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Module 9: ForecastingLearning OutcomesAfter completing this module, the students will able to: State the factors which make up a time series.  Identify the appropriate forecasting model to use.  List the types of the major forecasting approaches and their characteristics.  Describe the need for ...

Description

Module 9: Forecasting Learning Outcomes After completing this module, the students will able to:

           

State the factors which make up a time series. Identify the appropriate forecasting model to use. List the types of the major forecasting approaches and their characteristics. Describe the need for forecasting and the role it plays in decision making. Describe the major qualitative forecasting methods. Solve problems using exponential smoothing and moving average. Apply the forecast reliability of forecasting models in business operations. Determine when a forecast can be improved. Discuss the main considerations in selecting a forecasting technique. Calculate and interpret the linear regression equation. Calculate and interpret the coefficient of determination and the standard error or on equation estimate. Determine the confidence interval and the prediction interval in a linear regression equation.

Module Outline 9.1 Basic concepts 9.2 Simple Moving Average 9.3 Weighted Moving Averages 9.4 Simple Exponential Smoothing 9.5 Adjusted Exponential Smoothing 9.6 Forecast Reliability 9.7 Simple Linear Regression

What remains to be resolved is the question of knowing to what extent and up to what point these hypotheses are found to be confirmed by experience. Bernard Ripmann (1826-1866)

A forecast is a prediction, estimate, or determination of what will occur in the future based on a certain set of factors. The value being forecast may be sales, interest rates, funds, gross national product (GNP), technological status, and others. The factors on which a forecast is based may be any of the following past data, opinion or judgment, company data, or perceived pattern related to time. Major Categories of Forecasting Time Horizons 1. Short-term Forecast. It covers one day to one year and are used mainly for shortrun control such as employment, purchasing, scheduling, sales, and production rates. 2. Intermediate-term Forecast. A period ranging from one season to one or two years and is used for production schedules, revenues, cash flow, and budget planning. 3. Long-term Forecast. When a forecast covers from two to five years or more like market trends, technology, facilities expansion, and general policy. Forecasting Techniques 1. Qualitative Techniques. A technique that is based on qualitative data such as the collective opinion of the sales force to forecast the future. 2. Time Series Analysis. A statistical forecasting technique that is based solely on historical data accumulated over a period of time. 3. Causal Method. A method that define as relationships among independent and dependent variables in a system of related equations. Factors in Forecasting 1. Trend. It is the general movement of direction in the data. (e.g. The amount of supply and population in a certain city.) 2. Seasonal Factors. Forecasting factors in which variations in a time series associated with a particular period of time; say a quarter, or a month. (e.g. Sales of Christmas decorations during the months of November and December.) 3. Cyclical Factors. Forecasting factors applicable in longer-term regular fluctuations which make take several years to complete. (e.g. Economic activity of Japan after World War II to the present.) 4. Random Factors. These are events or effects that cannot be predicted with certainty but can impact on the data. (e.g. The price of materials for house construction in a certain city after a major earthquake.) Some of the forecasting methods (or time series methods) included in this text are the following which will be discussed in detailed in the succeeding sections. Forecasting Methods or Time Series Methods 1. Simple Moving Average 2. Weighted Moving Average 3. Simple Exponential Smoothing 4. Adjusted Exponential Smoothing 5. Forecast Reliability

Simple Moving Average is the un-weighted average of a consecutive number of data points. It is a forecasting method simply eliminates the effects seasonal, cyclical, and erratic fluctuations by getting the historical data. Thus, If seasonality, trend, and cyclical factors are not critical in the variable being forecast, the moving-average method is an appropriate tool. It can be used as a forecast seasonal adjustment of the data. To calculate a simple moving average, we simply choose the number of items in the time series data to include in the average. Then, as each time period changes, add the new period time and eliminate the oldest time-period data, and calculate a new average. It’s being computed using the formula: Simple Moving Average = Ʃ (most recent date values) or Number of time periods Where: Fι = Forecast for the time period = actual values for period t - 1 N = number of time periods used in the averaging process. Now let us apply the weighted averages to forecast the example in section 9.2. Example: The WSS motorcycle dealer in Quezon Avenue area wants to accurately forecast the demand for the WSS hybrid motorcycle during the next month. Because the distributor is in Germany, it is difficult to send motorcycle back or recorded it the proper number of motorcycles is not ordered a month ahead. From sales records, the dealer has accumulated the following data for the past 11 months. Determine the weighted moving averages forecast on demand with the following weights (a) 20%, 307%, and s0% and (b) 15%, 25%, and 60%. Month

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Motorcycle s

60

70

50

90

10

80

150

70

Sep t 110

Oct

Nov

150

130

Solution: Computation for the Forecast on 3-Month Moving Average: To compute for the demand forecast on the month of April, we will include the months prior to the month of April. Sowe will only include the demands on January, February, and March with demand values of 60, 70, and 50, respectively. The computation will be: April =

