###### Case Study #4- PAIN
December 22, 2017
###### Influence of mathematics on electronics
December 22, 2017

Question
Movie rental store problem

You are looking at opening a new movie rental store. You expect that customers will arrive at the store that will have one cashier at a mean rate of 30/hour. You need to hire a cashier. You have narrowed the search to two candidates. Tom has a lot of experience but you will have to pay him more. Jane has never been a cashier but you expect you can hire her at a cheaper rate. Both candidates you would expect to have an exponentially distributed service time with Tom having a mean of 1.2 minutes and Jane of 1.5 minutes. Revenue per month for the store is given by \$6000/Ws where Ws is the average waiting time (in minutes) of a customer in the system.

a) Compare the time that an average customer spends waiting in line for both Tom and Jane.

b) Compare the utilization rates for both Tom and Jane.

c) Assuming that we hire Tom. We know from experience that if 6 or more people are waiting in line, people will simply go somewhere else. If business grows, what is the maximum customer arrival rate that Tom can service before we need to hire another cashier (hint simply program the equations in Excel and trial and error until you get the desired number)? Assume that we will hire another cashier when the average queue length reached 6. What if we hire Jane instead of Tom?

d) Compare the revenue per month if we hire Tom vs. Jane.

e) What would Ws become if we hired BOTH Tom and Jane. Discuss your choice of using equations or simulation.

Please see attached & solve. Format is Excel. Do parts a, b, and d only (bid reduced to 4 credits).