Operation Research

7

SECTION A …10 marks

Instruction: Highlight the correct answer

1.
2. The components that makes up a typical time series are:
A. Trend and residual variation
B. Seasonal and residual variations
C. Trend and long-term cyclic variations
D. Trend, seasonal and residual variations

3. Short term but regular variations are:
A. sudden
B. determined by formula
C. seasonal
D. determined by some table values

4. The main purpose of a time series moving averages is to:
A. determine the coefficient of correlation
B. smooth out the time series
C. show the correlation between the time series and the regression line
D. determine the linear coefficient

5. The best fitting trend line is the one for which squares or errors are the:
A. most
B. least
C. positive
D. negative

6. Given a projected trend value of 66 and a seasonal value of 2.5. Based on the additive model, the estimated forecast data value for a particular period would be:
A. 64.5
B. 67.25
C. 68.5
D. 71

7. Which of the following is a
DISADVANTAGE
of using a moving average technique to determine time series trend?
A. The trend values obtained do not reflect the general trend.
B. Only one trend value can be obtained for either of the end points of the series.
C. No trend values are obtained for the beginning and end time points of the series.
D. Each moving average trend value obtained does not correspond with a time point

8. The original data value of a time series is 3.2 and the corresponding seasonal variation value is – 2.16. What is the seasonal adjusted value base on the additive model?
A. -5.23
B. 1.04
C. 5.23
D. 5.36

Use the following information to answer Questions 8 and 9

With reference to the following Time Series data:

Time Point

1

2

3

4

5

6

7

8

Data Values

9

14

17

12

10

14

19

15

9. What is the three (3) period moving total for time point 3?
A. 36
B. 39
C. 40
D. 43

10. What is the four (4) period centered moving average for time point 3?
A. 13
B. 13.125
C. 13.25
D. 15.75

11.
Given that the actual value using the additive time series model is:
A. -1.12
B. 2.6
C. 4.39
D. 5.41

Use the following information to answer Questions 11 – 13

The following is a time series for the first 5 months of 2006:

2006

45

50

52

48

55

12. The three point (3) moving totals are:
A. -110, -118, -130
B. 63, 59, 65
C. 120, 145, 112
D. 147, 150, 155

13. The three point moving averages are:
A. 20.3, 24, 25.3
B. 36.7, 39.3, 43.3
C. 40, 48.3, 37.3
D. 49, 50, 51.67

14.
Suppose the equation of the trend line for the time series is given by where t is the nth position of the time series, estimate the value of y at the end of the year.
A. 30
B. 34
C. 51
D. 63
15. Month by month changes in sales related to holiday and other special events would be an example of:
A. trend values
B. total sales
C. seasonal variations
D. residual variations

Use the following information to answer Questions 15and 16

The table shows the number of units (×1000) of an item sold by a company from 1991 – 2000.

X = 4-year centred moving averages

Year

Data

X

Year

Data

X

1991

9.47

1996

7.55

1992

9.26

1997

7.24

1993

8.86

1998

7.01

1994

7.81

1999

6.88

1995

8.01

2000

7.03

16. The first value for the 4-year centred moving average is:
A. 8.39
B. 8.76
C. 8.85
D. 8.96

17. Using values for the 4-year moving averages from question 15, the two values of the deviation y-for 1996 is:
A. – 0.23
B. – 0.10
C. 0.10
D. 0.23

18. Centred moving averages represents the:
A. seasonal variations
B. trend values
C. original values
D. residual variations
19.

