Forecasting

 Forecasting
 Process of Predicting the Future event using (time series related or
otherwise) data we have in hand
 Why are we interested?
 Affects the decisions we make today
 Underlying basis of all business decisions
 Production
 Inventory
 Personnel
 Facilities
 Where is forecasting used in POM
 forecast demand for products and services
 forecast availability/need for manpower
 forecast inventory and material needs daily
 Factory Capacity

Types of Forecasts
 Economic forecasts
 Predict a variety of economic indicators, like money supply, inflation rates,
interest rates, etc.
 Technological forecasts
 Predict rates of technological progress and innovation.
 Demand forecasts
 Predict the future demand for a company’s products or services.
Characteristics of Forecasts
 Forecasts are seldom perfect
 Most techniques assume an underlying stability in the system
 Product family and aggregated forecasts are more accurate than individual product
forecasts
 A good forecast is more than a single number
 Includes a mean value and standard deviation
 Includes accuracy range (high and low)
 Forecasts should not be used to the exclusion of known information
What Makes a Good Forecast?
 It should be timely
 It should be as accurate as possible
 It should be reliable
 It should be in meaningful units
 It should be presented in writing
  The method should be easy to use and understand in most cases.
Forecasting Time Horizons
 Short-range forecast
 Up to 1 year, generally less than 3 months
 Purchasing, job scheduling, workforce levels, job assignments, production
levels
 Medium-range forecast
 3 months to 3 years
 Sales and production planning, budgeting
 Long-range forecast
 3+ years
 New product planning, facility location, research and development
Forecasting Methods
• Types of Forecasting
• Qualitative
• Based on judgments, opinions, intuition, emotions, or personal
experiences and are subjective in nature. They do not rely on any
rigorous mathematical computations
• Quantitative
• Mathematical (quantitative) models, and are objective in nature. They
rely heavily on mathematical computations
Qualitative Methods (Subjective Approach)
1. Jury of executive opinion: Approach in which a group of managers (Jury) meet and
collectively develop a forecast
2. Sales force composite: Approach in which each salesperson estimates sales in his or
her region
3. Consumer Market Survey : Approach that uses interviews and surveys to judge
preferences of customer and to assess demand
4. Delphi method :Approach in which consensus agreement is reached among a group
of experts (Panel of experts, queried iteratively until consensus is reached)
Delphi Method
l. Choose the experts to participate. There should be a variety of knowledgeable people in
different areas.
2. Through a questionnaire (or E-mail), obtain forecasts (and any premises or
qualifications for the forecasts) from all participants.
3. Summarize the results and redistribute them to the participants along with appropriate
new questions.
4. Summarize again, refining forecasts and conditions, and again develop new questions.
5. Repeat Step 4 if necessary. Distribute the final results to all participants.
Quantitative Methods (Objective Approaches)
Associative model (often called causal models) : Assume that the variable being forecasted
is related to other variables in the environment. They try to project based upon those
associations.
Regression Model
Time-series models
Look at past patterns of data and attempt to predict the future based upon the underlying
patterns contained within those data.
1. Naive approach
2. Moving averages
3. Exponential smoothing
4. Trend projection

