 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

  32. Pictures

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