Henry Clements is a friend of yours who has a car rental agency in a major metropolitan area. Although he is an independent company he works closely with three other independent companies in the metro area. The three companies share information, with each forecasting the number of cars that will be needed the following week. Furthermore, if required the three partners will transfer cars between locations on Sunday when none of the agencies are open. If they have to go and get a car during the week, it will cost $75 each, considering the lost time and good will of making the customer wait. Moving on Sunday gives the customer the option to return the car to any of the four locations and it has allowed Henry and the other agencies access to extra cars to meet their needs. Everyone is happy with this arrangement. Henry reviewed his company's performance and he believes there is room for improvement. He has obtained records for the last three months. The data he has collated are shown below. It is Friday and he has to input his forecast for the number of cars needed tomorrow. He knows you have been taking a class in Quantitative Analysis and has asked you to review his data and help with his forecast and determine what else he might to do increase his performance. As you discuss the situation with him, you learn that he wants to meet the customers' requirement for a vehicle 95% of the time. He says he rarely ever gets complaints if the exact model is not available, as long as he has a vehicle available, so he does not try to anticipate particular size or model requests and lets randomness take care of that. Weekly demand is as follows.
Week 1: 126...........Week 4: 167...........Week 7: 243...........Week 10: 208
Week 2: 200........... Week 5: 132...........Week 8: 167...........Week 11: 251
Week 3: 243........... Week 6: 211...........Week 9: 131...........Week 12: 171
In the past Henry has used the average number of cars as his basic number and adjusted to meet his goal of 95% service. He asks you about some other methods he has heard about.
Discussion Questions
Q1. What should his forecast be using his method? What are the mean and standard deviation of the demand?
Q2. What would the forecast be if he used regression analysis? What is the regression formula? What is the r value?
Q3. What about time-series forecasting? There are at least six time-series methods. Which is best? What is the MAD of each option?
Q4. What will you tell him about which is the best option?