Problem 1
The director of career advising at Orange Community College wants to use decision analysis to provide information to help students decide which 2-year degree program they should pursue. The director has set up the following payoff table for six of the most popular and successful degree programs at OCC that shows the estimated 5-year gross income ($) from each degree for four future economic conditions:
|
Degree Program
|
Economic Conditions
|
|
Recession
|
Average
|
Good
|
Robust
|
|
Graphic Design
|
145,000
|
175,000
|
220,000
|
260,000
|
|
Nursing
|
150,000
|
180,000
|
205,000
|
215,000
|
|
Real Estate
|
115,000
|
165,000
|
220,000
|
320,000
|
|
Medical Tech
|
130,000
|
180,000
|
210,000
|
280,000
|
|
Culinary Tech
|
115,000
|
145,000
|
235,000
|
305,000
|
|
Computer IT
|
125,000
|
150,000
|
190,000
|
250,000
|
|
Probability
|
0.2
|
0.4
|
0.3
|
0.1
|
Determine the best degree program in terms of projected income, using the following decision criteria:
a. Maximax
b. Maximin
c. Equal likelihood
d. Hurwicz (alpha = .6)
e. Minimax regret
f. EOL (expected opportunity loss)
g. The director of career advising at Orange Community College has paid a small fee to a local investment firm to indicate a probability for each future economic condition over the next 5 years, which is shown in the last row of the above table. Using expected value determine the best degree program in terms of projected income.
h. Determine the EVPI of this problem.
Problem 2
The Americo Oil Company is considering making a bid for a shale oil development contract to be awarded by the federal government. The company has decided to bid $112 million. The company estimates that it has a 60% chance of winning the contract with this bid. If the firm wins the contract, it can choose one of three methods for getting the oil from the shale. It can develop a new method for oil extraction, use an existing (inefficient) process, or subcontract the processing to a number of smaller companies once the shale has been excavated. The results from these alternatives are as follows:
Develop new process: Use present process:
|
Outcomes
|
Probability
|
Profit ($1,000,000s)
|
|
Great success
|
.30
|
$ 600
|
|
Moderate success
|
.60
|
300
|
|
Failure
|
.10
|
-100
|
|
Outcomes
|
Probability
|
Profit ($1,000,000s)
|
|
Great success
|
.50
|
$ 300
|
|
Moderate success
|
.30
|
200
|
|
Failure
|
.20
|
-40
|
Subcontract:
|
Outcome
|
Probability
|
Profit ($1,000,000s)
|
|
Moderate success
|
1.00
|
250
|
The cost of preparing the contract proposal is $2 million. If the company does not make a bid, it will invest in an alternative venture with a guaranteed profit of $30 million. Construct a sequential decision tree for this decision situation and determine whether the company should make a bid.
Problem 3
Consider the following data from a small bookstore.
Number of sales people working------Sales (in $1000)
2---------------------10
3---------------------11
7---------------------13
9---------------------14
10---------------------18
10---------------------20
12---------------------20
15---------------------22
16---------------------22
20---------------------26
x = 10.4------------------y = 17.6
SD(x) = 5.64----------------SD(y) = 5.34
1. Calculate the mean and standard deviation of # of sales people (x) and sales (y). Find sample size n.
2. Calculate the correlation coefficient with all three methods (covariance method, z-score method, and correlation tool in Excel).
3. Find b0 and b1 for the linear regression model with all three methods (two different formulas and Solver). Interpret the meaning of b1 of this linear regression model.
4. Calculate Se and SST.
5. Calculate R square with both methods (correlation coefficient method and the formula r square = 1 - SSE/SST). Interpret the meaning of R square of this linear regression model.
6. Use Regression tool in Excel to find b0, b1, SSE, SST, r, R square, and Se.
7. Estimate the sales if the number of sales people working is 8, 13, and 19, respectively.
Problem 4
The manager of the Petroco Service Station wants to forecast the demand for unleaded gasoline next month so that the proper number of gallons can be ordered from the distributor. The owner has accumulated the following data on demand for unleaded gasoline from sales during the past 12 months:
Month Gasoline Demanded (gal.)
October 800
November 725
December 630
January 500
February 645
March 690
April 730
May 810
June 1,200
July 980
August 1,000
September 850
- Compute a 2-month moving average demand forecast for the months of December to September. Calculate MAD, MAPD and MSE.
- Compute the optimal 2-month weighted moving average demand forecast for the months of December to September. Calculate MAD, MAPD and MSE.
- Assume the demand forecast for October is equal to the actual demand of October, 800. Compute the optimal exponentially smoothed demand forecast for the months of November to September. Calculate MAD, MAPD and MSE.
- Assume the demand forecast for October is 800 and trend for October is 0. Compute the optimal double exponentially smoothed demand forecast for the months of November to September. Calculate MAD, MAPD and MSE.
- Compute linear trend line demand forecast for the months of October to September. Calculate MAD, MAPD and MSE.
- Compare the five forecasting methods by using MAD, MAPD and MSE and indicate which method is the best fit for the data based on MAD, MAPD (or MAPE), and MSE, respectively.
Problem 5
Consider a project which consists of the following set of activities:
|
Activity
|
Days Required
|
Immediate Predecessor Activities
|
|
A
|
3
|
--
|
|
B
|
4
|
A
|
|
C
|
4
|
A
|
|
D
|
3
|
A
|
|
E
|
3
|
D
|
|
F
|
4
|
B
|
|
G
|
6
|
B
|
|
H
|
5
|
F, C, E
|
|
I
|
6
|
G, H
|
|
J
|
4
|
F, C, E
|
|
K
|
2
|
D
|
|
L
|
6
|
I, J, K
|
- Draw the CPM network for this problem in Excel.
- Calculate the earliest and latest start and finish times, and the slack for each activity.
- Identify (Highlight) the critical path.
- Create a Gantt chart for this project in Excel.