Wait Line Models

No matter the business or the location, wait lines are found in every business and every day. Wait lines exist anywhere and everywhere from fast food restaurants and manufacturing operations, to airline passenger boarding and prescription refills. We all have to wait for some good or service.  As an example, consider how long it took you to renew your drivers license.  How long did it take you to buy that last minute loaf of bread? 

No matter the situation, customers do not like to wait. Granted, we are all locked in to the Department of Motor Vehicles, but if possible, customers will move to the competition with fewer wait times.  Wait lines must be analyzed and kept to a minimum cycle time.

Another tool in the MBAs Management Science toolbox is the Wait Line Model.  The Wait Line problem is a programming tool that is easily solved for with the use of Excel and the proper formulas. The Wait Line Model in an Excel template can solve for mean time between customers, time per service, traffic intensity, utilization rate of server, average number of customers waiting in line, average waiting time, and probability of no customers in the system.

In this assignment you will use the Excel data analysis tool known as Wait Line Single Server, Infinite Population, Poisson Arrival, Constant Service Time, Unlimited Queue Length tool. 

The Excel setup for this problem is .  There is no need to set up anything!  The embedded Excel file has all the formulas included.  You need only plug in the different values called out below to solve this Wait Line problem!

Assume you are in a medical providers office and there is a single provider. The waiting room is full.  Also, assume that the unit of time is hours, arrival rate of customers per hour is .9, and the service rate is .75 customers per hour.

Answer the following questions:

1. What is the mean time between arrivals?
2. Exact time per service?
3. Traffic intensity?
4. Utilization rate of server?
5. Average number of customers waiting in line?
6. Average number of customers in system?
7. Average time waiting in line?
8. Average time in system?
9. Probability of no customers in system?
10. Explain the implications of this wait line model on business operations. What steps need to be taken to optimize wait times without jeopardizing the health of the business? 
11. Provide a brief narrative of your wait line analyses and describe the importance of the use of this tool for business and industry. Insert this narrative as a text box in the excel file.

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2016 ECPI