Answer All Problems

Part I (22 points) Answer the following questions as true (T) or false (F)

1. The conservative approach to decision making (without probabilities) best protects the decision maker from undesirable results.
2.
3.
4. For quarterly data, if three seasonal indexes have a value greater than one, the other seasonal index must be less than one.
5.
6. The expected value of a decision alternative may never be negative
7. A positive forecast error results in next period's forecast being lower than the current forecast in an exponential smoothing model.
8. To deseasonalize a time series, each value is multiplied by its seasonal index.
9. The trend line for the number of units sold annually by a company is Tt = -15 +95t. It can be said that the number of units sold annually has been decreasing at the rate of 15 per year.
10. Qualitative forecasting techniques should be applied in situations where time series data exist, but when conditions are expected to change.
11. When a variable (such as sales) depends on several independent factors, the appropriate forecasting procedure is exponential smoothing.

Part II Answer all the following short answer problems. For partial credit, you must show all work.

1. (13 points) A furniture and insulation company is trying to decide how many cubic feet of insulation to buy from its supplier before a significant price increase goes into effect. The payoff table below indicates net profits in thousands that reflect ordering and inventory holding costs along with projected levels of sales.
 
 

	Low	Medium	High
d1	8	9	9
d2	9	16	15
d3	7	12	20

a) What decision would be made by the "optimist"?

b) What decision would be made by the "conservative"?

c) What decision would be made using the "minimax regret" approach?

d) Given the following probabilities (p(s1)=.4, p(s2)=.4 and p(s3)=.2), determine the best decision based on the expected value approach.
 

2. (18 points) Researchers have collected data on the hours of television watched per day and the age of a person. You are given the data below.
 

X (age in years)	TV viewing (hours)
30	2
65	7
72	6
41	4

a) Plot the above data in a scatter diagram.

b) Determine the "best fit" linear regression equation for these data.

c) Plot this regression equation on your scatter diagram graph.

d) Based on the above regression line, predict the TV-viewing hours of a 75 year old. Indicate this forecast value on your scatter diagram graph.

3. (14 points) Using the information below, answer the questions:

The Linear Trend Equation: T = 54.93 + 1.69t where T=trend value of the time series in period t
 
 

Time Period	Time Series Value	Forecast	Forecast Error
1	60
2	55
3	64
4	51
5	69
6	66

a) Determine the forecasts for period 7 thru 9.

b) Determine the MAD for the above forecast.

c) Determine the MSE for the above forecast.
 

4. (10 points)

If you had to obtain seasonal index values by hand for a time series data set, how would you go about doing it? There is no need to work out the calculations for a specific problem. Explain (or outline) the steps that would be involved in obtaining seasonal values.
 

5. (7 points)

Sales

Quarter	Year 1	Year 2	Year 3	Year 4
1	404	450	478	501
2	492	536	561	609
3	463	492	523	556
4	561	612	653	696

 

Quarter	Seasonal Index
1	.88
2	1.03
3	.94
4	1.14

Given the above sales data, seasonal index values and a trend line of T = 458.23 + 9.13t, determine the quarterly forecast values for Year 5.
 

6. (11 points)

a) Complete the following statements by filling in the blanks.

In a single-channel waiting line with an arrival rate of 2 trucks per hour and a mean service rate of 3 trucks per hour,

i) the probability that a truck will have to wait for service is       .

ii) the average number of trucks waiting for service is        .

iii) the average time a truck spends in the system is           .
 

b) Distinguish between a single-channel and a multi-channel queue (waiting line). Use simple illustrations.
 

7. (8 points) Martin's Service Station is considering investing in a heavy-snowplow this fall. Martin has analyzed the situation carefully and believes that it would be a profitable investment if the snowfall is heavy. Martin would make a small profit if the snowfall is moderate, but he would lose money if the snowfall is light. Specifically, Martin forecasts a profit of $7000 if the snowfall is heavy, $2000 if it is moderate, and a $9000 lose if the snowfall is light. Based on the weather bureau's long term forecast, Martin estimates that the P(heavy snowfall)=.4, the P(moderate snowfall)=.3 and the P(light snowfall)=.3.

a) Prepare a decision tree for Martin's problem.

b) Would the expected value approach recommend Martin invest in a snowplow. Why or why not?