No Slide Title1. List the features of a good forecast.
2. Outline the steps in the forecasting process.
3. Compare and contrast qualitative and quantitative approaches to forecasting.
4. Identify three qualitative forecasting methods.
5. Briefly describe averaging techniques, trend and seasonal techniques and regression analysis, and solve typical problems.
6. Describe two measures of forecast accuracy.
7. Describe two ways of evaluating and controlling forecasts.
Demand Forecasting
Features of Forecasts
1. Causal System. Forecast techniques generally assume that the same underlying causal system that existed in the past will continue to exist in the future.
2. Forecast Error. Forecasts are rarely perfect; actual results usually differ from predicted values.
3. Group Forecasts. Forecasts for groups of items tend to be more accurate than forecasts for individual items because forecasting errors among items in a group usually have a canceling effect.
4. Accuracy and Time. Forecast accuracy decreases as the time period covered by the forecast (i.e. the time horizon) increases. Generally, short-term forecasts must deal with fewer uncertainties than long-term forecasts.
Demand Forecasting
The process of forecasting has four clearly definable steps:
1. Determine the purpose of the forecast. The use to which the forecast will be used will determine both the technique to be used and the frequency with which the forecast has to be updated.
2. Establish a time horizon. How far forward are we interested in forecasting? Next week? Next month? Next year? Next 20 years? The choice of horizon affects the choice of technique and this, in turn, determines the amount of data and effort needed to prepare the forecast.
3. Prepare the forecast. This involves four steps:
a. Identify the assumptions in the forecast model you propose to use.
b. Gather the data.
c. Analyze the data.
d. Forecast.
4. Monitor the results. It is necessary to monitor forecast results to determine whether certain underlying factors in the model have undergone change. Has the trend weakened? Strengthened? Is the seasonal variation the same as in prior periods?
Demand Forecasting
Types of Forecasts
1. Qualitative - consists mainly of subjective inputs such as human factors, personal opinions or hunches which may be difficult or impossible to quantify.
2. Quantitative - involve the extension of historical data or development of associative models.
Time Series - extension of historical data by identifying patterns in the past that might reasonably be expected to continue in the future.
Causal models - development of an association between the variable we are interested in forecasting and one or more variables that might explain the variable of interest.
Demand Forecasting
Time Horizon
Accuracy Required
Management Level
Forecasting Methods
Qualitative Forecasting Methods
Executive Opinion. Forecasts that are based on the judgment and experience of managers.
Sales Force Composite. Forecasts compiled from estimates of demand made by members of a company’s sales force
Consumer Surveys. A forecasting method that seeks input from customers regarding future purchasing plans for existing products or services.
Market Research. This method tests hypothesis about new products or services or new markets for existing products or services.
Delphi Method. A forecasting technique using a group process that allows experts to make forecasts.
Demand Forecasting
These can be broken into two main categories:
1. Time Series (TS) Models. – A forecasting approach in which future values of a series can be estimated from past values of the series. Driving forward by looking at the rear view mirror. Types of TS models include:
Simple Average / Moving Average / Weighted Moving Average
Exponential Smoothing: Single, Trend, Seasonal, and Trend and Seasonal
Trend Projection
2. Associative (Causal) Models. A forecasting method which identifies related variables that can be used to predict values of the variable of interest. The essential element is the development of an equation that summarizes the effects of predictor variables. The primary method of analysis is known as regression.
Demand Forecasting
Time Series Models
A time series is a time-ordered sequence of observations taken at regular intervals over a period of time. Analysis of a time series requires an identification of the underlying behaviour of the series. This behaviour may have four patterns:
1. Trend refers to a gradual, long-term movement in the data. Population shifts, changing incomes and cultural changes often account for such movements.
2. Seasonality refers to short-term, fairly regular variations that are generally related to weather factors or to human-made factors such as holidays.
3. Cycles are wavelike variations of more than one year’s duration. These are often related to a variety of economic and political factors.
4. Irregular variations are due to unusual circumstances such as severe weather conditions, strikes or a major change in a product or service. They do not reflect typical behaviour, and they should be removed from the data before any analysis is done.
5. Random variations are the residual variations that remain after al the other behaviours have been accounted for.
Demand Forecasting
No trend, but seasonal variation
Trend, but no seasonal variation
Trend and seasonal variation
To average out
average out seasonality
Short term projection
Long term projection
5 - *
The data in the graph is monthly sales for a six-year period. Each year is graphed on top of the preceding one.
Question: What time series patterns exist in this data?
Demand Forecasting
Time Series: Averaging Techniques
1. Naive Forecasts - a naive forecast for any period equals the previous period’s actual value. Although it appears simplistic, it is a legitimate forecasting technique:
it has virtually no cost
forecasts are quick and easy to prepare
easy to understand
can be used for seasonal data (e.g. sales for this December equal sales for preceding December)
2. Moving Average - a forecasting technique that use a number of the most recent actual data values in generating a forecast. There are two types:
a. Simple moving average = SMA = Si Ai / n
where i = the “age” of the data
n = the number of periods in the moving average
Ai = actual value with age i
Note that each data value has the same importance (i.e. weight)
Demand Forecasting
b. Weighted moving average = WMA = Si Ai Wi
where Wi = the relative weight of each data point in the moving average
Note that the sum of all weights , SWi , must equal 1.
