Homework #5

Please submit the homework in hardcopy. I will not check the compass assignment dropbox.

1. Illini Walk-in clinics (IWC) is a chain of medical clinics that specialize in convenient treatment of a limited range of basic illnesses. A typical IWC is located in a drug store and is staffed by nurse practitioners (NP). The NPs are the only employees at a location. IWC has an average revenue of \$35 per patient visit, and an NP spends on average 20 minutes to process a patient although there is significant variability in this time. Assume the time is exponentially distributed. NPs are paid \$10 per hour (regardless of seeing a patient) plus additional \$15 per hour for the time that they are seeing a patient. For example, if a NP worked for 5 hours and saw patients for 3.5 hours during those 5 hours, the payment will be \$10*5+\$15*3.5 = \$50+\$52.5 = \$102.5.
1. (a) ?AparticularIWCbranchisstaffedwith2NPs.Patientsarriveatarateof3.9perhour.The time between patients is approximately exponentially distributed. What is the daily cost for both NPs for this branch? They open from 8AM to 8PM.
2. (b) ?Assumethatthereis\$1000/dayofadditionalfixedoperatingcostforeachbranch.How much profit is this branch making (each day)?
2. BIF Motors is a mid-sized, family-run auto dealership selling both new and used vehicles. Max has recently taken over the business from his father. Max has determined that the relative advantage of BIF has over small garages is doing large complicated repairs that take a full day or longer. To win more of this business BIF has a fleet of four “loaner” cars that customers may drive while their vehicles are being serviced. In an average week, 15.5 major repairs are scheduled for which owners request a loaner car (the service department is open five days per week). Of course, the exact number of loaner requests is random. The time between requests is exponentially distributed. If a loaner car is unavailable when the customer arrives at the dealership, BIF’s policy is to take \$50 off the cost of the service. Most repairs are done within a day but some take longer, resulting in a customer keeping a loaner car for several days. The mean service time 1.2 days. [HINT: The above setting can be interpreted as M/M/4/4 queue. This does not mean that customers will be “blocked” when there is no loaner car left. They will still get the service with \$50 off; however, they will be blocked in the sense that they are not receiving the loaner car.] (a) What is the probability (percentage) that a customer requesting a loaner car from BIF actually receives a loaner car? (b) On an average day, how many loaner cars are on BIF’s lot (not out with customers)?

BADM 375 Due: Apr. 6, 2016

(c) BIF leases the cars from an automaker at a rate of \$350 per month per car. This includes insurance on the vehicles as well. Max estimates that it costs \$12 per “loan.” This covers the cost of the necessary paperwork when the car goes out as well as cleaning the car when it is returned. What are BIF’s monthly costs of running the loaner car program (including discounts to those who do not receive loaners)? Assume 20 days per month.

[Hint: Cost consists of 3 parts: (a) \$12 per loan variable cost; (b) \$50 discount; (c) lease]

3. American Laboratory Services (ALS) performs medical tests. Physicians send in samples for testing randomly over the day. (Past efforts to put sample submissions on a regulated schedule were unsuccessful.) ALS has had problems managing samples waiting for processing. About 50% of arriving samples require refrigeration. ALS often runs short of refrigerated-storage space. ALC currently cannot afford to hire more technicians or add refrigerated-storage space. Suggest an alternative that requires spending no money. Explain how this will alleviate the storage problem.