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Lecture 6. Forecasting


Introduction Lecture 6. Forecasting * Mean Absolute Deviation (MAD) Mean Absolute Deviation (MAD) MAD is often use to forecast errors. When errors that occurs in the ... – PowerPoint PPT presentation

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Title: Lecture 6. Forecasting

  • Lecture 6. Forecasting

  • Course content
  • Demand Management
  • Components of demand
  • Qualitative technique in forecasting
  • Time series analysis
  • Causal relationship forecasting

  • Forecast plans It is not possible to make
    decisions in production scheduling, purchasing,
    and inventory levels until forecasts are
    developed that give reasonably accurate views of
    demand over the forecasting horizon.
  • Forecasting is a prediction of future events used
    for planning process
  • Management needed accurate forecast to ensure
    supply chain management

  • Accurate forecast allows schedulers to use
    capacity efficiently, reduce customer response
    times and cut inventories.
  • Managers need forecast to anticipate changes in
    prices or costs or to prepare for new laws or
    regulations, competitors, resource shortages or

Demand Management
  • Demand Management
  • - Demand management is to coordinate and control
    all sources of demand so the productive system
    can be used efficiently and the product delivered
    on time.
  • Demand are of two types
  • Dependent Demand
  • If the demand can be tabulated from the end item
    configuration. For developing a Car, number of
    tires, wheel barrow etc can be known. Usually
    sub-components of the final product.
  • 2. Independent Demand
  • It cannot be derived directly from that of other
    products. E.g sales prediction

Handling Demand
  • Handling Demand
  • Holistic approach or active approach to influence
  • (Developing aggressive marketing strategy to
    influence demand)
  • 2. Passive role or simply respond to demand
  • (Firm accept the demand and runs with it
    passively accepting it)
  • Our primary interest is in forecasting for
    independent demand

Components of Demand
  • Demand for product or service can be broken down
    to six components
  • Average demand for the period
  • Trend
  • Seasonal elements
  • Cyclical elements
  • Random variation
  • Autocorrelation

Components of Demand
  • Trend are the usual pattern of demand. Trends are
    of 4 types. Trend is a systematic increase or
    decrease over time.

Linear Trend It is a straight continuous
Asymptotic trends starts with the highest demand
growth at the beginning but then tappers off.
Objective of capturing the market and gradually
saturating it.
An exponential curve is common in products with
explosive growth. The explosive trend suggests
that sales will continue to increase.
S-Curve is typical of product growth and maturity
cycle. Important point in S-Curve is a point
where the trend change from slow to fast growth
Components of Demand
  • 1. Seasonal Elements Seasonal fluctuation in
  • 2. Cyclical Elements Cyclical influence on
    demand comes from macroeconomic factors as
    political, war, sociological pressure etc. Time
    span is unknown and cause of cycle may not be
  • 3. Random variations are caused by chance events.
    The cause for the this type of demand is unknown.
  • 4. Autocorrelation It denotes the persistence of
    occurrence. The value expected at any point is
    highly correlated to its own past.

Historical product demand consisting of growth
trend and seasonal demand
Number of units demanded
Average demand
Types of Forecasting
  • Forecasting is classified into four basic types
  • Qualitative Technique
  • Time series analysis
  • Causal Relationship
  • Simulation

Quantitative Technique
Qualitative Techniques of Forecasting
  • Qualitative analysis are subjective, judgmental
    and based on estimate and opinions
  • Grass Roots
  • As per this, the person near to the customer
    knows the market more better. His information is
    taken as a base for further forecasting.
  • 2. Market Research
  • Market survey, personal calling, data collection
    etc are done to collect information from market
    and then test the hypothesis to better understand
    the management decision problem (MDP).
  • 3. Panel Consensus
  • Group discussion to exchange the ideas. The
    problem is the lower management staff may not
    fully participate in idea sharing.
  • 4. Historical analogy
  • Grouping of the customer based on product
    category purchased. If an person has bought a
    DVD, then it is likely that he is interested in
    purchasing DVD movies. Also people who had
    previously purchase some items before are
    interested in new product of same category.

Qualitative Techniques of Forecasting
  • 5. Delphi method
  • Delphi method is a form of panel consensus but
    the identity of the individual participating is
    not open. The view of everyone has same weight.
  • View of individual is known through open end and
    closed end questionnaire.
  • The result from all the participant is
  • Distribute the final result to participants.

