Question: The management of a major ski resort wants to simulate the rental program during the high season.* The resort has two types of customers: people who pay cash and people who use a credit card. The interarrival times of these customers is exponentially distributed with means of 130 and 60 s, respectively. After arrival, customers must fill out a waiver form. The time taken to fill out the waiver form is normally distributed with a mean of 60 and a standard deviation of 20 s.
After filling out the form, customers get in-line to pay. Time to pay depends on the method of payment. The time required to pay in cash is uniformly distributed between 30 and 45 s; the time required to pay by credit card is uniformly distributed between 90 and 120 s.
Three types of rental equipment-boots, skis, and poles-are rented in that order of frequency. Not everyone rents all three types of equipment because some people already have some of the equipment. After paying, 80% of the people rent boots, 10% go directly to skis, and the rest only rent poles. At the boot counter, an employee takes a normally distributed time with a mean of 90 and a standard deviation of 5 s to obtain the boots for each customer. The time to try the boots is uniformly distributed between 60 and 240 s. About 20% of the people need a different size boot; the rest go to get their skis.
At the ski rental counter, everyone waits until a resort employee is free to obtain the right size ski, which takes a uniformly distributed time between 45 and 75 s. Twenty percent of these people need their bindings adjusted. The binding-adjustment process is exponentially distributed with a mean of 180 s. (The binding-adjustment process is considered separately in terms of staffing.) Seventy percent of the people go on to get poles; the rest leave. Ninety percent of the people who get their bindings adjusted go on to get poles, and the rest leave. At the station where the poles are rented, service is normally distributed with a mean of 60 and a standard deviation of 10 s.
a. Assume that one employee is located in each service station (one at the cash register, one at the boots counter, one at the skis counter, and one at the poles). Simulate this process for 60 days and collect the daily average cycle time. Set a 95% confidence interval with the data collected during the simulation.
b. Test the hypothesis (using a 5% significance level) that a difference in the mean cycle time results when one employee is added to the boots counter.
c. Test the hypothesis (using a 5% significance level) that a difference in the mean cycle time results when one employee is added to the ski counter.
d. Test the hypothesis (using a 5% significance level) that a difference in the mean cycle time results when two employees are added, one to the boots counter and one to the ski counter.