16-03-2023

WHAT IS FORECASTING?

 Process of predicting a
future event
 Underlying basis of ??
all business decisions
 Production
 Inventory

FORECASTING
 Personnel
 Facilities

FORECASTING TIME HORIZONS DISTINGUISHING DIFFERENCES

 Short-range forecast  Medium/long range forecasts deal with more comprehensive issues and
 Up to 1 year, generally less than 3 months support management decisions regarding planning and products, plants
 Purchasing, job scheduling, workforce levels, job assignments, production levels
and processes
 Medium-range forecast
 3 months to 3 years  Short-term forecasts tend to be more accurate than longer-term forecasts
 Sales and production planning, budgeting
 Long-range forecast
 3+ years
 New product planning, facility location, research and development

TYPES OF FORECASTS APPROACH TO DEMAND FORECASTING

 Economic forecasts  Understand the objective of forecasting
 Address business cycle – inflation rate, money supply, housing starts, etc.
 Integrate demand planning and forecasting throughout the
 Technological forecasts supply chain
 Predict rate of technological progress
 Impacts development of new products  Understand and identify customer segments

 Demand forecasts  Identify major factors that influence the demand forecast
 Predict sales of existing products and services  Determine the appropriate forecasting technique

 Establish performance and error measures for the forecast.

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SEVEN STEPS IN FORECASTING THE REALITIES!

 Determine the use of the forecast Forecasts are seldom perfect

 Select the items to be forecasted Most techniques assume an underlying stability in the system
 Determine the time horizon of the forecast Product family and aggregated forecasts are more accurate
 Select the forecasting model(s) than individual product forecasts
 Gather the data
 Make the forecast
 Validate and implement results

FORECASTING APPROACHES FORECASTING APPROACHES

Qualitative Methods (Judge-mental) Quantitative Methods (Statistical)
Used when situation is vague and little data exist Used when situation is ‘stable’ and historical data exist
New products Existing products
New technology Current technology
Involves intuition, experience Involves mathematical techniques
e.g., forecasting sales on Internet e.g., forecasting sales of color televisions

JURY OF EXECUTIVE OPINION SALES FORCE COMPOSITE

Involves small group of high-level experts and managers Each salesperson projects his or her sales
Group estimates demand by working together Combined at district and national levels
Combines managerial experience with statistical models Sales reps know customers’ wants
Relatively quick Tends to be overly optimistic
‘Group-think’
disadvantage

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DELPHI METHOD CONSUMER MARKET SURVEY

 Iterative group process, Decision Makers Ask customers about purchasing plans
continues until consensus is (Evaluate
reached responses and What consumers say, and what they actually do are often
 3 types of participants make decisions) different
 Decision makers
 Staff Staff Sometimes difficult to answer
(Administering
 Respondents survey)

Respondents
(People who can
make valuable
judgments)

OVERVIEW OF QUANTITATIVE APPROACHES COMPONENTS OF DEMAND

Trend
1. Naive approach component
Demand for product or service

Seasonal peaks
2. Moving averages Time-Series
Models
3. Exponential smoothing
Actual
4. Trend projection demand
Associative
5. Linear regression Model Average
demand over
Random four years
variation
| | | |
1 2 3 4
Year

NAIVE APPROACH MOVING AVERAGE METHOD

 Assumes demand in next  MA is a series of arithmetic means
period is the same as  Used if little or no trend
demand in most recent period
 Used often for smoothing
 e.g., If January sales were 68, then February sales will be 68
 Provides overall impression of data over time
 Sometimes cost effective and efficient
 Can be good starting point

∑ demand in previous n periods

Moving average = n

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MOVING AVERAGE EXAMPLE GRAPH OF MOVING AVERAGE

Actual 3-Month Moving

Month Shed Sales Moving Average 30 –
Average
28 –
Forecast
January 10 26 – Actual
February 12 24 – Sales

Shed Sales
March 13 22 –
April 16 (10 + 12 + 13)/3 = 11 2/3 20 –
18 –
May 19 (12 + 13 + 16)/3 = 13 2/3
16 –
June 23 (13 + 16 + 19)/3 = 16 14 –
July 26 (16 + 19 + 23)/3 = 19 1/3 12 –
10 –
| | | | | | | | | | | |
J F M A M J J A S O N D

Weights Applied Period

WEIGHTED MOVING AVERAGE WEIGHTED MOVING AVERAGE
3 Last month
2 Two months ago
 Used when trend is present 1 Three months ago
6 Sum of weights
 Older data usually less important
 Weights based on experience and intuition Actual 3-Month Weighted
Month Shed Sales Moving Average
January 10
February 12
March 13
∑ (weight for period n) April 16 [(3 x 13) + (2 x 12) + (10)]/6 = 121/6
Weighted x (demand in period n) May 19 [(3 x 16) + (2 x 13) + (12)]/6 = 141/3
moving average = ∑ weights June 23 [(3 x 19) + (2 x 16) + (13)]/6 = 17
July 26 [(3 x 23) + (2 x 19) + (16)]/6 = 201/2

MOVING AVERAGE AND

POTENTIAL PROBLEMS WITH MOVING AVERAGE WEIGHTED MOVING AVERAGE

 Increasing n smooth’s the forecast but makes it less sensitive Weighted

to changes 30 – moving
average
 Do not forecast trends well 25 –
Sales demand

 Require extensive historical data 20 – Actual

sales
15 –
Moving
10 – average

5 –
| | | | | | | | | | | |
J F M A M J J A S O N D
Figure 4.2

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 The monthly demand for a company for the past 10 months is as per below. The
manager has accumulated the data for ten months and wants to compute the three EXPONENTIAL SMOOTHING
and five months moving averages.
Month Units
January 120
 Form of weighted moving average
February 90  Weights decline exponentially
March 100
April 75  Most recent data weighted most
May 110
June 50  Requires smoothing constant ()
July 75  Ranges from 0 to 1
August 130
September 110  Subjectively chosen
October 90
 Involves little record keeping of past data
 The manager wants to identify if there is a variation in the forecast in case he uses three months
weighted moving average with the weights for latest three months before the month’s demand to be
forecasted as 0.17; 0.33 and 0.50 in sequence of n-3; n-2 and n-1 month. Draw a graph to show the
variation.