Time series Analysis
  • Predict the future based on past data. The
    analogy of past weeks data can be used to predict
    the future data.
  • Short term forecast under 3 mts
  • Medium term forecast 3 mts 2 years
  • Long term forecast greater than 2 years.
  • Short term compensate for tackling, problem in
  • Medium term compensate for seasonal effects
  • Long term compensate for identifying change in
    trends and consumer habits
  • Forecasting models available for firm are
  • Time Horizon to forecast
  • Data Availability
  • Accuracy required
  • Size of forecasting budget
  • Availability of qualified personals

Time Series Analysis
  • Calculation of the forecasting based on time
    series analysis can be done on following basis
  • Simple Moving Average
  • Weighted Moving Average
  • Exponential Smoothing
  • Simple Moving Average
  • The demand for the product or service is
    relatively constant, neither growing nor
    declining, with no seasonal slump, then in such
    scenario, a moving average is preferred.
  • The simple moving average method is used to
    estimate the average of a demand time series and
    thereby remove the effects of random fluctuation.

Simple Moving Average
  • Applying a moving average model simply involves
    calculating the average demand for the n most
    recent periods and using it as the forecast for
    the next time period.

Where D actual demand in period t n total
number of periods in the average
Forecast for period t1
With the moving average method, the forecast of
next periods demand equals the average
calculated at the end of this period
Simple Moving Average
  • a. Compare a three-week moving average forecast
    for the arrival of medical clinic patients in
    week 4. The number of arrivals for the past
    three weeks were

Weeks Patient arrival
1 400
2 380
3 411
b. If the actual number of patient arrivals in
week 4 is 415, what is the forecast for week 5
Simple Moving Average
  • Solution
  • The moving average forecast at the end of week 3

b. The forecast for week 5 requires the actual
arrivals from weeks 2-4, the three most Recent
weeks of data
The forecast at the end of week 3 would have been
397 patients for week 4. The forecast For week 5,
made at at the end of week 4, would have been 402
patients. In addition, at the end of week 4, the
forecast for week 6 and beyond is also 402
Simple Moving Average
  • Determining the value of n
  • The stability of the demand series generally
    determines how many periods to include (i.e the
    value of n). Stable demand series are those for
    which the average (to be estimated by the
    forecasting method) only infrequently experiences
  • Large values of n should be used for demand
    series that are stable and small values of n for
    those that are susceptible to change in
    underlying average.
  • If the underlying average in the series is
    changing, however, the forecasts will tend to lag
    behind the changes for a longer time interval
    because of the additional time required to remove
    the old data from the forecast.

Simple Moving Average
Example Exhibit 13.5 Pg. 546 Eleventh Edition
Chase/ jacob
Weighted Moving Average
  • In simple moving average, each demand has the
    same weight in the average. But in the weighted
    moving average method, each historical demand in
    the average can have its own weight.
  • The sum of the weights equal to 1.
  • The Formula for a weighted moving average is

Where W1weight to be given to the actual
occurrence for the period t-1 W2weight to be
given to the actual occurrence for the period
t-2 Wn weight to be given to the actual
occurrence for the period t-n ntotal number of
periods in the forecast
Weighted Moving Average
  • A department store may find that in a four month
    period, the best forecast is derived by using 40
    of the actual sales for the most recent month,
    30 for two months ago, 20 for three month ago
    and 10 of four months ago. If actual sales
    experience was

January February March April May
100 90 105 95 ?
0.1 0.2 0.3 0.4
Find the forecast for month 6 if the sales for 5
mts turned out to be 110 (Ans 102.5)
Weighted Moving Average
  • Using the weighted moving average method to
    estimate average Demand
  • a. The analyst for the medical clinic has
    assigned weights of 0.70 to the most recent
    demand, 0.2 to the demand one week ago, and 0.10
    to the demand two weeks ago. Use the data for the
    first three weeks from the table below to
    calculate the weighted average for week 4. (Ans
  • b. If the actual demand for 4th week is 415
    Patients, what would be the forecast for week 5.
    (Ans. 410)