Time-series models

Time Series Pattern

 Trend
Data exhibit a steady growth or decline over time.
 Seasonality
Data exhibit upward and downward swings in a short to intermediate time frame
(most notably during a year)
 Cycles
Data exhibit upward and downward swings in over a very long time frame.
 Random variations
Erratic and unpredictable variation in the data over time with no discernable pattern
Notation Conventions
 Let D1, D2, . . . Dn, . . . be the past values of the series to be predicted. If we are
making a forecast during period t (for the future), assume we have observed Dt , Dt-1
etc.
 Let Ft, t + t = forecast made in period t for the demand in period t + t where t =
1, 2, 3, …
 Then Ft -1, t is the forecast made in t-1 for t and
 Ft, t+1 is the forecast made in t for t+1. (one step ahead) Use shorthand
notation Ft = Ft - 1, t
Moving Averages
The arithmetic average of the n most recent observations. For a one-step-ahead
forecast:
Ft = (1/N) (Dt - 1 + Dt - 2 + . . . + Dt - n )
Simple moving average method
The forecast for next period (period t+1) will be equal to the average of a specified number
of the most recent observations, with each observation receiving the same emphasis
(weight).
Weighted Moving Averages
 This method looks at past data and tries to logically attach importance to certain
data over other data
 Weighting factors must add to one
 Can weight recent higher than older or specific data above others
 The forecast for next period (period t+1) will be equal to a weighted average of a
specified number of the most recent observations
Exponential Smoothing Method
 A type of weighted moving average that applies declining weights to past data.
New Forecast = α (most recent observation) + (1 - α) (last forecast)
ð New Forecast = last forecast - α (last forecast error)
Where a is a smoothing coefficient, 0 < α < 1 and generally is small for stability of forecasts
The exponential smoothing method only requires that you dig up two pieces of data to
apply it (the most recent actual demand and the most recent forecast)
Effect of a value on the Forecast
 Small values of a means that the forecasted value will be stable (show low variability
 Low a increases the lag of the forecast to the actual data if a trend is present
 Large values of a mean that the forecast will more closely track the actual time
series
Exponential Smoothing
An attractive feature of this method is that forecasts made with this model will include a
portion of every piece of historical demand. Furthermore, there will be different weights
placed on these historical demand values, with older data receiving lower weights
In symbols:
Ft+1 = α Dt + (1 - α ) Ft
= α Dt + (1 - α ) (α Dt-1 + (1 - α ) Ft-1)
= α Dt + (1 - α )( α )Dt-1 + (1 - α)2 (α )Dt - 2 + . . .
{Or : Ft + 1 = Ft - α (Ft - Dt) }
 Hence the method applies a set of exponentially declining weights to past data.
It is easy to show that the sum of the weights is exactly one.
Comparison of MA and ES
 Similarities
 Both methods are appropriate for stationary series
 Both methods depend on a single parameter
 Both methods lag behind a trend
 One can achieve the same distribution of forecast error by setting:
α = 2/ ( N + 1) or N = (2 - α)/ α
 Differences
 ES carries all past history
 MA eliminates “bad” data after N periods
  MA requires all N past data points to compute new forecast estimate while
ES only requires last forecast and last observation of ‘demand’ to continue
MEASURING FORECAST ACCURACY
Mean Forecast Error (MFE)
Forecast error is a measure of how accurate our forecast was in a given time period.
It is calculated as the actual demand minus the forecast,
i.e., Et = At – Ft
Forecast error in one time period does not convey much information, so one need to look at
the accumulation of errors over time. The average value of these forecast errors over time
can be calculated (i.e., a Mean Forecast Error, or MFE).
Unfortunately, the accumulation of the Et values is not always very revealing, for some of
them will be positive errors and some will be negative. These positive and negative errors
cancel one another, and looking at them alone (or looking at the MFE over time) might give
a false sense of security.
Mean Absolute Deviation (MAD)
To eliminate the problem of positive errors cancelling negative errors, a simple measure is
one that looks at the absolute value of the error (size of the deviation, regardless of sign).
If we accumulate these absolute deviations over time and find the average value of these
absolute deviations, we refer to this measure as the mean absolute deviation (MAD).

Another Method When Trend is Present

 Double exponential smoothing, of which Holt’s method is the most common
example, can also be used to forecast when there is a linear trend present in the
data. The method requires separate smoothing constants for slope and intercept.
 The advantage is that once we begin building a forecast model, we can quickly
revise the slope and signal constituents with the separate smoothing coefficients.
Begin with an estimate of the intercept and slope at the start (by Lin. Regression)
 Ft = α Di + (1- α)(Si-1 + Gi-1)
 Gi = (Si – Si-1) + (1- )Gi-1
 Di is obs. demand; Si is current est. of ‘intercept’;
 Gi is current est. of slope; Si-1 is last est. of ‘intercept’; Gi-1 is last est. of slope
Ft,t+t = St + t*Gt (forecast for time t into the future)

Exponential Smoothing with Trend

An upward or downward trend in data over a sequence of time periods causes the
exponential forecast to always lag behind the actual occurrence. It can be corrected somewhat
by adding a trend adjustment. Besides the smoothing constant α, the trend equation also uses
another smoothing constant . Both alpha and beta reduce the impact of the error that occurs
between the actual and forecast.
Begin with manually entered trend value based on educated guess or a computation based on
observed past data.
Ft = FITt-1 + α (At-1 – FITt-1)
Tt = Tt-1 +  (Ft – FITt-1)
FITt = Ft + Tt
Where
Ft = The exponentially smoothed forecast that does not include trend for period t
Tt = The exponentially smoothed trend for period t
FITt = The forecast including trend for period t
FITt-1= The forecast including trend made for the prior period
At-1 = The actual demand for the prior period
α = Smoothing constant (alpha)
 = Smoothing constant (beta)
Examples:

