18ME56 Operations Management- Module 2-Forecasting

Dept. of ME, JSSATE, Bengaluru 1
―I never think of the future — it comes
soon enough.‖
— Albert Einstein

Module – 2:
• Forecasting:
• Steps in forecasting process, approaches to
forecasting, forecasts based on judgment
and opinion, analysis of time series data,
accuracy and control of forecasts, choosing
a forecasting technique, elements of a
good forecast.
(8 hours)
2Dept. of ME, JSSATE, Bengaluru

Module Outcome:
At the end of this module, you will be able to:
CO# Course Outcome
Bloom’s
Level
2
Examine various approaches for forecasting the sales
demand for an organization.
4
Forecasting
Learning Objectives:
After completing this module, you should be able to:
• List the elements of a good forecast.
• Outline the steps in the forecasting process.
• Describe qualitative forecasting techniques.
• Prepare forecasts using quantitative techniques.
• Compute forecast errors and comment on them.

• Forecast is a prediction of what will occur in the future.
• Meteorologists forecast the weather, sportscasters and
gamblers predict the winners of football games, and
companies attempt to predict how much of their product will
be sold in the future.
• A forecast of product demand is the basis for most important
planning decisions.
• Planning decisions regarding scheduling, inventory,
production, facility layout and design, workforce, distribution,
purchasing, and so on, are functions of customer demand.
• Long-range, strategic plans by top management are based on
forecasts of the type of products consumers will demand in
the future and the size and location of product markets.
Forecasting - Introduction

5
Dept. of ME, JSSATE, Bengaluru
• The forecast should be accurate, and the degree of
accuracy should be stated.
• The forecast should be reliable; it should work
consistently.
• The forecast should be expressed in meaningful
units.
• The forecast should be in writing.
• The forecasting technique should be simple to
understand and use.
• The forecast should be cost-effective. The benefits
should outweigh the costs.
• The forecast should be timely.
Forecasting Elements
Source: OM by W J Stevenson, 2018

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• Accounting: New product/process cost estimates, profit
projections, cash management.
• Finance: Equipment/equipment replacement needs, timing
and amount of funding/borrowing needs.
• Human resources: Hiring activities, including recruitment,
interviewing, and training; layoff planning, including
outplacement counseling.
• Marketing: Pricing and promotion, e-business strategies,
global competition strategies.
• Operations: Schedules, capacity planning, work assignments
and workloads, inventory planning, make-or-buy decisions,
outsourcing, project management.
• Product/service design: Revision of current features, design
of new products or services.
Uses of Forecasts

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• Determine the purpose / use of the forecast.
• Establish the time horizon of the forecast.
• Obtain, clean, and analyze appropriate data
• Select the forecasting technique / model(s).
• Make the forecast.
• Implement results and Monitor forecasts errors to
adjust when needed.
Steps in Forecasting

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• Determine the purpose / use of the forecast.
• The level of detail required in the forecast (what is
needed? when will it be needed?; how will it be
used?)
• The amount of resources (personnel, computer time,
money) that can be justified, and the level of
accuracy necessary.

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• Establish the time horizon of the forecast.
• It is the length of time in the future for which the
forecast is to be prepared.
• The forecast must indicate a time interval.
• Accuracy of forecast decreases as the time horizon
increases.
• Walmart basically forecasts taking a quarter-time period for
forecasting its revenues and other expenditures such as cost of
goods sold, purchase expenditure, promotional expenditure, etc.

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• Forecasting time horizons.
• Short-range (to mid-range) forecasts are typically for daily,
weekly, or monthly sales demand for up to approximately two
years into the future, depending on the company and the type of
industry. They are primarily used to determine production and
delivery schedules and to establish inventory levels.
• E.g., HP’s printers/month upto 12 – 18 months in future
• A long-range forecast: is usually for a period longer than two years
into the future. A long-range forecast is normally used for strategic
planning—to establish long-term goals, plan new products for
changing markets, enter new markets, develop new facilities,
develop technology, design the supply chain, and implement
strategic programs.
• E.g., Fiat (Italian automaker): strategic plans for new and
continuing products go 10 years into the future.

