Supplementary Material in Forecasting
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Forecasting ProductionPlanningandInventoryControl
Eng.NidalDwaikat IndustrialEngineeringDepartment
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FORECASTING
Learning Objectives:
To recognize that different forecasting methods are appropriate in different situations To become familiar with the various methods of forecasting To learn measures for analyzing the performance of forecast methods
Contents
Introduction to Forecasting
Forecasting Methods:
Qualitative Time Series
o Simple Moving Averageo Weighted Moving Averageo Exponential Smoothingo Adjusting for trends - Double Exponential Smoothingo Multiplicative Seasonal Method
Causal Methods Focus Forecasting
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FORECASTING- a method for translating past experience into estimates of the future
Key questions which must be answered:
what is the purpose of the forecast? what specifically do we wish to forecast? how important is the past in predicting the future? what system will be used to make the forecast?
forecasting horizons:
long-term: more than 2 years medium-term: 3 months to 2 years short-term: 0 to 3 months
forecasting methods:
qualitative methods
quantitative methods
- causal methods
- time series methods
QUALITATIVE FORECASTING METHODS
qualitative forecasting methods arebased on educated opinionsof appropriate persons
1. delphi method:forecast is developed by apanel of expertswho anonymously answer a series
of questions; responses are fed back to panel members who then may change their original
responses
- very time consuming and expensive
- new groupware makes this process much more feasible
2. market research:panels, questionnaires, test markets, surveys, etc.
3. product life-cycle analogy:forecasts based on life-cycles of similar products, services, or
processes
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4. expert judgementby management, sales force, or other knowledgeable persons
QUANTITATIVE FORECASTING METHODS
TIME SERIES FORECASTING METHODS
time series forecasting methods are based on analysis of historical data (time series: a set of
observations measured at successive times or over successive periods). They make the
assumption that past patterns in data can be used to forecast future data points.
1. moving averages (simple moving average, weighted moving average): forecast is based on
arithmetic average of a given number of past data points
2. exponential smoothing (single exponential smoothing, double exponential smoothing): a type
of weighted moving average that allows inclusion of trends, etc.
3. mathematical models (trend lines, log-linear models, Fourier series, etc.): linear or non-linear
models fitted to time-series data, usually by regression methods
4. Box-Jenkins methods: autocorrelation methods used to identify underlying time series and to
fit the "best" model
COMPONENTS OF TIME SERIES DEMAND
1. average: the mean of the observations over time
2. trend:a gradual increase or decrease in the average over time
3. seasonal influence:predictable short-term cycling behaviour due to time of day, week,
month, season, year, etc.
4. cyclical movement:unpredictable long-term cycling behaviour due to business cycle or
product/service life cycle
5. random error: remaining variation that cannot be explained by the other four components
SIMPLE MOVING AVERAGE
moving average techniques forecast demand by calculating an average of actual demands from a
specified number of prior periods
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each new forecast drops the demand in the oldest period and replaces it with the demand in the
most recent period; thus, the data in the calculation "moves" over time
simple moving average: At= Dt+ Dt-1+ Dt-2+ ... + Dt-N+1 / N
where N = total number of periods in the average
forecast for period t+1: Ft+1= At
Key Decision:N - How many periods should be considered in the forecast
Tradeoff:Higher value of N - greater smoothing, lower responsiveness
Lower value of N - less smoothing, more responsiveness
- the more periods (N) over which the moving average is calculated, the less susceptible the
forecast is to random variations, but the less responsive it is to changes
- a large value of N is appropriate if the underlying pattern of demand is stable
- a smaller value of N is appropriate if the underlying pattern is changing or if it is important to
identify short-term fluctuations
WEIGHTED MOVING AVERAGE
a weighted moving average is a moving average where each historical demand may be weighteddifferently
average: At= W1Dt+ W2Dt-1+ W3Dt-2+ ... + WNDt-N+1
where:
N = total number of periods in the average
Wt= weight applied to period t's demand
Sum of all the weights = 1
forecast: Ft+1= At= forecast for period t+1
EXPONENTIAL SMOOTHING
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exponential smoothing gives greater weight to demand in more recent periods, and less weight to
demand in earlier periods
average: At= a Dt+ (1 -a) At-1= a Dt+ (1 - a) Ft
forecast for period t+1: Ft+1= At
where:
At-1= "series average" calculated by the exponential smoothing model to period t-1
a = smoothing parameter between 0 and 1
the larger the smoothing parameter , the greater the weight given to the most recent demand
DOUBLE EXPONENTIAL SMOOTHING
(TREND-ADJUSTED EXPONENTIAL SMOOTHING)
when a trend exists, the forecasting technique must consider the trend as well as the series
average ignoring the trend will cause the forecast to always be below (with an increasing trend)
or above (with a decreasing trend) actual demand
double exponential smoothing smooths (averages) both the series average and the trend
forecast for period t+1: Ft+1= At+ Tt
average: At= aDt+ (1 - a) (At-1+ Tt-1) = aDt+ (1 -a) Ft
average trend: Tt=B CTt+ (1 -B) Tt-1
current trend: CTt= At- At-1
forecast for p periods into the future: Ft+p= At+ p Tt
where:
At= exponentially smoothed average of the series in period t
Tt= exponentially smoothed average of the trend in period t
CTt= current estimate of the trend in period t
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a = smoothing parameter between 0 and 1 for smoothing the averages
B = smoothing parameter between 0 and 1 for smoothing the trend
MULTIPLICATIVE SEASONAL METHOD
What happens when the patterns you are trying to predict display seasonal effects?