Weeks Patient Arrival
1 400
2 380
3 411
Exponential Smoothing
  • Exponential Smoothing is method is actually a
    weighted moving average method that calculates
    the average of the time series by giving recent
    demands more weights than earlier demands.
  • It is most frequently used for forecasting due to
    its simplicity and the amount of data needed to
    support it.
  • Weighted moving average requires n periods of
    past demand and n weights, whereas exponential
    smoothing requires only three items to calculate
  • The last periods forecast
  • The demand for this period
  • Smoothing parameter alpha (a) (Value of a is
    between 0 and 1)

Exponential Smoothing
  • The equation for forecast is

Smoothing constant a is the level of smoothing
and the speed of reaction between forecasts and
actual occurrences. Value for smoothing constant
can be taken from organization requirement as per
their volume of demand. Or mathematically it can
be taken as 2/(n1)
The equation for exponential smoothing
highlights, the old forecast error portion
between previous forecast and what actually
Exponential Smoothing
  • E.g In the given table below, consider the
    arrival of patients, at the end of 3 weeks, using
    a0.10, calculate the exponential smoothing for
    week 4. Assume initial forecast as 390

Weeks Patient Arrival
1 400
2 380
3 411
Exponential Smoothing
  • In the above example, if the demand for 4th week
    becomes 415, the new forecast for week 5 would be
    as follow

Conclusion Using the exponential smoothing
model, the analysts forecasts would have been
392 patients for week 4 and then 394 patients for
week 5 and beyond. As Soon as the actual demand
for week 5 is known, then the forecast for week6
will be Updated.
Trend Effect in Exponential Smoothing
  • Exponential smoothing has an advantages of
    simplicity, minimal data requirement, inexpensive
    and attractive to firm.
  • But its simplicity is a disadvantage if the
    underlying average is changing, as in case of
    demand series with a trend.
  • Higher values of Smoothing constant (a) may help
    to reduce forecast error to some extent, when
    there is a change in the average of the time
    series however, the lag will still be there if
    the average is changing systematically.

Trend Effect in Exponential Smoothing
  • Assume that actual demand is steadily increasing
    at 10units per period. Forecast using exponential
    smoothing with a0.3

As we see, forecast using exponential smoothing
with a0.3 will lag severely behind the actual
demand even if the first forecast is perfect. To
improve the forecast, we need to calculate an
estimate of the trend, we start by calculating
the current estimate of the trend which is the
difference between the average of the series
computed in the current period and the average
computed last period. Another smoothing constant
delta (?) is added to reduce impact of error
Trend Effects in Exponential Smoothing Model
FITt Ft Tt Ft FITt-1 a(At-1 - FITt-1) Tt
Tt-1 ? (Ft - FITt-1 )
Ft the exponentially smoothened forecast for
period t Tt the exponentially smoothened trend
for period t FITt the forecast including trend
for period t FITt-1 the forecast including
trend made in prior period or period t-1 At-1
actual demand for prior period or period t-1 a
,? smoothing constants
Assume a initial starting Ft of 100 units, a
trend of 10 units, an alpha of 0.20 and a delta
of 0.30. If actual demand turned out to be 115
rather then the forecast 100, calculate the
forecast for the next period.
Hence, the forecast for next period turned out to
be 121.3 with a trend of initial 100 units.
Mean Absolute Deviation (MAD)
  • MAD is the average error in forecasts, using
    absolute values.
  • MAD is computed using the differences between the
    actual demand and the forecast demand without
    regard to sign.
  • It equals the sum of the absolute deviation
    divided by the number of data points or stated in
    equation as follow
  • Where
  • tperiod number
  • Aactual demand for the period
  • F forecast demand for the period
  • Ntotal number of period

Mean Absolute Deviation (MAD)
Month Motorcycle sales
Jan 9
Feb 7
March 10
April 8
May 7
June 12
July 10
August 11
Sept 12
Oct 10
Nov 14
Dec 16
  1. Compute a 3 month moving average forecast of
    demand for April through January (of the next
  2. Compute a 5 months average for June through
  3. Compare the two forecasts computed in parts a and
    b using MAD. Which one should the dealer use of
    January of the next year.
  • e.g