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• Obtain, clean, and analyze appropriate data
• Statistical data and Accumulated expertise who
collect the data.
• The data may need to be “cleaned” to get rid of
outliers and obviously incorrect data before analysis.
• Obtaining the data can involve significant effort.

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• Select the forecasting technique / model(s).
• Qualitative and Quantitative
• Make the forecast
• Implement results and Monitor forecasts errors to
adjust when needed.

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• Based on judgments,
opinions, intuition, emotions,
or personal experiences. They
do not rely on any rigorous
mathematical computations.
• Based on mathematical
(quantitative) models, and are
objective in nature. They rely
heavily on mathematical
computations.
Forecasting Methods (Approaches)
Qualitative
or
Subjective Forecasting
Methods
Quantitative
or
Objective Forecasting
Methods

14
Forecasting Methods
The best-guess estimates
of a company's
executives. Each
executive submits an
estimate of the company's
sales, which are then
averaged to form the
overall sales forecast.
Information related to
the market that cannot
be collected from the
company's internal
records or the
externally published
sources of data.

15
Forecasting Methods
Delphi Method

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Forecasting Methods
Sequence of observations taken
at regular intervals (e.g., hourly,
daily, weekly, monthly, quarterly,
annually).
Regression (or causal) forecasting methods
attempt to develop a mathematical
relationship (in the form of a regression
model) between demand and factors that
cause it to behave the way it does.

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• Trend: refers to a long-term upward or downward movement in
the data. Population shifts, changing incomes, and cultural
changes often account for such movements.
• Seasonality: refers to short-term, fairly regular variations
generally related to factors such as the calendar or time of day.
Restaurants, supermarkets, and theaters experience weekly and
even daily “seasonal” variations.
• Cycles are wavelike variations of more than one year’s duration.
These are often related to a variety of economic, political, and
even agricultural conditions.
• Irregular variations are due to unusual circumstances such as
severe weather conditions, strikes, or a major change in a
product or service.
• Random variations are residual variations that remain after all
other behaviors have been accounted for.
Components of Time Series – Demand Behavior

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Components of Time-series – Demand Behavior
Trend
Seasonal
Cyclical
Trend with seasonal pattern
Source: OM by Russel & Taylor

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Time Series Methods (Models)
Method (Method) Description
Naïve Uses last period’s actual demand value as a forecast
Simple Average Uses an average of all past data as a forecast
Simple Moving Average Uses an average of a specified number of the most
recent observations, with each observation
receiving the same emphasis (weight)
Weighted Moving
Average
Uses an average of a specified number of the most
recent observations, with each observation
receiving a different emphasis (weight)
Exponential Smoothing A weighted average procedure with weights
declining exponentially as data become older
Trend Projection
(Causal method)
Technique that uses the least squares method to fit
a straight line to the data
Seasonal Indexes A mechanism for adjusting the forecast to
accommodate any seasonal patterns inherent in the
data

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Year Actual Demand, Dt Forecast, Ft
1 310 --
2 345 310
3 325 345
4 398 325
5 450 398
6 465 450
7 465
Naïve Method
One weakness of the naive method is that the forecast just traces
the actual data, with a lag of one period; it does not smooth at all.
tA1tF

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1 38 42 (assumpn.)
2 44 38
3 43 41.00
4 39 41.66
5 48 41.00
6 52 42.40
7 44.00
Simple Average n/AF t1t 

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1 310 --
2 365
3 395 337.50
4 415 356.66
5 450 371.25
6 465 387.00
7 400.00
Simple Average

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Simple Moving Average
• This method uses an average of a specified number of the most
recent observations (actual demand data), with each observation
receiving the same emphasis (weight).
• The moving average forecast can be computed using the following
equation:

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Year Actual Demand, Dt Forecast, Ft (2 yr MA)
1 42 --
2 40 --
3 43
4 40
5 41
6 38
7

25
Year Actual Demand, Dt Forecast, Ft (2 yr MA)
1 310 300 (assumpn)
2 365 310 (naïve)
3 395 337.500
4 415 380.00
5 450 405.00
6 465 432.50
7 457.50