In a time series analysis, if the value for the and , then the seasonal variation would be:
A. 5
B. 10
C. 15
D. 20

20. Which of the following is NOT a characteristic of exponential smoothing?
A. Smooth’s random variations in a data
B. Easily altered weighting scheme
C. Weights each historical value equally
D. Has minimal data storage requirements

21. A six – months moving average forecast is better than a three – months moving average forecast if demand:
A. is rather stable
B. has been changing due to recent promotional efforts
C. follows an upward trend
D. follows a downward trend

22. When there is no significant upward or downward movement (or trend) in a time series data overtime, then the data is said to be:
A. Critical
B. Invalid
C. Non-stationary
D. Stationary

Use the following information to answer Questions 22 -24

The table below contains the number of complaints received from the students in 2013:

Month

Complaints

Weight

January

44

0.0

February

49

0.1

March

57

0.2

April

80

0.3

May

121

0.4

June

150

0.5

23. If a three term moving average is used to smooth this series, what would be the second calculated term?
A. 43
B. 62
C. 86
D. 117

24. What would be the last term of a 4-month moving average?
A. 85
B. 98
C. 102
D. 117

25. If the weights listed on the column 3 of the table are applied, what is the moving average at the month of May?
A. 10.0
B. 18.6
C. 34.4
D. 58.5

26. ___________ use(s) management judgement, expertise and opinion to make forecasts.
A. Qualitative methods
B. Quantitative methods
C. Regression
D. Time series
27. In exponential smoothing, the closer alpha is to _____, the greater the reaction to the most recent demand.
A. – 1
B. 0
C. 1
D. – 1 or 1

28. _______ is the difference between the forecast and actual demand.
A. Forecast mistake
B. Forecast error
C. Forecast accuracy
D. Mean Absolute Deviation, MAD

29. Which of the following is NOT present in a time series?
A. Operational variations
B. Seasonality
C. Trend
D. Random variations

30.

In a time series analysis, Calculate the actual value
y
using the time series model.
A. 30
B. 80
C. 150
D. 160

31. All the following are forecasting techniques
EXCEPT
:
A. Causal models
B. Qualitative models
C. Optimistic Predictor models
D. Time-series models

32. Time-Series analysis is described best as the forecasting techniques that:
Attempt to incorporate judgemental or subjective factors in decision making.
Relies on quantitative data and incorporates variables or factors that might influence quantity being forecasted.
Develops the best statistical relationship between dependent and independent variables.
Make assumption about what will happen in the future as a function of what happened in the past.

33. Bob forecasted the total hospital impatient days for three months.

Months

January

February

March

Forecast

250

300

275

Actual

243

315

286

With the actual data received, the mean absolute deviation (MAD) of his forecasted model is:
1
3
11
33

34. Which of the following is
NOT
a quantitative forecasting model?
A. Exponential Smoothing
B. Trend Analysis
C. Consumer Market Survey
D. Causal Regression Analysis

35. The time series demand pattern that is shown in the diagram is:

Cyclic
Horizontal
Seasonal
Trend
36.
In exponential smoothing, the smoothing constant has a value:
A. less than 0
B. between -1 and 1 inclusive
C. between 0 and 1 inclusive
D. greater than 1

SECTION B…30 marks

Instruction: Answer ALL questions. ALL working must be CLEARLY shown.

Building Materials Ltd. wants to predict their sales for the fiscal year 2020, and the financial team was provided with the following table with actual sales value in thousands of dollars:

Month

Sales ($’000)

January

153

February

147

March

204

April

198

May

216

June

139

July

162

Writing all answers to the nearest whole number:
(i) Compute a four – month simple moving average forecast for the sales from May to August 2020.

(4 marks)

(ii) If the actual sales for August is $183,000, what is the percentage error in the forecast? (2 marks)

(iii)
Compute a four – month weighted moving average forecast for the sales from May to August 2020, using the weights: . (4 marks)

(iv)
Compute the exponential smoothing forecast from February to August using and an initial forecast for January as $150,000. (6 marks)

(v) Calculate the Mean Absolute Deviation (MAD) for each forecasting method. (4 marks)

(vi) Calculate the Mean Square Error (MSE)for the weighted moving average (3 marks)

(vii) Calculate the Mean Absolute Percentage Error (MAPE) for the exponential smooth forecast. ( 7 marks)

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