Measuring the Effect of Waiting Time 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).

RETAIL DECISIONS & INFORMATION  Point of Sales Data  Loyalty Card / 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 2

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 – Number of cashiers open so that less than 4 customers are waiting in line. – Inventory needed to attain a 95% demand fill rate. How would you choose an appropriate level of service? – Trade-off: operating costs vs service levels – Link between service levels and customer purchase behavior 3 Research Goal

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

Customer Choice Set 5 Require waiting (W) No waiting

Matching Operational Data with Customer Transactions Issue: do not know what the queue looked like (Q,E) when a customer visited the deli section Use marketing and operations management tools to model the evolution of the queue between snapshots (e.g., 4:45 and 5:15) : – Choice Models: how likely is a customer to join the line if Q customers are waiting? – Queuing theory: how many customers will remain in the queue by the time a new customer arrives? 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 Queue length Number of employees

Modeling Customer Choice 7 Require waiting (W) No waiting Waiting cost for products in W Consumption rate & inventoryPrice sensitivity consumer product visit Seasonality

Queueing/Choice Model 8 Erlang model (M/M/c) with joining probability 01 2 cc+1 ……

If we knew all model parameters and visit time: estimating the Observed Queue Length 9 t ¿ Time customer approaches queue t+1

But, visit time is unobserved! 10 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.

Model Estimation Details 11 Store traffic data => Arrival Rate ¸ Empirical distribution of Q, d k, ¸, queuing model => Service Rate ¹ Initial guess of choice model d k Previous snapshot, d k, ¸, ¹ and queuing model => Queue Length faced by the customer Queue length faced by the customer and loyalty card data => Choice Model d k queue length freq.

Simulation 12

RESULTS 13

Results: What drives purchases? Customer behavior is better predicted by queue length (Q) than expected waiting time (W, which is proportional to Q/E) 14

Question: Consider two hypothetical scenarios: – What if we double the number of employees behind the counter? – What if the length of the line is reduced from 10 to 5 customers? Both half the expected waiting time, but which one would have a stronger impact on customer purchase behavior? What’s the implication? 15

16 > Single line checkout for faster shopping

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) 17

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) 18

19 – 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

Estimated Parameters 20 Effect is non-linear Increase from Q=5 to 10 customers in line => equivalent to 1.7% price increase Increase from Q=10 to 15 customers in line => equivalent to 5.5% price increase Pre-packaged products don’t help much. Attract only 7% of deli lost sales when Q=5 -> Q=10 Correlation between price & waiting sensitivity Effect is non-linear Increase from Q=5 to 10 customers in line => equivalent to 1.7% price increase Increase from Q=10 to 15 customers in line => equivalent to 5.5% price increase Pre-packaged products don’t help much. Attract only 7% of deli lost sales when Q=5 -> Q=10 Correlation between price & waiting sensitivity

Waiting & Price Sensitivity 21

Waiting & Price Sensitivity 22

Managerial Implications: Category Pricing Example: – Two products H and L with different qualities and prices: p H > p L – Customers sensitive to price are insensitive to waiting and vice versa. – What if we offer a discount on the price of the L product? 23

Congestion & Demand Externalities 24 $$$ $ $ $$ $$$ $ Price Discount on Product L $

Managerial Implications: Category Pricing Example: – Two products H and L with different prices: p H > p L – Customers sensitive to price are insensitive to waiting and vice versa. – What if we offer a discount on the price of the L product? – If price and waiting sensitivity are negatively correlated, a significant fraction of H customers may decide not to purchase 25 Correlation between price and waiting sensitivity Waiting None Sensitivity Medium Heterogeneity High Cross-price elasticity of demand: % change in demand of H product after 1% price reduction on L product

Conclusions New technology enables us to better understand the link between service performance and customer behavior Estimation challenge: limited information about the queue – Combine choice models with queuing theory 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 26

QUESTIONS? 27

Summary Statistics 28

Queues and Traffic: Congestion Effects 29 Queue length and transaction volume are positively correlated due to congestion

Empirical vs Theoretical Queue distributions: 30

Model Estimation Details 1.Customer arrival rate ( ¸ ): store traffic data 2.Service rate ( ¹ ): given ¸ and an initial guess of d k we estimate ¹ by matching the observed distribution of queue lengths with that implied by the Erlang model. 3.Queue length: Given ¹ and ¸, and the initial guess of d k we estimate the queue length that customers faced (integrating the uncertainty about the time when they visited the deli). 4.The estimated queue lengths is used to estimate the probability of joining the queue: d k. 5.Go to step 2 until d k converges. 31