Bullseye Stores, Inc. is a large retailer of household and grocery merchandise w
ID: 2747513 • Letter: B
Question
Bullseye Stores, Inc. is a large retailer of household and grocery merchandise with 3900 stores in the US. At one Bullseye store located in a major shopping complex in Knoxville there are 40 permanently-installed checkout lanes. Of course the Bullseye seldom opens all 40 lanes, but they need this capacity to serve customers during the peak Christmas buying season. During the Christmas season the Bullseye store in Knoxville is open from 6 AM to 12 AM 7 days a week. The store’s manager has received forecasts for daily store traffic between Black Friday and Christmas Eve, which show the average number of buying patrons varies through a normal day. The table below shows the average number of patrons entering the store during four intervals in a normal weekday. These counts only show patrons who ultimately purchase something and need to join a checkout line.
From
Till
Avg. Number of Buying Patrons
Entering the Store per Hour
6:00 AM
10:00 AM
325
10:00 AM
2:00 PM
475
2:00 PM
6:00 PM
360
6:00 PM
9:00 PM
410
9:00 PM
12:00 AM
240
The average transaction time at the checkout stand is 3 minutes and 45 seconds, which includes time to scan items, bag them, and payment with cash, card, or phone. There’s obviously significant variation in this number from one patron to the next.
a. Help Bullseye determine how many checkout lanes to open during each time time in a normal Christmas shopping weekday. Keep in mind these 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 7 minutes.
b. It’s been discovered someone fat-fingered the forecasting report for the 6:00 PM to 9:00 PM window. Instead of 410 purchasing patrons expected per hour the real number is 610. A reduction in average transaction time is needed to maintain customer service standards. What should the new average transaction time? The four assumptions from Part A also apply here.
From
Till
Avg. Number of Buying Patrons
Entering the Store per Hour
6:00 AM
10:00 AM
325
10:00 AM
2:00 PM
475
2:00 PM
6:00 PM
360
6:00 PM
9:00 PM
410
9:00 PM
12:00 AM
240
Explanation / Answer
Average transaction time at the check out stand is 3 minutes and 45 seconds.
Arrival rate is given in terms of average number of buying patrons per hour, therefore the above information about the check outs is restated as 16 persons per hour. (3600/225)
In case all the 40 lanes are open then the service rate will be 640 persons per hour.
In any case the in each time interval we should have service rate more than the arrival rates.
Therefore number of minimum channels are as follows:
In case of b) it will be
From Till Entering the Store per Hour Number of check out lanes 6:00 AM 10:00 AM 325 21 (325/16) 10:00 AM 2:00 PM 475 30 475/16) 2:00 PM 6:00 PM 360 23 (360/16) 6:00 PM 9:00 PM 410 26 (410/16) 9:00 PM 12:00 AM 240 16 (240/16)Related Questions
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