Bullseye Stores, Inc. is a large retailer of household and grocery merchandise with 3900 stores in the United States and Canada. At one Bullseye store located in a major shopping complex in Charlotte there are 40 permanently-installed checkout lanes. Of course the Bullseye seldom opens all 40 lanes. However, they need much of this capacity to serve customers during the peak Christmas buying season.

During the Christmas season the Bullseye store in Charlotte extends its hours and is open from 6 AM to 12 AM 7 days a week. The store’s manager has evaluated daily store traffic between Black Friday and Christmas Eve for the past five years and has found the average number of buying patrons who enter the store varies through a normal day. The table below shows the average number of patrons entering the store per hour during four intervals in a normal weekday. These counts only include patrons who ultimately purchase something in the store and thus need to join a checkout line.

From   Till   Avg. Number of Buying Patrons

Entering the Store per Hour

6:00 AM   10:00 AM   300

10:00 AM   2:00 PM   425

2:00 PM   6:00 PM   350

6:00 PM   9:00 PM   550

9:00 PM   12:00 AM   225

The average transaction time at the checkout stand is 2 minutes and 45 seconds, which includes time to scan items, bag them, and payment with cash, card, Apple Pay, or Samsung Pay. Obviously there can be significant variation in this number from one patron to the next. Help Bullseye determine how many checkout stands to open during each block of time in their normal Christmas shopping week day. Keep in mind the following assumptions:

1. All checkout lanes are parallel single-server systems.

2. Balking, reneging, and switching behavior are minimal.

3. Customers have no preference on which open checkout lane to join.

4. Bullseye sets a minimal customer service target of having the average waiting time in the checkout queue be no longer than 4 minutes.