1. The demand for a product in each of the last five months is shown below.
Month 1 2 3 4 5
Demand ('00s) 13 17 19 23 24
Use a two month moving average to generate a forecast for demand in month 6.
(Ans.: 23.5 MSD 16.67)
Apply exponential smoothing with a smoothing constant of 0.9 to generate a forecast for demand
for demand in month 6. (Ans. 23.86 MSD 10.44)
Which of these two forecasts do you prefer and why? (Ans. Exponential Smoothing / Less MSD)

2. The table below shows the demand for a new aftershave in a shop for each of the last 7
months.
Month 1 2 3 4 5 6 7
Demand 23 29 33 40 41 43 49
 Calculate a two month moving average for months two to seven. What would be your
forecast for the demand in month eight? (Ans. 46 MSD 41.1)
 Apply exponential smoothing with a smoothing constant of 0.1 to derive a forecast for
the demand in month eight. (Ans. 31.11 MSD 203.15)
 Which of the two forecasts for month eight do you prefer and why?

3. The table below shows the demand for a particular brand of razor in a shop for each of
the last nine months.
Month 1 2 3 4 5 6 7 8 9
Demand 10 12 13 17 15 19 20 21 20
 Calculate a three month moving average for months three to nine. What would be your
forecast for the demand in month ten? (Ans. 2033 MSD 10.57)
 Apply exponential smoothing with a smoothing constant of 0.3 to derive a forecast for
the demand in month ten. (Ans. 18.57 MSD 15.08)
 Which of the two forecasts for month ten do you prefer and why?

4. The table below shows the demand for a particular brand of fax machine in a department
store in each of the last twelve months.
Month 1 2 3 4 5 6 7 8 9 10 11 12
Demand 12 15 19 23 27 30 32 33 37 41 49 58
 Calculate the four month moving average for months 4 to 12. What would be your
forecast for the demand in month 13? (Ans. 46.25 MSD 107.43)
 Apply exponential smoothing with a smoothing constant of 0.2 to derive a forecast for
the demand in month 13. (Ans. 38.618 MSD 176.05)
 Which of the two forecasts for month 13 do you prefer and why?
 What other factors, not considered in the above calculations, might influence demand for
the fax machine in month 13?
5. The table below shows the demand for a particular brand of microwave oven in a
department store in each of the last twelve months.
Month 1 2 3 4 5 6 7 8 9 10 11 12
Demand 27 31 29 30 32 34 36 35 37 39 40 42
 Calculate a six month moving average for each month. What would be your forecast for
the demand in month 13? (Ans. 38.17 MSD 21.66)
 Apply exponential smoothing with a smoothing constant of 0.7 to derive a forecast for
the demand in month 13. (Ans. 41.24 MSD 5.25)
 Which of the two forecasts for month 13 do you prefer and why?

6. The table below shows the temperature (degrees C), at 11 p.m., over the last ten days:
Day 1 2 3 4 5 6 7 8 9 10
Temperature 1.5 2.3 3.7 3.0 1.4 -1.3 -2.4 -3.7 -0.5 1.3
 Calculate a three day moving average for each day.
 What would be your forecast for the temperature at 11 p.m. on day 11?
(Ans. -0.97 MSD 7.90)
 Apply exponential smoothing with a smoothing constant of 0.8 to derive a forecast for
the temperature at 11 p.m. on day 11. (Ans. 0.83 MSD 3.86)
 Which of the two forecasts for the temperature at 11 p.m. on day 11 do you prefer and
why?

7. The table below shows the sales of a toy robot over the last 11 months.
Month 1 2 3 4 5 6 7 8 9 10 11
Sales 3651 4015 3874 3501 3307 3105 2986 3100 3209 3450 3507
 Calculate a four month moving average for each month. What would be your forecast for
the sales in month 12? (Ans. 3316.50 MSD 141407.9)
 Apply exponential smoothing with a smoothing constant of 0.9 to derive a forecast for
the sales in month 12. (Ans. 3498.77 MSD 51008.3)
 Which of the two forecasts for month 12 do you prefer and why?

