Question

Boise Cascade Corporation

At the Boise Cascade Corporation, lumber mill logs arrive by truck and are scaled (measured to determine the number of board feet) before they are dumped into a log pond. The figure below shows the basic flow.

The mill manager must determine how many scale stations to have open during various times of the day. If too many stations are open, the scalers will have excessive idle time and the cost of scaling will be unnecessarily high. On the other hand, if too few scale stations are open, some log trucks will have to wait.

The manager has studied the truck arrival patterns and has determined that throughout the day, trucks randomly arrive at 17 per hour on average. Each scale station can scale 5 trucks per hour (12 minutes each). If the manager knew how many trucks would arrive during the hour, she would know how many scale stations to have open. For example, 0-5 trucks, open 1 scale station; 6-10 trucks, open 2 scale stations, etc.

However, the number of trucks is a random variable and is uncertain. Your task is to provide guidance for the decision.

1) Based on the mean rate of 17 trucks per hour, what probability distribution should be used?

2) Use the probabilities from the first probability distribution above to create a probability distribution for the number of scale stations to open. For example, 0-5 trucks, open 1 scale station; 6-10 trucks, open 2 scale stations, etc. What is the expected number of scale stations needed?

3) Are there additional factors that should be considered? What are your recommendations for handling those factors?

· You need to answer the questions above in paragraph form as if you are writing to the mill manager.

· Students can work together on the case study. However, each student must turn in their answers in their own words. Your paper needs to be uploaded to Blackboard. It should not be longer than 1 page.

Answer 1

Given that,

At the Boise Cascade Corporation, lumber mill logs arrive by truck and are scaled (measured to determine the number of board feet) before theyare dumped into a log pond.

a) Based on the mean rate of 17 trucks per hour,the possion distribution is used when

possion distribution  

b)here scale 1=0-5

scale 2=6-10

scale 3=11-15

let x=Random variable is no of arrival of trucks

=

=0.0007

p(N-2)=(6,17)+p(7,17)+p(8,17)+p(9,17)+p(10,17)

=

=

p(N-3)=

=01659

Now expected no of stations needed is

E(N)=En*p(N=n)

=1(0.0007)+2(0.0484)+3(0.1659)

3) Many different trucks additional trucks additional factors it would required different operating procedures.

Allowance most be made for such an eventually,.so,atleast 3 scaling stations should be operational to create reduency.

note: If you do not get anything in this solution, please put a comment and I will help you out.