What is seasonality? - It can range from true variation between seasons, to variation between
months, weeks, days in the week and even variation during a single day or hour.
To deal with seasonal effects in forecasting two tasks must be completed:
1. a forecast for the entire period (ie year) must be made using whatever forecastingtechnique is appropriate. This forecast will be developed using whatever
2. the forecast must be adjust to reflect the seasonal effects in each period (ie month orquarter)
the multiplicative seasonal method adjusts a given forecast by multiplying the forecast by a
seasonal factor
Step 1: calculate the average demand yper period for each year (y) of past data by dividing total
demand for the year by the number of periods in the year
Step 2: divide the actual demand Dy,tfor each period (t) by the average demand yper period
(calculated in Step 1) to get a seasonal factor fy,tfor each period; repeat for each year of data
Step 3: calculate the average seasonal factor tfor each period by summing all the seasonal factors
fy,tfor that period and dividing by the number of seasonal factors
Step 4: determine the forecast for a given period in a future year by multiplying the average
seasonal factor tby the forecasted demand in that future year
Seasonal Forecasting(multiplicative method)
Actual Demand
Year Q1 Q2 Q3 Q4 Total Avg
1 100 70 60 90 320 80
2 120 80 70 110 380 95
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3 134 80 70 100 381 96
Seasonal Factor
Year Q1 Q2 Q3 Q4
1 1.25 .875 .75 1.125
2 1.26 .84 .74 1.16
3 1.4 .83 .73 1.04
Avg. Seasonal Factor 1.30 .85 .74 1.083
Seasonal Factor - the percentage of average quarterly demand that occurs in each quarter.
Annual Forecast for year 4 is predicted to be 400 units.
Average forecast per quarter is 400/4 = 100 units.
Quarterly Forecast = avg. forecast seasonal factor.
Q1: 1.303(100) = 130 Q2: .85(100) = 85 Q3: .74(100) = 74 Q4: 1.083(100) = 108
CAUSAL FORECASTING METHODS
causal forecasting methods are based on a known or perceived relationship between the factor to
be forecast and other external or internal factors
1. regression: mathematical equation relates a dependent variable to one or more independent
variables that are believed to influence the dependent variable
2. econometric models: system of interdependent regression equations that describe some sector
of economic activity
3. input-output models: describes the flows from one sector of the economy to another, and so
predicts the inputs required to produce outputs in another sector
4. simulation modelling
MEASURING FORECAST ERRORS
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There are two aspects of forecasting errors to be concerned about - Bias and Accuracy
Bias- A forecast is biased if it errs more in one direction than in the other
- The method tends to under-forecasts or over-forecasts.
Accuracy- Forecast accuracy refers to the distance of the forecasts from actual demand ignore
the direction of that error.
Example: For six periods forecasts and actual demand have been tracked The following table
gives actual demand Dtand forecast demand Ftfor six periods:
t Dt Ft Et (Et)2
|Et| | Et|/Dt
1 170 200 -30 900 30 17.6%
2 230 195 35 1225 35 15.2%
3 250 210 40 1600 40 16.0%
4 200 220 -20 400 20 10.0%
5 185 210 -25 625 25 13.5%
6 180 200 -20 400 20 11.1%
Total -20 5150 170 83.5%
Forecast Measure
1. cumulative sum of forecast errors (CFE) = -202. mean absolute deviation (MAD) = 170 / 6 = 28.333. mean squared error (MSE) = 5150 / 6 = 858.334. standard deviation of forecast errors = 5150 / 6 = 29.305. mean absolute percent error (MAPE) = 83.4% / 6 = 13.9%
What information does each give?
1.2.3.4.5.
conclusions:
forecast has a tendency to over-estimate demand
average error per forecast was 28.33 units, or 13.9% of actual demand
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sampling distribution of forecast errors has standard deviation of 29.3 units.
CRITERIA FOR SELECTING AFORECASTING METHOD
Objectives: 1. Maximize Accuracy and 2. Minimize Bias
Potential Rules for selecting a time series forecasting method. Select the method that
1. gives the smallest bias, as measured by cumulative forecast error (CFE); or2. gives the smallest mean absolute deviation (MAD); or3. gives the smallest tracking signal; or4. supports management's beliefs about the underlying pattern of demand
or others. It appears obvious that some measure of both accuracy and bias should be used
together. How?
What about the number of periods to be sampled?
if demand is inherently stable, low values of and and higher values of N are suggested if demand is inherently unstable, high values of and and lower values of N are suggested
FOCUS FORECASTING
"focus forecasting" refers to an approach to forecasting that develops forecasts by varioustechniques, then picks the forecast that was produced by the "best" of these techniques, where
"best" is determined by some measure of forecast error.
FOCUS FORECASTING: EXAMPLE
For the first six months of the year, the demand for a retail item has been 15, 14, 15, 17, 19, and
18 units.
A retailer uses a focus forecasting system based on two forecasting techniques: a two-period
moving average, and a trend-adjusted exponential smoothing model with = 0.1 and = 0.1. With
the exponential model, the forecast for January was 15 and the trend average at the end ofDecember was 1.
The retailer uses the mean absolute deviation (MAD) for the last three months as the criterion for
choosing which model will be used to forecast for the next month.
a. What will be the forecast for July and which model will be used?
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b. Would you answer to Part a. be different if the demand for May had been 14 instead of 19?