60+70+50 ═ 180 ═ 60 3 3

We will apply the procedure for the succeeding months, as shown below May = 70+50+90 = 210 =70 3 3

September = 80+150+70 = 300 = 100 3 3

June = 50+90+10 = 150 = 50

October = 150+70+110 = 330 =110

3

3

3

3

July = 90+10+80 = 180 = 60 3 3

November = 70+110+150 = 330 =110 3 3

August = 10+80+150 = 240 = 80 3 3

December = 110+150+130 = 390 =130 3 3

Computation for the Forecast on 5- Month Moving Average June = 60+70+50+90+10 = 280 = 56 5 5

October = 10+80+150+70+110 = 420 = 84 5 5

July = 70+50+90+10+80 = 300 = 60 5 5

November = 80+150+70+110+150 = 560 =112 5 5

August = 50+90+10+80+150 = 380 = 76 5 5

December = 150+70+11=+150+130 = 610 = 122 5 5

September = 90+10+80+50+70 = 400 =80 5 5 Table 9.1 shows the summary table for the forecast of three- and five-month moving averages. It can also be noted demand forecast of motorcycles for the month of December is 130 units using 3-month moving average, while 122 units using 5-month moving averages. Period

Month

Actual Demand

1 2 3 4 5 6 7 8 9 10 11 12

January February March April May June July August September October November December

60 70 50 90 10 80 150 70 110 150 130 --

3-Months Moving Average ---60 70 50 60 80 100 110 110 130

5-Months Moving Average -----56 60 76 80 84 112 122

After we obtained the forecasts we have to plot the graph as reflected in Figure 9.1. Notice that longer the period over which the averaging takes place, the smoother the forecast function.

Enrichment Exercise 9.2 The sales (in 000s of units) of product were monitored over 10-month period; the results are shown in the table. Find the three-month and four-month moving averages. Graph the data and give comments on the results. Mont h Sales

Feb

Mar

Apr

May

Jun

Jul

Aug

Sept

Oct

Dec

230

240

250

266

246

235

284

297

301

314

9.3 Weighted Moving Average A weighted moving average is a time series forecasting method in which the most recent data are weighted heavier compared to later data. This is desirable to vary the weights given to historical data forecast future demand or sales. Smoothing Constant is a weighting is a weighting factor used in the exponential smoothing forecasting technique. Mathematically, the weighted moving average is computed as follows:

Where : = forecast for the time period = actual values for period t – i N = Number of time periods used in averaging process = weight given to (t – i) th period in the averaging process .

Now let us apply the weighted averages to forecast the example in section 9.2. Example: The WSS motorcycle dealer in Quezon Avenue area wants to accurately forecast the demand for the WSS hybrid motorcycle during the next month. Because the distributor is in Germany, it is difficult to send motorcycle back or recorded if the proper number of motorcycles is not ordered a month ahead. From sales records, the dealer has accumulated the following data for the past 11 months. Determine the weighted

moving averages forecast on demand with the following weights (a) 20%, 30%, and 50% (b) 15%, 25%, and 60%. Month