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(3 yr MA)
1 310 300 (assumpn)
2 365 310 (naïve)
3 395 365 (naïve)
4 415 356.66
5 450 391.66
6 465 420.00
7 433.33

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Year Actual Demand, Dt Forecast, Ft (3 yr WMA)
1 310 (0.2) 300 (aasumpn)
2 365 (0.3) 310 (naïve)
3 395 (0.5) 365 (naïve)
4 415 369.00
5 450 399.00
6 465 428.50
7 450.50
Weighted Moving Average
The forecast for next period (period t+1) will be equal to a
weighted average of a specified number of the most recent
observations. Weights to be used: 0.5, 0.3, 0.2
 tt1t ACF Ct - Weight for a period; All weights must add to 100% or 1.00

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observations. Weights to be used: 0.5, 0.3, 0.2
Sample Calculations:
Forecast for 4th year = {(D3*0.5) + (D2*0.3) + (D1*0.2)} /
(0.5+0.3+0.2)
= (395*0.5 + 365*0.3 + 310*0.2)/1 = 369
Forecast for 5th year = {(D4*0.5) + (D3*0.3) + (D2*0.2)} /
(0.5+0.3+0.2)
= (415*0.5 + 395*0.3 + 365*0.2)/1 = 399

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Year Actual Demand, Dt Forecast, Ft (4 yr WMA)
1 510 500 (assumpn.)
2 565 510 (naïve)
3 590 565 (naïve)
4 620 590 (naïve)
5 662
6 694
7 707 659.2
8 685.4
Weights to be used: 0.4, 0.3, 0.2, 0.1

observations. Weights to be used: 0.4, 0.3, 0.2, 0.1
Forecast for 5th year = {(D4*0.4) + (D3*0.3) + (D2*0.2) +
(D1*0.1)} / (0.4+0.3+0.2+0.1)
= (620*0.4 + 590*0.3 + 565*0.2 + 510*0.1)/1 = 589
Forecast for 6th year = {(D5*0.4) + (D4*0.3) + (D3*0.2) +
(D2*0.1)} / (0.4+0.3+0.2+0.1)
= (662*0.4 + 620*0.3 + 590*0.2 + 565*0.1)/1 = 625.3

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Exponential Smoothing
  tt1t Fα1αDF 
Where, Ft+1 – Forecast for the period t+1 (required forecast)
Ft - Last period’s forecast
Dt - Last periods actual sales or demand value
 - smoothing coefficient or constant (between 0 and
1.0), reflects the weight given to the most recent
demand data.
If no last period forecast is available, average the last few periods
or use naive method.
An averaging method that weights the most recent data more
strongly.
As such, the forecast will react more to recent changes in demand.
Virtually, all forecasting computer software packages include
modules for exponential smoothing.

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Problem 1: A firm uses simple exponential smoothing with to
forecast demand. The forecast for the week of January 1 was
500 units whereas the actual demand turned out to be 450
units. Calculate the demand forecast for the week of January
8.
Given: Forecast for 1st January, F1 = 500 units
Actual demand for 1st January, D1 = 450 units;  = 0.4
Forecast for 8th January, F2 = D1 + (1- ) F1
= 0.4 * 450 + (1-0.4) * 500 = 480 units

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Month Actual
Demand, Dt
Forecast Month Actual
Demand, Dt
Forecast
1 37 7 43
2 40 8 47
3 41 9 56
4 37 10 52
5 45 11 55
6 50 12 54
Problem 2: A company has accumulated the demand data for the
past 12 months as shown in the table below. Compute the forecast
from 2nd to 13th month using exponential smoothing method. Use
smoothing constants  equal to 0.30 and 0.50. Consider the first
month forecast as 37 units.

