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?

supplementary material in forecasting

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