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Motorcycle s

60

70

50

90

10

80

150

70

Sep t 110

Oct

Nov

150

130

Solution: April

= (0.20)(60)+ (0.30)(70)+ (0.50)(50)=12+21+25= 58

May

= (0.20)(70)+ (0.30)(50)+ (0.50)(90)=14+15+45=74

June

= (0.20)(50)+ (0.30)(90)+ (0.50)(10)=10+27+5=42

July

= (0.20)(90)+ (0.30)(10)+ (0.50)(80)=18+3+40=61

August

=(0.20)(10)+ (0.30)(80)+ (0.50)(150)=2+24+75=101

September

=(0.20)(80)+ (0.30)(150)+ (0.50)(70)=16+45+35=96

October

=(0.20)(150)+ (0.30)(70)+ (0.50)(110)=30+21+55=106

November

=(0.20)(70)+ (0.30)(110)+ (0.50)(150)=14+33+75=122

December

=(0.20)(110)+ (0.30)(150)+ (0.50)(130)=22+45+65+132

Computation of Weighted Moving Average (15%, 25%, 60%) April

= (0.15)(60) + (0.25)(70) + (0.60)(50) = 9.0 + 17.5 + 30 = 56.5

May

= (0.15)(70) + (0.25)(50) + (0.60)(90) = 10.5 + 12.5 + 54 = 77.0

June

= (0.15)(50) + (0.25)(90) + (0.60)(10) = 7.5 + 22.5 + 6 = 36.0

July

= (0.15)(90) + (0.25)(10) + (0.60)(80) = 13.5 + 2.5 + 48 = 64.0

August

= (0.15)(10) + (0.25)(80) + (0.60)(150) = 1.5 + 20.0 + 90 = 111.5

September

= (0.15)(80) + (0.25)(150) + (0.60)(70) = 12.0 + 37.5 + 42 = 91.5

October

= (0.15)(150) + (0.25)(70) + (0.60)(110) = 22.5 + 17.5 + 66 = 106.0

November

= (0.15)(70) + (0.25)(110) + (0.60)(150) = 10.5 + 27.5 + 90 = 128.0

December

= (0.15)(110) + (0.25)(150) + (0.60)(130) = 16.5 + 36.5 + 78 = 132.0

Table 9.2 Exponential Smoothing Forecast Actual Demand WMA(20%,30%,50%) WMA(15%,25%,60%) 60 70 50 90 58 56.5 10 74 77.0

Month January February March April May June

80

42

36.0

July August September October November December

150 70 110 150 130 -

61 101 96 106 122 132

64.0 111.5 91.5 106.0 128.0 132.0

Enrichment Exercise 9.3 The number of orders received by a pizza shop has been recorded over first twelve days of December. Determine forecasts using the weighted moving average with weight of 20% 35% and 45%, respectively. Sketch the graph of the actual and the forecasts values and compare the results. Week

1

2

3

4

5

6

7

8

9

10

11

12

Sales

21

25

23

33

29

30

36

38

40

45

48

50

9.4 Simple Exponential Smoothing Exponential Smoothing refers to family of forecasting models that are very similar to the weighted moving average that weights the most recent past data more than distant past data. The value of is between 00.0 and 1.00. The value of determines the degree of smoothing that takes place and how responsive the model is to fluctuations of the variable being forecast. The setting of is typically not specific and is usually done by trial and error. The formula simplest exponential Smoothing model is of the following terms: Or Where:

Forecast =(last value) + (1 – a)(last forecast) = Forecast for the next period = Actual data in the present period. = The previously determined forecast for the present period. = weighting factor referred to as the smoothing constant.

Now let us apply the simple exponential Smoothing to forecast the example in section 9.2. Example: The WSS motorcycle dealer in Quezon Avenue area wants to accurately forecast the demand for the WSS hybrid motorcycle during the next month. Because the distributor is in Germany, It is difficult to send motorcycle back or recorded if the proper number of motorcycles is not ordered a month ahead. From ales records, the dealer has accumulated the following data for the past 11 months. Establish the forecasts using simple exponential Smoothing if a = 0.10 and a = 0.30. Month

Jan

Feb

Mar

Apr

May

Jun

Jul

Aug

Sept

Oct

Nov

Motorcycles

60

70

50

90

10

80

150

70

110

150

130

Solution: If we will use a = 0.10, therefore (1 - a) is 0.90, then the substitute to the exponential Smoothing formula = (0.10) (70) + (0.90) (60.00) = 7 + 54.00 = 61.00 = (0.10) (50) + (0.90) (61.00) = 5 + 54.90 = 59.50 = (0.10) (90) + (0.90) (59.90) = 7 + 53.91 = 62.91 = (0.10) (10) + (0.90) (62.91) = 7 + 56.62 = 57.62 = (0.10) (80) + (0.90) (57.62) = 7 + 51.86 = 59.86

= (0.10) (150) + (0.90) (59.86) = 15 + 53.87 = 68.87 = (0.10) (70) + (0.90) (68.98) = 11 + 62.08 = 68.98 = (0.10) (110) + (0.90) (68.98) = 11 + 62.08 = 73.08 = (0.10) (150) + (0.90) (73.08) = 15 +65.77 = 80.77 = (0.10) (130) + (0.90) (80.77) = 13 + 72.69 = 85.69 Solution of exponential Smoothing when a = 0.30, therefore (1 – a) = 0.70, then substitute to simple exponential smoothing = (0.30) (70) + (0.70) (60.00) = 21 + 42.00 = 63.00 = (0.30) (50) + (0.70) (63.00) = 15 + 44.10 = 59.10 = (0.30) (90) + (0.70) (59.10) = 27 + 41.37 = 68.37 = (0.30) (10) + (0.70) (68.37) = 3 + 47.86 = 50.86 = (0.30) (80) + (0.70) (50.86) = 24 + 35.60 = 59.60 = (0.30) (150) + (0.70) (59.60) = 45 + 41.72 = 86.72 = (0.30) (70) + (0.70) (60.00) = 21 + 60.70 = 81.70 = (0.30) (110) + (0.70) (81.70) = 33 + 57.19 = 90.19 = (0.30) (150) + (0.70) (90.19) = 45 + 63.13 = 108.13 = (0.30) (130) + (0.70) (108.13) = 39 + 75.69 = 11.69 Table 9.3 shows the summary table for the simple exponential smoothing forecasts with a = 0.10 and a = 0.30, and figure 9.3 shows its graphical representation. Table 9.3 Simple exponential Smoothing Forecast MONTH