Given: Forecast for 1st year, F1 = 37 units (assumption)
Actual demand for 1st year, D1 = 37 units;  = 0.3
Forecast for 2nd month, F2 = D1 + (1- ) F1
= 0.3 * 37 + (1-0.3) * 37 = 37 units
Forecast for 3rd month, F3 = D2 + (1- ) F2
= 0.3*40 + (1-0.3)*37 = 37.9 units
Forecast for 4th month, F4 = D3 + (1- ) F3
= 0.3*41 + (1-0.3)*37.9 = 38.83 units
Similarcomputationswith=0.5

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Month Actual Demand, Dt Forecast
1 310 300 (given)
2 365
3 395
4 415
5 450
6 465
7
Problem 3: A company has accumulated the demand data for the
past 6 months as shown in the table below. Compute the forecast
from 2nd to 7th month using exponential smoothing method. Use
smoothing constant,  equal to 0.10 Consider the first month
forecast as 300 units.

Given: Forecast for 1st year, F1 = 300 units.
= 0.1 * 310 + (1-0.1) * 300 = 301 units
= 0.1*365 + (1-0.1)*301 = 307.4 units
= 0.1*395 + (1-0.3)*307.4 = 316.16 units

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Month Actual Demand, Dt Forecast
1 13
2 17
3 19
4 23
5 24
Problem 4: The demand for a product in each of the last five
months is shown below. Apply exponential smoothing with a
smoothing constant of 0.9 to generate a forecast for demand
in month 6.

Given: Forecast for 1st year, F1 = 13 units (assumed)
= 0.9 * 13 + (1-0.9) * 13 = 13 units
= 0.9*17 + (1-0.9)*13 = 13.4 units
= 0.9*19 + (1-0.9)*13.4 = 13.96 units

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months is shown below. Apply exponential smoothing with
smoothing constants of 0.2 & 0.8 to generate a forecast for
demand in month 6.
Month Actual Forecasted
Jan 1,325
1,370
(given)
Feb 1,353 1,361
Mar 1,305 1,359
Apr 1,275 1,349
May 1,210 1,334
Jun -- 1,309
 = 0.2

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months is shown below. Apply exponential smoothing with
smoothing constants of 0.2 & 0.8 to generate a forecast for
demand in month 6.
 = 0.8Month Actual Forecast
Jan 1,325
1,370
(given)
Feb 1,353 1,334
Mar 1,305 1,349
Apr 1,275 1,314
May 1,210 1,283
Jun ? 1,225

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Exponential Smoothing – Effect of 
1200
1220
1240
1260
1280
1300
1320
1340
1360
1380
0 1 2 3 4 5 6 7
Actual
a = 0.2
a = 0.8

• What will happen to a moving average or exponential
smoothing model when there is a trend in the data?
• Exponential smoothing forecast with an adjustment
for the trend (added or subtracted).
Trend Adjusted Exponential Smoothing
Sales
Month
Actual
Data
Forecast
Regular exponential
smoothing will always
lag behind the trend.

• Trend Adjusted Exponential Smoothing Forecast is given by
• Where, T = an exponentially smoothed trend factor. It is a
forecast model for trend.
• Where, Tt = the current period’s trend factor.
•  = a smoothing factor for trend, a value
between 0.0 and 1.0.
•  reflects the weight given to the most recent trend data. It is
usually determined subjectively based on the judgment of the
forecaster. Dept. of ME, JSSATE, Bengaluru 44
111   ttt TFAF
tttt TFFT )1()( 11   
OR, FITt = Ft + Tt
  )T(Fα1αDF ttt1t 

• Compute the trend adjusted exponential forecast for
the 9th month for a firm with the following data.
Assume the forecast for 1st month as 600 units and
corresponding initial trend factor as 0. Take  = 0.1 & 
= 0.2.
Month Actual
Demand, Dt
Forecast Month Actual
Demand, Dt
Forecast
1 650 600
(given)
7 700
2 600 8 710
3 550 9 ?
4 650
5 675
6 625

• Given: F1 = 600 units; T1 = 0; D1 = 650 units
111   ttt TFAF That is, AF9= F9 + T9
8899 )1()( TFFT  
  )T(Fα1αDF 8889 
&
Now, start with 2nd month: AF2= F2 + T2
1122 )1()( TFFT    )T(Fα1αDF 1112 

• Given: F1 = 600 units; T1 = 0; D1 = 650 units;  = 0.1; 
= 0.2.
Now, AF2= F2 + T2
1122 )1()( TFFT  
  )T(Fα1αDF 1112 
  )0(6001.01650*0.1F2 
That is, T2 = 1.0
&
0*)2.01()600605(2.02 T
Hence, AF2= 605 + 1 = 606
That is, F2 = 605 units

