Lecture 6. Forecasting

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Introduction

• Lecture 6. Forecasting

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

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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

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Forecasting

• 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
  technologies.

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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

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Handling Demand

• Handling Demand
• Holistic approach or active approach to influence
  demand
• (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

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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

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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
relationship
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
sales
quarters
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Components of Demand

• 1. Seasonal Elements Seasonal fluctuation in
  demand
• 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
  considered.
• 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.

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Historical product demand consisting of growth
trend and seasonal demand
Number of units demanded
Trend
Average demand
seasonal
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Types of Forecasting

• Forecasting is classified into four basic types
• Qualitative Technique
• Time series analysis
• Causal Relationship
• Simulation

Quantitative Technique
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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.

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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
  summarized.
• Distribute the final result to participants.

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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
  hand,
• 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

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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.

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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
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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
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Simple Moving Average

• Solution
• The moving average forecast at the end of week 3
  is

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
patient.
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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
  changes.
• 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.

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Simple Moving Average
Example Exhibit 13.5 Pg. 546 Eleventh Edition
Chase/ jacob
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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
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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)
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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
  403)
• 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
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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
  demand
• The last periods forecast
• The demand for this period
• Smoothing parameter alpha (a) (Value of a is
  between 0 and 1)

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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
occurred.
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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
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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.
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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.

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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
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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
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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.
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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

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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
   year)
2. Compute a 5 months average for June through
   January
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

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Mean Absolute Deviation (MAD)
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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

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Mean Absolute Deviation (MAD)

• The value of MAD to forecast in case of
  exponentially smoothing is as follow

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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

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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.
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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.

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Linear Regression Analysis

• Linear regression is used in for both time series
  forecasting and for casual relationship
  forecasting.
• 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.

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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
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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
  product.

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
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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
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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

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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
  forecasting.
• E.g increase in rain will increase sales of
  umbrella
• Increase in car accidents, increase in number of
  insurance
• 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
  happen.
• Other non casual relationships just seem to exist
  as a coincidence.

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Casual Relationship Forecasting
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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)

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End of Lecture