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.

At a facility’s loading dock, delivery vehicles arrive randomly, starting at 8:00 AM, at a rate of 2.0 per hour. If the dock is occupied by another vehicle, the driver must park in a waiting area until the dock is clear; this occurs with probability 0.20, independent of the time of day or other variables. Identify the family and parameter(s) of each of the following random variables (for instance, “Bernoulli(0.5)”). If it is not one of our “famous” families indicate “other”; if the parameters cannot be determined indicate so.

(a) The time elapsed before the next vehicle arrives.

(b) The number of arrivals between 8:00 AM and 10:00 AM.

(c) The number of vehicles in the loading dock.

(d) Of the next 10 deliveries to arrive, the number than have to wait for the dock to clear.

(e) The number of vehicles in the waiting area.

(f) The number of deliveries made up to and including the first that has to wait for the dock to clear.

(g) The arrival time of the third delivery on a given day

Suppose that the government of Saskatchewan decides to help farmers in the province during pandemic times. Government officials designed a plan that consists of setting a minimum price for grains in local markets above the equilibrium price. We learned in Lecture 2 that a minimum price above the equilibrium price will benefit farmers (because they are now receiving a higher price). You are being asked your opinion about this policy, what could you say about the effect of the policy on total surplus (consumer and producer surpluses)? Is there any downside to this policy, who wins and who loses? Show it graphically.

Alden Construction is bidding against Forbes Construction for a project. Alden believes that Forbes’s bid is a random variable B with the following mass function: P(B $6,000) .40, P(B $8,000) .30, P(B $11,000) .30. It will cost Alden $6,000 to complete the project. Use each of the decision criteria of this section to determine Alden’s bid. Assume that in case of a tie, Alden wins the bidding. (Hint: Let p Alden’s bid. For p 6,000, 6,000 p 8,000, 8,000 p 11,000, and p 11,000, determine Alden’s profit in terms of Alden’s bid and Forbes’s bid.)

“Abed is an avid gambler. On a trip to Las Vegas, he bets $1 on the roulette, and wins big: $1,000! His best friend, Troy, who’s sitting next to him, says:
“You should bet all your winnings on the next spin! If you win, you could end up with one million dollars. And
anyway, it’s the casino’s money you’re playing with, not yours, so no big deal if you lose.”
What do you think of the logic of Troy’s argument, in relation to ideas we have covered in this course? A graph may help but is not strictly necessary.”

The Rogers Construction Company is trying to decide whether to make a bid on a project against 4 competitors. The lowest bid will win the contract and be paid the amount they bid. It believes it will cost the company £10,000 to complete the project (if it wins the contract) and £350 to prepare the bid. Based on historical data, Rogers believes each competitor’s bid has a normal distribution with mean £15,000 and standard deviation £1,500.

a) Set up a simulation model in excel to help the company make the decision of how much to bid.

b) Discuss on the obtained results and make suggestions. For example, what if the competitor’s bid has different distributions?

Assume that an individual wins a lottery. Assume also that the individual was working before the lottery win and had no other nonlabor income before the lottery win.

a) Using the basic static model of individual labour supply, discuss both graphically and explain in your own words how the lottery win will affect the individual’s level of hours worked. Discuss all relevant effects.

b) Is it possible that the individual decides to stop working following the lottery win? In your answer discuss the concept of reservation wages and add the individual’s reservation wage before and after the lottery win to your graph.

Assume that an individual wins a lottery. Assume also that the individual was working before the lottery win and had no other nonlabor income before the lottery win.

a) Using the basic static model of individual labour supply, discuss both graphically and explain in your own words how the lottery win will affect the individual’s level of hours worked. Discuss all relevant effects.

b) Is it possible that the individual decides to stop working following the lottery win? In your answer discuss the concept of reservation wages and add the individual’s reservation wage before and after the lottery win to your graph.