• Given: F2 = 605 units; T2 = 1; D2 = 600 units;  = 0.1; 
= 0.2.
Now, AF3= F3 + T3
2233 )1()( TFFT  
  )T(Fα1αDF 2223 
  )1(6051.01600*0.1F3 
That is, T3 = 0.88
&
1*)2.01()6054.605(2.03 T
Hence, AF3= 605.4 + 0.88 = 606.28
That is, F3 = 605.4 units

• Given: F3 = 605.4 units; T3 = 0.88; D3 = 550 units;  =
0.1;  = 0.2.
Now, AF4= F4 + T4
3344 )1()( TFFT  
  )T(Fα1αDF 3334 
  )0.88(605.41.01550*0.1F4 
That is, T4 = -0.245
&
88.0*)2.01()4.60565.600(2.04 T
Hence, AF4= 600.65 - 0.245 = 600.405
That is, F4 = 600.65 units

• Given: F4 = 600.65 units; T4 = -0.245; D4 = 650 units; 
= 0.1;  = 0.2.
F5 =
F6 =
F7 =
F8 =
F9 =
T5 =
T6 =
T7 =
T8 =
T9 =
AF5=
AF6=
AF7=
AF8=
AF9=

• A seasonal pattern is a repetitive increase and
decrease in demand.
• Many demand items exhibit seasonal behavior.
• Examples: Clothing, Greeting cards, Cold drinks, ACs,
Sweatshirts, Resort services, Restaurants, etc.
• Seasonal patterns can also occur on a monthly, weekly,
or even daily basis (restaurants, shopping malls, movie
theatres, etc.)
• Seasonal factor (index) is a method for reflecting
seasonal patterns in a time series forecast.
• A seasonal factor, Si is a numerical value between 0 &
1.
Forecast Using Seasonal Indices

• Seasonal factor is the portion of total annual demand
assigned to each season.
• Seasonal factor, Si is computed as:
• Where, Di = sum of seasonal demand; D = Grand
total demand for all the seasons across all the given
years.
• To compute adjusted forecasts for each season, the
seasonal factors are multiplied by the annual
forecasted demand.
Seasonal Indices or Factors

53
Seasonal Indices
The total demand of all the quarters in three years = 148.7
units.
If this is spread across 12 quarters (3x4),
The average demand per quarter would be
= 148.7/12
= 12.39 units
Ave. demand 14 9.83 7.3 18.43

54
Seasonal Indices or Factors

• Let, the company has made forecast (by some
projection method) for the next three years as below:
• The seasonally adjusted forecast for the four quarters
of each is computed as:
Seasonal Forecasts
Year Forecast, units
2011 58.17
2012 62.47
2013 66.77

Seasonal Forecasts
2011 (F5):

• 2012 (F6)
• SF1 = S1 * F6 = 0.28 * 62.47 = 17.49 units
• SF2 = S2 * F6 = 0.20 * 62.47 = 12.49
• SF2 = S3 * F6 = 0.15 * 62.47 = 9.37
• SF2 = S4 * F6 = 0.37 * 62.47 = 23.11
• 2013 (F7)
• SF1 = S1 * F7 = 0.28 * 66.77 = 18.69 units
• SF2 = S2 * F7 = 0.20 * 66.77 = 13.35
• SF2 = S3 * F7 = 0.15 * 66.77 = 10.01
• SF2 = S4 * F7 = 0.37 * 66.77 = 24.70
Seasonal Forecasts

• A company has accumulated the quarterly demand data
for one of its products for the last six years.
• It has made a forecast of the demand for the next 4 years
as: Year 7: 505 units; Year 8: 535 units; Year 9: 565 units;
Year 10: 595 units.
• Compute the seasonal forecasts for the years 7th to 10th.
Seasonal Forecasts

• Solution:
• Compute the total quarterly demand and annual
demand.
Seasonal Forecasts
Total 480 720 852 348 2400

