Microsoft Word - POM601 Problem Set 2
Questions (1-3)Full Limo Inc
Full Limo Inc. offers high-end transportation services between the King of Prussia Mall (KPM) and Center City Philadelphia (22.5 miles). The invested capital is $800,000, corresponding to the investment in the 4 luxury vans it owns (you can ignore all other invested capital). Each van can carry 10 passengers. Each van makes 12 daily trips from Philadelphia to KPM and 12 from KPM to Philadelphia. The company charges $10 for each one-way ride. The current load factor is 40% (that is, each ride has 4 passengers on average). A significant source of operating costs is the fuel cost. The company vans have a fuel economy of each of 20 mpg (miles/gallon). Current fuel prices are 2.629 $/gallon. The staff costs and other costs of operating the service and running the business are $1M per year. The company operates 365 days a year.
1. What is the total fuel cost the company incurs per year?
2. What is the ROIC?
3. Assume that the company can increase the fuel efficiency of the vans to 25mpg. What would be the new ROIC?
Process Capability
In preparation for the 2012 Olympic games, the managers of the Olympic park in London tested the swimming pool in order to comply with the standards established by FINA (Federation Internationale de Natation). In particular, these standards require the temperature of the pool to be in the range of 25 to 28 degrees Celsius. The group in charge of the testing took daily samples with five temperature measurements over 10 consecutive days. To ensure consistency, the measurements were taken at the same times during the day (7AM, 10AM, 1PM, 4PM and 7PM). Using the samples the group measured that the new overall temperature mean was 26.6 degrees with a standard deviation of 0.45 degrees.
1. What is the process capability index?
Tom - the Single Server
Tom, a second-year undergraduate, takes a job at the Drexel bookstore. His only responsibility is to answer telephone calls, most of which are inquires about the store hours and book availability. As Tom is the only person answering calls, the store manager is concerned about waiting problems.
Currently, the bookstore receives an average of one call every 3 minutes, with a standard deviation in this inter-arrival time of 3 minutes. Tom requires an average of 2 minutes to handle a call. The standard deviation in this processing time is 1 minute.
The telephone company charges $5.00 per hour per line for the telephone lines whenever they are in use (either while a customer is in conversation with Tom or while waiting to be helped). Assume that there are no limits on the number of customers that can be on hold and that customer do not hang up even if forced to wait a long time.
a. For one of his courses, Tom has to read a book (The Machine that Changed the World, by J. Womack, D. Jones, and D. Roos). He can read 1 page per minute. Tom's boss has agreed that Tom could use his idle time for studying, as long as he drops the book as soon as a call comes in. How many pages can Tom read during an 8-hour shift?
b. How long does a customer have to wait, on average, before talking to Tom?
c. What is the average total cost of telephone lines over an 8-hour shift? (Again, the store is billed whenever a line is in use, including when a line is used to put customers on hold.)
FastBoys Inc
FastBoys Inc provides a broad set of car repair services in the Chicago metropolitan area. The company owns five garages that are dedicated to repair cars only for FastBoys' customers. In any given day, FastBoys receives 3 customer requests for service, on average. The coefficient of variation of the time between customer requests is equal to one. After receiving a request for service, the vehicle is sent to the first available garage. If all the garages are busy repairing other vehicles, the car is kept on the company's central parking lot until one of the garages becomes idle. The average time to repair a vehicle is 1.5 days, with a standard deviation of one day. The travel time between the parking lot and any of the garages is negligible. To provide premium customer service, FastBoys pays for a rental car to each of their customers during the time their vehicle is under repair (this includes the time the vehicle is in the central parking lot waiting to be repaired and the time it is actually been repaired at the garage). The cost of this car rental is $50 per day and can be rented for any fraction of a day (e.g. can be rented for one fourth of a day at a price of $50/4 = $12.5).
1. How long does, on average, a vehicle spend in the central parking lot before it is sent to a garage for repair?
2. How many vehicles are, on average, at the central parking lot at any point in time?
3. How long does a customer have to wait, on average, to get their car repaired (this includes the time the car is in the central parking lot and the time at the garage)?
4. How much does the company spend, on average, in car rentals for its customers in any given day?