For both the SMA and the WMA, a key issue is how many data points will be used to calculate the average. A large number of data points results in a smooth average: a small number of data points means the the model responds very quickly to the most recent changes.
If responsiveness in important, a simple moving average with relatively few data points, or a weighted moving average with a heavy weight on recent data, should be used.
A decision maker must weigh the risk of responding quickly to what might be random fluctuations in the data against the risk of responding slowly to real changes.
Demand Forecasting
5 - *
3. Exponential Smoothing - This is a special case of a weighted moving average in which the weights are determined by mathematical formula, rather than assigned by the decision maker.
Each new forecast is based on a percentage of the previous period’s demand and a percentage of the previous period’s forecast. That is:
Ft + 1 = aDt + (1-a)Ft
where Ft+1 = forecast of the time series for period t + 1
Dt = actual value of the time series for period t
Ft = forecast value for the time series for period t
a = smoothing constant (0 1)
Demand Forecasting
5 - *
Alpha () is a weighting factor with values between zero and one. The sensitivity of forecast adjustments is determined by this smoothing constant.
The closer is to zero, the slower the forecast will be to adjust to forecast errors (i.e. the greater the smoothing). Conversely, the closer the value of is to 1.00, the greater the sensitivity and the less the smoothing.
Commonly used values of range from .05 to .50.
Weight
.1
.2
.3
.4
.5
Values
Impact of a Values on the Weight Attached to Observations in a Time Series
Dt
Dt-1
Dt-2
Dt-3
Dt-4
Dt-5
Dt-6
Dt-7
.1000
.0900
.0810
.0729
.0656
.0590
.0531
.0478
.2000
.1600
.1280
.1024
.0819
.0655
.0524
.0419
.3000
.2100
.1470
.1029
.0720
.0504
.0353
.0247
.4000
.2400
.1440
.0864
.0518
.0311
.0187
.0112
.5000
.2500
.1250
.0625
.0313
.0156
.0078
.0039
Simple Moving Average - Illustration
Compute a three-period simple moving average forecast given demand for gizmos for the last five periods:
Period
1
2
3
4
5
Age
5
4
3
2
1
Demand
42
40
43
40
41
MA3 = (43 + 40 + 41) / 3 = 41.33
If actual demand in period 6 is 39, the forecast for period 7 will be: MA3 = (40 + 41 + 39) / 3 = 40.00
Note that in a moving average, as each new actual value becomes available, the forecast is updated by adding the newest value and dropping the oldest and then recomputing the average. Therefore, the forecast “moves” by reflecting only the most recent values.
Demand Forecasting
Exponential Smoothing Models
1. Simple Model - assumes the time series is flat with no trend or seasonality.
Ft + 1 = aDt + (1-a)Ft
2. Exponential Smoothing for Trend - assumes the time series has a long term
linear trend. Trend may exhibit growth or decline.
At = aDt + (1-a)(At-1 + Tt-1)
Ft + 1 = At + Tt
3. Exponential Smoothing for Trend and Seasonal - assumes the time series has both a long-term trend and seasonal variation. Seasonal variation should occur at approximately the same time each year and be of the same degree.