• Compute the seasonal indices or factors every quarter.
• Compute the seasonal forecast
Seasonal Forecasts
Total 480 720 852 348 2400
Quarter I 2 3 4
Seasonal
Index
480/2400
= 0.2
720/2400
= 0.3
852/2400
= 0.355
348/2400
= 0.145

Seasonal Forecasts

• Linear regression is a method of forecasting in which a
mathematical relationship is developed between
demand and some other factor that causes demand
behavior.
• A linear trend line relates a dependent variable (…
demand), to one independent variable, time, in the
form of a linear equation:
• Where, a = intercept (at period 0)
• b = slope of the line
• x = the time period
• y = forecast for demand for period xDept. of ME, JSSATE, Bengaluru 62
Forecast by Linear Trend Line (Regression)

The parameters of the linear trend line can be calculated
using the least squares formulas for linear regression:

• A company has collected 12 months demand data for
one of its products. Compute the forecast for 13th
month by linear trend line (regression).
Month, x 1 2 3 4 5 6 7 8 9 10 11 12
Demand,
y
37 40 41 37 45 50 43 47 56 52 55 54

• Solution:

• Parameters b and a
Therefore, the linear trend line
equation is
The forecast for 13th month will be
y = 35.2 + 1.72 x 13
= 57.56 units

a
Slope of the line, b = 1.72

• Cell phone sales for a firm over the last 10 weeks are
shown in the following table. Plot the data, and visually
check to see if a linear trend line would be appropriate.
Then determine the equation of the trend line, and
predict sales for weeks 11 and 12.
Week, x 1 2 3 4 5 6 7 8 9 10
Unit
Sales, y
700 724 720 728 740 742 758 750 770 775
Source: OM by W J Stevenson

• Solution: a) Plotting a graph to see the existence of a
linear trend.
69
Existence of linear trend

• Solution: b) Computing the parameters of trend line
70
Week, x Unit Sales, y x*y x2
1 700 700 1
2 724 1448 4
3 720 2160 9
4 728 2912 16
5 740 3700 25
6 742 4452 36
7 758 5306 49
8 750 6000 64
9 770 6930 81
10 775 7750 100
55 7407 41358 385Total=

• Solution: b) Computing the parameters of trend line
• n= 10;
• x-bar = 55/10 = 5.5
• y-bar = 7407/10 = 740.7; xy = 41358
71
&
Hence, b = 7.51
Hence, a = 699.40
The equation of trend line is, y = 699.40 + 7.51x

• Solution: b) Computing the forecasts
• Substituting values of x into the trend line equation,
the forecasts for the next two periods (i.e., x = 11
and x = 12) are:
• F11 = 699.40 + 7.51(11) = 782.01
• F12 = 699.40 + 7.51(12) = 789.52
72

• Solution:
• For purposes of illustration, the original data, the trend line, and
the two projections (forecasts) are shown on the following graph:
73

• A firm believes that its annual profit (Rs. Lakhs) depends on the
expenditures (Rs. Lakhs) made on R & D activities. The data on
expenditures on R&D activities and the profit of the firm has
been collected for the past six years. Compute the profit of the
firm when the expenditure is Rs. 6 lakhs.
Source: OM by Panneerselvam

• Solution:

• Solution:
The Linear Trend Line Equation (model) is Y = a + bX = 20 + 2X
The profit when the expenditure is Rs. 6 lakhs is
Y = 20 + 2*6 = 32 (Rs. 32 lakhs)

• The manager of BCCI wants to develop budget for the coming year
using a forecast for spectators’ attendance to matches. The
manager believes that the attendance is directly related to the
number of wins by the team in the past matches. The data on total
annual average attendance for the past eight years is collected.
• The manager believes that the team will win at least seven games
next year. Develop a simple regression equation for this data to
forecast attendance for this level of success.
Forecast by Linear Regression

• Solution:

• Solution:
= 4.06
The linear trend line developed is
y = 18.46 + 4.06 x
Thus, for x = 7 (wins), the forecast for
attendance is
y = 18.46 + 4.06(7) = 46.88 or 46, 880
spectators

