Case Study:

The Acme Grocery Store is a medium$-$sized store with $6$ checkout counters. The store is open from $7$am to $9$pm$,7$ days a week. The store manager is concerned about long lines at the checkout registers during the peak hours of $3$:$30-6$:$30$pm Mon$-$Fri. Currently two checkout clerks work two registers during this time period. The manager wants to determine the optimal number of registers and employees 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 $3$:$30$pm to $6$:$00$pm 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 in the file Week $4$ S$2024$ Case Study Data.xlsx Download Week $4$ S$2024$ Case Study Data.xlsx to determine arrival rate to use in the Excel Queueing Tool Week $3$ Rev $2$ Template S$2024.$xlsx Download Week $3$ Rev $2$ Template S$2024.$xlsx to answer questions below in your simulation model.

Queuing and Simulation Questions:

What is the average arrival rate of customers at the checkout registers?

What is the average service rate of the checkout registers?

What is the average wait time for customers with the current two checkout clerks?

What is the probability that more than $5$ customers are in the system when there are $2$ checkout clerks?

What is the optimal number of registers and employees needed to minimize customer wait times of less than $3$ mins in the checkout queue?