The task is to analyze the store's data and provide recommendations regarding the number of registers and employees needed at the checkout to minimize queues lengths and reduce wait times to less than 3 mins.

The Acme Grocery Store is a medium-sized store with 6 checkout counters. The store is open from 7am to 9pm, 7 days a week. The store manager is concerned about long lines at the checkout registers during the peak hours of 3:30-6:30pm Mon-Fri. Currently two checkout clerks work two registers during this time period. The manager wants to determine the optimal number ofregistersandemployees needed to minimize customer wait times to less than 3 minutes. Data was collected on the arrival rates of customers to the checkout registers from 3:30pm to 6:00pm during the week. Overall arrival rate is said to be poisson distributed. Service time is exponentially distributed with each checkout clerk servicing a mean of 17 customers every hour.

Use the Arrival Time Data below:

Arrival Time of Customers

15:31

15:33

15:35

15:38

15:40

15:42

15:45

15:48

15:51

15:55

15:56

15:57

15:58

15:59

16:02

16:05

16:10

16:11

16:15

16:15

16:16

16:16

16:18

16:20

16:23

16:24

16:27

16:30

16:31

16:31

16:33

16:33

16:35

16:37

16:37

16:37

16:40

16:41

16:45

16:46

16:47

16:50

16:52

16:56

16:56

17:02

17:03

17:03

17:07

17:08

17:10

17:12

17:13

17:15

17:18

17:21

17:22

17:24

17:26

17:28

17:32

17:34

17:36

17:41

17:44

17:44

17:45

17:47

17:50

17:52

The following queuing and simulation questions can be used to analyze the Acme Grocery Store checkout process in Excel. Be sure to define the time period used with your answer.

1. What is the average arrival rate of customers at the checkout registers?
2. What is the average service rate of the checkout registers?
3. What is the average wait time for customers with the current two checkout clerks?
4. What is the probability that more than 5 customers are in the system when there are 2 checkout clerks?
5. What is the optimal number of registers and employees needed to minimize customer wait times of less than 3 mins in the checkout queue?

To answer these questions, we can use a queuing simulation model. The simulation model can be used to generate random numbers for the arrival rate of customers and the service rate of the checkout registers. The simulation model can also be used to track the wait times of customers.

The results of the simulation model can be used to determine the optimal number of registers and employees needed to minimize customer wait times. The manager of the Acme Grocery Store can use this information to make decisions about staffing and scheduling.