• A forecast is never completely accurate; forecasts will
always deviate from the actual demand.
• This difference between the forecast and the actual is the
forecast error.
• Although forecast error is inevitable, the objective of
forecasting is that it be as slight as possible. A large degree
of error may indicate that either the forecasting technique is
the wrong one or it needs to be adjusted by changing its
parameters (for example, in the exponential smoothing
forecast).
• Forecast error is given by Et = Dt – Ft
• Forecast accuracy is measured in terms of the errors.
Forecast Accuracy

• The model may be inadequate due to (a) the omission
of an important variable, (b) a change or shift in the
variable that the model cannot deal with (e.g., sudden
appearance of a trend or cycle), or (c) the appearance
of a new variable (e.g., new competitor).
• Irregular variations may occur due to severe weather
or other natural phenomena, temporary shortages or
breakdowns, catastrophes, or similar events.
• Random variations. Randomness is the inherent
variation that remains in the data after all causes of
variation have been accounted for.
Sources for Forecast Errors

• Mean Absolute Deviation (MAD)
• The mean absolute deviation, or MAD, is one of the
most popular and simplest to use measures of forecast
error.
• MAD is an average of the absolute difference between
the forecast and actual demand, as computed by the
following formula:
• t = the period number; Dt = demand in period t; Ft = the
forecast for period t; n = the total number of periods
Measures of Forecast Accuracy

• The actual demand and forecast values for a specific
commodity have been given in the table below. Compute
the MAD and comment on it.
Month Actual Demand, Dt Forecast, Ft
1 310 315
2 365 375
3 395 390
4 415 405
5 450 435
6 465 480

• Solution:
Month Actual Demand,
Dt
Forecast, Ft Et = Dt – Ft
1 310 315 -5
2 365 375 -10
3 395 390 5
4 415 405 10
5 450 435 15
6 465 480 -15

• Solution:
Dt
Forecast,
Ft
Et = Dt – Ft Dt – Ft
1 310 315 -5 5
2 365 375 -10 10
3 395 390 5 5
4 415 405 10 10
5 450 435 15 15
6 465 480 -15 15
Total 60
MAD = 60/6 = 10
The smaller the value of MAD, the more accurate is the forecast

• Mean Absolute Percent Deviation (MAPD)
• The mean absolute percent deviation (MAPD) measures
the absolute error as a percentage of demand rather
than per period.
• It eliminates the problem of interpreting the measure
of accuracy relative to the magnitude of the demand
and forecast values, as MAD does.
• The mean absolute percent deviation is computed
according to the following formula:

the MAPD and comment on it.
1 310 315
2 365 375
3 395 390
4 415 405
5 450 435
6 465 480

• Solution:
Dt
Forecast, Ft Et = Dt – Ft
1 310 315 -5
2 365 375 -10
3 395 390 5
4 415 405 10
5 450 435 15
6 465 480 -15
= 2400

• Solution:
Month Actual Demand, Dt Forecast, Ft Et = Dt – Ft Dt – Ft
1 310 315 -5 5
2 365 375 -10 10
3 395 390 5 5
4 415 405 10 10
5 450 435 15 15
6 465 480 -15 15
Total = 2400 = 60
MAPD = 60/2400 =
.025 or 2.5%
A lower percent deviation implies a more accurate forecast.

• Cumulative Error (CE):
• Cumulative error is computed simply by summing the
forecast errors, as shown in the following formula.
• Large +E indicates forecast is biased low; large -E,
forecast is biased high.
• A preponderance of positive values shows the forecast
is consistently less than the actual value and vice versa.
E =  et

• Average Error (AE) or Bias:
• It is computed by averaging the cumulative error over
the number of time periods, using the formula:
• The average error is interpreted similarly to the
cumulative error.
• A positive value indicates low bias, and a negative value
indicates high bias. A value close to zero implies a lack
of bias.