At = a(Dt / It-L) + (1-a)(At-1 + Tt-1)
Tt = b(At - At-1) + (1 - b)Tt-1
It = g(Dt/At) + (1-g)Rt-L
Demand Forecasting
1
2
3
4
5
6
7
8
9
10
11
12
13
170
210
190
230
180
160
200
180
220
200
180
190
200
170.0
170.0
174.0
175.6
181.0
180.9
178.8
181.0
180.9
184.8
186.1
185.7
186.1
187.5
0.0
40.0
16.0
54.4
-1.0
-20.9
21.2
-1.0
39.1
15.2
-6.1
4.3
13.9
0.0
1600.0
256.0
2959.4
1.1
438.3
447.6
0.9
1531.8
231.8
39.7
18.8
193.2
t
Actual
Demand
Forecast
= |Dt-Ft| = 233.4
= |Dt-Ft| = 235.7
Demand Forecasting
(in '000s At Tt (forecast) Dt-Ft (absolute (squared
t of tons) (average) (trend) At+Tt (error) error) error)
0 205.00 11.00
Sum of Forecast Errors - 3.42
Sum of Absolute Forecast Errors 143.18
Sum of Squared Forecast Errors 3824.59
A(t) + T(t) = F(t)
205 + 11 = 216
216 + 11 = 227
Assume A0 = 205; T0 = 11; = .2; = .1
Demand Forecasting
(in At Tt (seasonal (forecast) Dt-Ft (absolute (squared
t units) (average) (trend) ratio) [At+Tt]*It-L+K (error) error) error)
0
5 5800 5689 47 0.96 4950 850 850 722500
6 5200 5889 85 0.84 4589 611 611 373457
7 6800 6016 96 1.12 6572 228 228 52104
8 7400 6123 99 1.20 7334 66 66 4367
9 6000 6227 100 0.96 5971 29 29 849
10 5600 6393 116 0.86 5324 276 276 75911
11 7500 6552 127 1.13 7259 241 241 58115
12 7800 6639 117 1.19 8044 -244 244 59764
13 6300 6715 107 0.95 6497 -197 197 38811
14 5900 6832 109 0.86 5858 42 42 1727
15 8000 6969 116 1.14 7843 157 157 24772
16 8400 7080 115 1.19 8428 -28 28 804
17 6835
18 6296
19 8457
20 8958
2030
2970
1413181
Exponential Smoothing With Trend and Seasonal: An Illustration
Assume A0 = 5500; T0 = 0; L = 4; I0 = 1.20; I-1 = 1.10; I-2 = 0.80; I-3= 0.90; a = .20; b = .25; g = .50
Demand Forecasting
Trend Projection: An Alternative to Exponential Smoothing
Whazzit? A method of taking time series data and separating (decomposing) it into one or more components of trend, seasonal, cyclical, and random variation. Once the data has been “decomposed”, we can estimate the values of the individual components and use these estimates to predict future values of the time series.
Steps:
2. Centre the moving average.
3. Divide the centered moving average into the demand values. This is the seasonal-random component.
4. Average the seasonal-random component for the same time period in successive years. This average is the seasonal factor for the time period.
5. Divide each actual demand value by its seasonal factor. This produces deseasonalized demand.
6. Regress deseasonalized demand against time and calculate the trend value and the constant term.
7. Develop a trend forecast.
8. Multiply the trend forecast by the seasonal factor. This is the actual forecast.
Demand Forecasting
Year Quarter Period Sales Average Average Component Factor Sales
Year 1 1 1 4800 0.932 5149
2 2 4100 5350 0.838 4894
3 3 6000 5600 5475 1.096 1.093 5488
4 4 6500 5875 5738 1.133 1.143 5685
Year 2 1 5 5800 6075 5975 0.971 0.932 6222
2 6 5200 6300 6188 0.840 0.838 6207
3 7 6800 6350 6325 1.075 1.093 6219
4 8 7400 6450 6400 1.156 1.143 6472
Year 3 1 9 6000 6625 6538 0.918 0.932 6436
2 10 5600 6725 6675 0.839 0.838 6684
3 11 7500 6800 6763 1.109 1.093 6860
4 12 7800 6875 6838 1.141 1.143 6822
Year 4 1 13 6300 7000 6938 0.908 0.932 6758
2 14 5900 7150 7075 0.834 0.838 7043
3 15 8000 1.093 7317
4 16 8400 1.143 7347
(Step 1 ) ( Step 2 ) ( Step 3 ) ( Step 4 ) ( Step 5 )
Trend Projection: An Illustration
Regression Output: Trend Forecast: Quarterly Forecast:
Constant = 5099.5 T(17) = 5100 + 147(17) = 7601 F(17) = 7601 x .932 = 7084
Std Err of Est = 212.6531
R Squared = 0.920804 T(18) = 5100 + 147(18) = 7748 F(18) = 7748 x .838 = 6493
No. of Observations = 16
Degrees of Freedom = 14 T(19) = 5100 + 147(19) = 7895 F(19) = 7895 x 1.093 = 8629
X Coefficient(s) 147.1397 T(20) = 5100 + 147(20) = 8042 F(20) = 8042 x 1.143 = 9192
Std Err of Coef. 11.53273
( Step 6 ) ( Step 7 ) ( Step 8 )
Demand Forecasting
Demand Forecasting- Additional Illustration # 1
National Mixer Inc. sells can openers. Monthly sales for a seven-month period were as follows:
Month Sales
Feb 20
Mar 18
Apr 15
May 20
Jun 18
Jul 22
Aug 20
a. Plot the monthly data on a sheet of graph paper.
b. Forecast September sales volume using each of the following:
(1) A linear trend equation.
(2) A five-month moving average.
(3) Exponential smoothing with a smoothing constant (a) equal to .20, and a March forecast of 19.
(4) The naive approach
c. Which method seems least appropriate? Why?
d. What does the use of the term sales rather than demand presume?
Demand Forecasting
Demand Forecasting- Additional Illustration # 2
a. Develop a linear trend equation for the following data on freight car loadings, and use it to predict
loadings for periods 11 through 14.
b. Use trend-adjusted exponential smoothing with a = .3 and b = .2 to smooth the data. Forecast periods
11 through 14.
Year Number(‘00)
ACTUAL vs FORECAST