ACTUAL

January February March April May June July August

60 70 50 90 10 80 150 70

Forecast, F1+1 a = 0.10 a = 0.30 - - 60.00 60.00 61.00 63.00 59.90 59.10 62.91 68.37 57.62 50.86 59.86 59.60 68.87 86.72

September October November December

110 150 130 -

68.98 73.08 80.77 85.69

-

81.70 90.18 1.8.13 114.69

Figure 9.3: Simple Exponential Smoothing Forecasts with a = 0.10 and a = 0.30 Enrichment Exercise 9.4 Α mobile phone manufacturing firm wishes to forecast the demand for its release model of mobile phone. Determine demand forecasts of mobile phone given its 10 week sales in all its outlets in Metro Manda using simple exponential smoothing with = 0.20 Week

1

2

3

4

5

6

Sales

15 0

16 0

17 8

19 0

200 14 8

7

8

9

10

16 3

19 8

210

15 0

9.5 Adjusted Exponential Smoothing The exponential smoothing forecasting technique adjusted for trend changes and seasonal patterns. It consists of simple exponential smoothing forecast with trend adjustment factor added to it. The value of the β is a value is also between 0.00 to 1.00 similar to. It reflects the weight given to the recent data. In addition, both and β is often determine subjectively based on the judgment of the forecaster. Mathematically, the adjusted exponential smoothing model can be described αs follows:

Where:

= Adjusted exponential smoothing in the present period.

T = Αn exponentially smoothed trend factor. = The last period trend factor. β = Exponential smoothed trend factor for time period t. This time let us apply the adjusted exponential smoothing to forecast example in section 9.2 Example: The WSS motorcade dealer in Quezon Avenue area wants to accurately forecast the demand for the WSS hybrid motorcade during next month. Because distributor is in Germany, it is difficult to send motorcycle back or recorded if proper number of motorcycle is not intended ordered a month ahead. From sales record, the dealer has accumulated the following data for the past 11 months. Establish the forecast using adjusted exponential smoothing if β=0.20.

Solution: Using β= 0.20, therefore (1 – β) = 0.80 substitute to adjusted forecasts: Month Jan Feb Mar Apr May Jun Jul Aug Sept Oct Motorcycles 60

70

50

90

T_(t+1)=β(F_(1+1)-F_1 )+(1-β)T_t

-

〖AF〗_(t+1)=F_(t+1) ((1-β)/β)T_(t+1) -

10

80

150 70

110

No v 150 130

T_(t+1)= (0.20) (F_(1+1)-F_1 ) 0.80T_t 〖AF〗_(t+1)=(t+1)(1 - 0.20)/0.20)T_(t+1)

We, will Let T2 = 0 T3= 0.20(F3 – F2) + 0.80T2 = 0.209(61 – 60) = 0.80(0) = 0.20(1) + 0 = 0.20 + 0 = 0.20 AF3 = F3 + 4T3 = 61 + 4 (0.20) = 61 + 0.80 = 61.80 T4= 0.20(F4 – F3) + 0.80T3 = 0.20(59.9 – 61) = 0.8090.20) = 0.20(-1.1) + 0.16 = -0.16 AF4 = F4 + 4T4 = 59.9 + 4 (-0.06) = 59.9 + 0.24 = 59.66 T5 = 0.20(F5 – F4) + 0.80T4 = 0.20(62.9 –59.9) = 0.80(-0.06) = 0.20(3.01) -0.048 = 0.602 – 0.048 = 0,55 AF5 = F5 + 4T5 = 62.91 + 4 (0.55) = 62.91 + 2.20 = 65.11 T6 = 0.20(F6 – F5) + 0.80T5 = 0.20(57.62 – 62.91) + 0.80(0.55) = 0.20(-5.29) + 0.044 = 1.058 – 0.044 = -0.62 AF6 = F6 + 4T6 = 57.62 + 4 (-0.62) = 57.62 - 2.48 = 55.14

T7 = 0.20(F7 – F6) + 0.80T6 = 0.20(59.86 – 57.62) + 0.80(-0.62) = 0.20(2.24) + 0. 448 – 0.048 – 0.496 = -0.05 AF7 = F7 + 4T7 = 59.86 – 0.20 = 59.66 T8 = 0.20(F8 – F7) + 0.80T7 = 0.20(68.87–59.86) + 0.80(-0.05) = 0.20(9.01) – 0.04 = 1.76 AF8 = F8 + 4T8 = 68.87 + 4(1.76) = 68.87 + 7.04 = 75.91 T9 = 0.20(F9 – F8) + 0.80T8 = 0.20(68.98 –68.87) + 0.80(1.76) = 0.20(0.11) +1.408 = 1.43 AF9 = F + ...