• Mean Squared Error (MSE):
• This measure is obtained by taking the mean of the
square of the error terms.
• Regardless of whether the forecast error has a positive
or negative sign, the squared error will always have a
positive sign.
• Squaring of the error terms serves the important
purpose of amplifying the forecast errors.
• In situations demanding low tolerance for forecast
errors it is desirable to make use of this measure.
• The MSE is computed using: MSE = (Dt – Ft)2 /n
Source: OM by B Mahadevan

the CE, AE & MSE.
1 310 315
2 365 375
3 395 390
4 415 405
5 450 435
6 465 480

Month Actual
Demand, Dt
Forecast,
Ft
Et = Dt – Ft (Et)2
1 310 315 -5 25
2 365 375 -10 100
3 395 390 5 25
4 415 405 10 100
5 450 435 15 225
6 465 480 -15 225
= 2400 Et = 0 = 700
Cumulative Error, E = 0; Average Error = 0; MSE = 700/6 = 116.7

• The following table shows the actual sales of a product for a
furniture manufacturer and the forecasts made for each of the last
eight months. Calculate CFE, MSE, MAD, and MAPD (MAPE) for
this product.
Absolute
Error Absolute Percent
Month, Demand, Forecast, Error, Squared, Error, Devn. (Error),
t Dt Ft Et Et
2 |Et| (|Et|/Dt)(100)
1 200 225 -25 625 25 12.5%
2 240 220 20 400 20 8.3
3 300 285 15 225 15 5.0
4 270 290 –20 400 20 7.4
5 230 250 –20 400 20 8.7
6 260 240 20 400 20 7.7
7 210 250 –40 1600 40 19.0
8 275 240 35 1225 35 12.7
Total –15 5275 195 81.3%

CFE = – 15Cumulative forecast error (bias):
E = = – 1.875
– 15
8
Average forecast error (mean bias):
MSE = = 659.4
5275
8
Mean squared error:
MAD = = 24.4
195
8
Mean absolute deviation:
MAPE = = 10.2%
81.3%
8
Mean absolute percent error:
Tracking signal = = = -0.6148
CFE
MAD
-15
24.4

• The manager of a large manufacturer of industrial pumps
must choose between two alternative forecasting
techniques. Both techniques have been used to prepare
forecasts for a six month period. Using MAD & MAPD as
criteria, which technique has the better performance
record?

• Solution:
Conclusion:
Technique 1 is superior in this
comparison because its MAD is smaller.

• Tracking Signal (TS):
• The ratio of cumulative forecast error to the
corresponding value of MAD, used to monitor a
forecast.
• It tells whether the forecasting system is consistently
under or over estimates the demand.
• Forecasts can go “out of control” and start providing
inaccurate forecasts for several reasons
• TS is recomputed each period, with updated, running
values of cumulative error and MAD.
Controlling Forecasts

• Given the following data, compute the tracking signal.
1 8 10
2 11 10
3 12 10
4 14 10
Month
Actual
Demand
Forecast
Demand

Actual Forecast Absolute Tracking
Month Demand Demand Error Error MAD Signal
1 8 10 -2 2 2 -1
2 11 10 1 1 1.5 -0.67
3 12 10 2 2 1.67 0.6
4 14 10 4 4 2.25 2.22

• Given the forecast demand and actual demand for a
specific product, compute the tracking signal and MAD.
Year
Forecast
Demand, Units
Actual Demand,
Units
1 78 71
2 75 80
3 83 101
4 84 84
5 88 60
6 85 73

• Solution
Year
Forecast
Demand
Actual
Demand
Error
Cumulative
FE
1 78 71 -7 -7
2 75 80 5 -2
3 83 101 18 16
4 84 84 0 16
5 88 60 -28 -12
6 85 73 -12 -24

• Solution
Year
Forecast
Demand
Actual
Demand
|Forecast
Error|
Cumulative
Error
MAD
Tracking
Signal
1 78 71 7 7 -7 7.0 -1.0
2 75 80 5 12 -2 6.0 -0.3
3 83 101 18 30 16 10.0 +1.6
4 84 84 0 30 16 7.5 +2.1
5 88 60 28 58 -12 11.6 -1.0
6 85 73 12 70 -24 11.7 -2.1

• Table below has data pertaining to the actual demand
and the forecast for a product using a forecasting system
for 18 time periods in the past. Compute the measures
of forecast accuracy and comment on the usefulness of
the forecasting system.

18ME56 Operations Management- Module 2-Forecasting

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18ME56 Operations Management- Module 2-Forecasting