8. The table below shows the movement of the price of a commodity over 12 months.
Month 1 2 3 4 5 6 7 8 9 10 11 12
Price 25 30 32 33 32 31 30 29 28 28 29 31
 Calculate a 6 month moving average for each month. What is the forecast for month 13?
(Ans. 29.17 )
 Apply exponential smoothing with smoothing constants of 0.7 and 0.8 to derive forecasts
for month 13. Ans. 30.32 and 30.56 MSD 4.97 and 4.43)
 Which of the two forecasts based on exponential smoothing for month 13 do you prefer
and why?
9. Assume previous forecast, including a trend of 110 units, a previous trend estimate of 10
units, an alpha of 0.20 and a beta of 0.20. If actual demand turned out to be 115 rather
than the forecast 110, calculate the forecast for the next period.
10. Assume that in past years, a firm sold an average of 1000 unit of a particular product line
each year. On the average 200 units were sold in the spring, 350 in the summer, 300 in
the rainy and 150 in the winter. The seasonal factor (or index) is the ratio of the amount
sold during each season divided by the average for all season.
11. SS company markets doughnuts through a chain of food stores. It has been experiencing
overproduction and underproduction because forecasting errors. The following data are
its demand in dozens of doughnuts for the past four weeks. Droughnuts are made for the
following day, i.e., Sunday’s doughnuts production is for Monday’s sales. And so on.
The bakery is closed on Sunday, so Saturday’s production must satisfy demand for both
Sunday and Monday.
Days 4 weeks ago 3 weeks ago 2 weeks ago last week
Monday 2800 2700 3000 2900
Tuesday 2200 2400 2300 2400
Wednesday 2000 2100 2200 2200
Thursday 2300 2400 2300 2500
Friday 1800 1900 1800 2000
Saturday 190 1800 2100 2000
Sunday (Closed)
Make a forecast for this week based on the following:
a. Daily, using a simple four-week moving average
b. Daily, using a weighted moving average with weights of 0.40, 0.30, 0.20 and 0.10
(most recent to the oldest).
c. SS is also planning its purchases of ingredients for bread production. If bread
demand had been forecast for last week at 22000 loaves and only 21000 loaves
were actually demanded. What would SS forecast be for this week using
exponential smoothing with α =0.10?
d. Suppose with the forecast made in (c) above, this week’s demand actually turn out
to be 22500, what would be the new forecast for the next week?
12. Given the following information, make a forecast for May using exponential smoothing
with trend.
Month January February March April
Demand 700 760 780 790
For exponential smoothing with trend, assume that the previous forecast (for April)
including trend was 800 units and the previous trend component was 50 units. Also
α=0.30 and = 0.10.
 13. The following are quarterly data for the past two years. From these data, prepare a
forecast for the upcoming year using suitable methods.
Period Actual Period Actual
1 300 5 416
2 540 6 760
3 885 7 1191
4 580 8 760

14. A specific forecasting model was used to forecast demand for a product. The forecasts
and the corresponding demand that subsequently occurred are shown as follows. Use the
MAD, evaluate the accuracy of the forecasting method.
Month Actual Forecast
October 700 660
November 760 840
December 780 750
January 790 835
February 850 910
March 950 890
15. Actual demand for a product for the past three months was
Three months ago 400 units
Two months ago 350 units
Last month 325 units
a. Using a simple three-month moving average, make a forecast for this month.
b. If 300 units were actually demanded this month, what would your forecast be for
next month?
c. Using simple exponential smoothing, what would your forecast be for this month
if the exponential smoothed forecast for three months ago was 450 units and the
smoothing constant was 0.20?
16. The following table contains the demand from the last 10 months.
Month Actual demand Month Actual Demand
1 31 6 36
2 34 7 38
3 33 8 40
4 35 9 40
5 37 10 41
a. Calculate the single exponential smoothing forecast for these data using an α of 0.30, an initial
forecast of 31.
b. Calculate the exponential smoothing with trend forecast for these data using α of 0.30 and  of
0.30, an initial trend forecast of 1 and an initial exponential smoothing forecast of 30.
c. Calculate the Mean Absolute Deviation (MAD) for each forecast to identify the best one.
17. The following table gives the weekly sales of black and colour cartridges by a computer
accessories store, for the past 12 weeks.
Black Cartridges Colour Cartridges
Week Sales Week Sales
1 58 1 40
2 62 2 38
3 65 3 41
4 68 4 46
5 72 5 42
6 75 6 41
7 98 7 41
8 84 8 47
9 87 9 42
10 90 10 43
11 93 11 42
12 92 12 49
Prepare a weekly forecast for the next four weeks for both types of cartridges, justifying
the method(s) used.
18. The following data gives the gross bank credit extended to MSME over the period from
2005 to 2021. The figure given are the outstanding Gross Bank Credit as on last reporting
Friday of March of each year.
Year MSME-Outstanding in Rs Year MSME-Outstanding in Rs
2005 53805 2014 178999
2006 61689 2015 200133
2007 65249 2016 218839
2008 78662 2017 229523
2009 80482 2018 295562
2010 102310 2019 313065
2011 124937 2020 426892
2012 138548 2021 549057
2013 161038
Use appropriate method to forecast the Gross Bank Credit for the year 2022.