Mean Absolute Deviation (MAD)
Mean Absolute Deviation (MAD)
  • MAD is often use to forecast errors.
  • When errors that occurs in the forecast are
    normally distributed, the mean absolute deviation
    relates to the standard deviation as
  • Standard deviation

Conversely, 1 MAD 0.8 Standard Deviation
  • The ideal MAD is zero which would mean there is
    no forecasting error
  • The larger the MAD, the less the accurate the
    resulting model

Mean Absolute Deviation (MAD)
  • The value of MAD to forecast in case of
    exponentially smoothing is as follow

Measurement of Error
  • Tracking Signal
  • It is a measurement that indicates whether the
    forecast average is keeping pace with any genuine
    upward or downward changes in demand.
  • Tracking signal is the number of mean absolute
    deviations that the forecast value is above or
    below the actual occurrence.
  • Tracking signal (TS) RSFE/ MAD
  • RSFE running sum of forecast error, considering
    the nature of the error

Measurement of Error
  • Computing MAD and Tracking signal

In a perfect forecasting model, the sum of actual
forecast errors would be zero the error that
results in overestimates should be offset by
errors that are underestimate. The tracking
signal would then be also zero, indicating an
unbiased model, neither leading nor lagging the
actual demand.
Linear Regression Analysis
  • Regression is a functional relationship between
    two or more correlated variables.
  • It is used to predict one variable to other. Or
    more precisely, relation of dependent and
    independent variables.
  • Linear regression line is of the form Ymx C
  • Where Y is the value of dependent variable that
    we are solving for, C is the intercept and m is
    slope, x is the independent variable.
  • ? In linear regression forecasting, the past data
    and future projection are assumed to fall about a
    straight line.

Linear Regression Analysis
  • Linear regression is used in for both time series
    forecasting and for casual relationship
  • When the dependent variable changes as a result
    of time, it is time series analysis.
  • If one variable changes because of the change in
    another variable, this is called casual
    relationship. E.g Death of lung cancer increasing
    with the increase in number of people smoking.
  • Casual Method provides the most sophisticated
    forecasting tools and are very good for
    predicting turning points on demand and preparing
    long range forecast.

Linear Regression Analysis
  • Least square method fits the line to the data
    that minimizes the sum of the squares of the
    vertical distance between each data point and its
    corresponding point on the line.
  • Equation of st. line is Yabx

Standard Error of Estimate
Linear Regression Analysis
  • Example
  • Following are the sales and advertising data for
    past five months. The marketing manager says that
    the next month, the company will spend 1750 on
    advertising of product. Use linear regression to
    develop an equation and forecast for this

Month Sales (Y) Thousands of unit Advertising Thousand of
1 264 2.5
2 116 1.3
3 165 1.4
4 101 1.0
5 209 2.0
Linear Regression Analysis
Month Sales (Y) Thousands of unit Advertising(X) Thousand of X.Y X2
1 264 2.5 660 6.75
2 116 1.3 150.8 1.69
3 165 1.4 231 1.96
4 101 1.0 101 1
5 209 2.0 418 4
Correlation Coefficient for regression
  • Correlation coefficients shows the strength
    between the dependent and independent variable.
  • The value of correlation coefficient lies between
    -1 to 1.
  • If r-1, it shows, negatively correlated
  • If r0, there is not linear relationship
  • If r1, highly correleted

Casual Relationship Forecasting
  • Casual relationship forecasting is the one in
    which the causing element is known enough in
    advance, it can be used as a basis for
  • E.g increase in rain will increase sales of
  • Increase in car accidents, increase in number of
  • Identify the occurrence that are really the
    cause. Often leading indicators are not the
    casual relationship, but in some indirect way,
    they may suggest that some other things might
  • Other non casual relationships just seem to exist
    as a coincidence.

Casual Relationship Forecasting
Important Questions discussion
  • PU 2003 Fall
  • 5.a) From the choice of a simple moving average,
    weighted moving average, exponential smoothing,
    and linear regression analysis, which forecasting
    technique would you consider the most accurate?
    Why? (7)
  • 4.a)what is the difference between dependent
    demand and independent demand. Why do firms keep
    inventory? (5)
  • 6.c) Explain the features of a good forecasting
    technique. (5)
  • 2.B What do you mean by demand management?
    Differentiate between dependent demand and
    independent demand. (5)

End of Lecture
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