Question

Henry Clements is an associate of yours who has a car rental agency in a major metropolitan area. Although his is a self-governing company, Henry works thoroughly with three other independent companies in the metro area. They share information also each week they forecast the number of cars each will need the following week. Then if desirable they will transfer cars between locations on Sunday when none of the agencies are open. If they have to go as well as get a car during the week it will cost $75 per car considering the lost time and good will of making the customer wait. Moving on Sunday stretches 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 joyful with this arrangement

Henry revised his company's performance and he believes there is room for improvement. He has found records for the last three months. The data he composed are shown below. It is Friday in addition he has to input his forecast for the number of cars needed tomorrow. He sees you have been taking a class in Quantitative Analysis and has asked you to review his data and help with his forecast to determine what else he might to do increase his performance. As you kind the situation with him you learn that he wants to be able to meet the customer's requirement for a vehicle 95% of the time. He says he infrequently ever gets complaints if the exact model is not available as long as he has a vehicle available, therefore he does not try to anticipate particular size or model requests and lets randomness take care of that. Weekly request is as follows

Week  Demand  Week   Demand
1           126         7         243
2           200         8         167
3           243         9         131
4           167        10        208
5           132        11        251
6           211        12        171

In the past Henry has utilized 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

1. What must his forecast be using this method?

2. What would the prediction be if he used regression analysis?

3. What about time-series forecasting?

4. What will you say him about which is the best option?

Henry has two persons who can check cars out for a rental. One works at the service counter and the other works in the office then can come out to help if needed. Henry has resolute that people arrive following a Poisson distribution. Rentals average about 24 per day also the service person takes about 15 minutes to process a customer for a rental. Henry gets that the agent at the service counter in not busy all the time so he is contemplating not keeping the office person trained and leaving only the service counter person

5. Is this a intelligent move?

6. What is the average time the customer takes after when he/she arrives until he/she has a car?

Presently when the office person in serving customers a second line forms in front of the counter

7. Is that how Henry must set up the waiting area or is there a better way?

When a car is returned to his place, Henry has three staffs who prepare the car for the next rental. As a car reaches one of the employees takes the car and washes, cleans, vacuums, and inspects it, prepares the paperwork for the next rental and returns the car to the lot. The employees all take a car in sequence. Henry has experiential the process and has observed the time each takes to complete each step. The information near the times (in minutes) is as follow

8. Is there is a better way to organize this part of the operations?

Each rental needs two agreement forms one for when the car is checked out and one when it is checked in. Henry orders these forms from a local printer. The printer charges Henry $40 to set up the printer. The forms cost 50cents each. For the reason that of the damage to the forms and the forms becoming obsolete it cost Henry 25% to store the forms. The printer will merely accept orders in multiples of 100

9. If the three months of data collected in addition to presented above is indicative of all demand, how many forms should Henry order?

The printer proposals Henry a 10% discount if Henry orders 5000 or more form at a time

10. Would this be beneficial to Henry? How abundant money would it save if any?

Henry is currently ready compute what do with the cars on Sunday. The other locations report the following on-hand and needed cars. Henry will have 150 cars on-hand Saturday night

Based on past experience, the cost to move cars is

Between And Cost
Henry Location North $12
Henry Location East $22
Henry Location South $17
Location North Location East $7
Location North Location South $28
Location East Location South $14

11 How various cars will need to be moved and what will the total cost of the move be?

12 Based on all the above calculations what would you recommend to Henry about his operation and what changes would you propose (if any)?

Excel QM needs to be used