EXPONENTIAL SMOOTHING IMPACT OF DIFFERENT 

225 –
New forecast = Last period’s forecast
+  (Last period’s actual demand Actual  = .5
200 – demand
– Last period’s forecast)
Demand

Ft = Ft – 1 + (Dt – 1 - Ft – 1) 175 –

where Ft = new forecast  = .1

Ft – 1 = previous forecast 150 – | | | | | | | | |
1 2 3 4 5 6 7 8 9
 = smoothing (or weighting)
constant (0 ≤  ≤ 1) Quarter

IMPACT OF DIFFERENT  CHOOSING 

225 –
The objective is to obtain the most
Actual  = .5 accurate forecast no matter the
 Chose
200 – high values of 
demand technique
Demand

when underlying average

is likely to change We generally do this by selecting the
 Choose low values of 
175 – model that gives us the lowest forecast
when underlying average error
 = .1
is stable|
150 – | | | | | | | |
Forecast error = Actual demand - Forecast value
1 2 3 4 5 6 7 8 9
Quarter = At - Ft

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PROBLEM 1
 The monthly demand for units manufactured by the Acme Rocket Company has been Current Month Ft+1 Forecast Month
as follows: = αDt + (1 – α) Ft.
Month Units May 0.2 x 100 + 0.8(105) = 104 June
May 100 June 0.2 x 80 + 0.8(104) = 99 July
June 80
July 0.2 x 110 + 0.8(99) = 101 August
July 110
August 115 August 0.2 x 115 + 0.8(101) = 104 September
September 105 September 0.2 x 105 + 0.8(104) = 104 October
October 110 October 0.2 x 110 + 0.8(104) = 105 November
November 125
November 0.2 x 125 + 0.8(105) = 109 December
December 120
December 0.2 x 120 + 0.8(109) = 111 January
 Use the exponential smoothing method to forecast the number of units for June-
January. The initial forecast for May was 105 units and α = 0.2.

 The monthly demand for computers for MS computers for the past 12 months. The
manager wants to use the exponential smoothing forecasts using smoothing COMMON MEASURES OF ERROR
constants equal to 0.30 and 0.50
Month Units
January 37
February 40
March 41 Mean Absolute Deviation (MAD):
April 37
May 45
June 50
∑ |Actual - Forecast|
July 43
MAD =
n
August 47
September 56
October 52 Mean Squared Error (MSE):
November 55
measures the vaiance of forcast error with standard normal distribution
December 54
∑ (Forecast Errors)2
 Use the exponential smoothing method to forecast the number of units for January MSE =
next year. The initial forecast for January this year may be taken as equal to demand.
n

COMMON MEASURES OF ERROR COMPARISON OF FORECAST ERROR

Rounded Absolute Rounded Absolute

Actual Forecast Deviation Forecast Deviation
Tonnage with for with for
Quarter Unloaded  = .10  = .10  = .50  = .50
Mean Absolute Percent Error (MAPE)
1 180 175 5.00 175 5.00
2 168
n 3 159
∑100|Actuali - Forecasti|/Actuali 4
5
175
190
MAPE = i=1
6 205
n 7 180
8 182

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COMPARISON OF FORECAST ERROR COMPARISON OF FORECAST ERROR

Rounded Absolute Rounded Absolute

∑ |deviations|
Rounded Absolute Rounded Absolute
Actual Forecast Deviation Forecast Deviation MADActual
= Forecast Deviation Forecast Deviation
Tonnage with for with for Tonnage n
with for with for
Quarter Unloaded  = .10  = .10  = .50  = .50 Quarter Unloaded  = .10  = .10  = .50  = .50
1 180 175 5.00 175 5.00 1
For 180
= .10 175 5.00 175 5.00
2 168 175.5 7.50 177.50 9.50 2 168 = 82.45/8
175.5 = 10.31
7.50 177.50 9.50
3 159 174.75 15.75 172.75 13.75 3 159 174.75 15.75 172.75 13.75
4 175 173.18 1.82 165.88 9.12 4 For 175
= .50 173.18 1.82 165.88 9.12
5 190 173.36 16.64 170.44 19.56 5 190 173.36 16.64 170.44 19.56
6 205 175.02 29.98 180.22 24.78 6 205 = 98.62/8
175.02 = 12.33
29.98 180.22 24.78
7 180 178.02 1.98 192.61 12.61 7 180 178.02 1.98 192.61 12.61
8 182 178.22 3.78 186.30 4.30 8 182 178.22 3.78 186.30 4.30
82.45 98.62 82.45 98.62

COMPARISON OF FORECAST ERROR COMPARISON OF FORECAST ERROR

n
∑ (forecast errors)2 ∑100|deviationi|/actuali
Rounded Absolute Rounded Absolute Rounded Absolute Rounded Absolute
MSE = Actual Forecast Deviation Forecast Deviation MAPE = i=1
Actual Forecast Deviation Forecast Deviation
Tonnage
n
with for with for Tonnage with n for with for
Quarter Unloaded  = .10  = .10  = .50  = .50 Quarter Unloaded  = .10  = .10  = .50  = .50
1
For 180
= .10 175 5.00 175 5.00 1
 = .10 175
For 180 5.00 175 5.00
2 = 1,526.54/8
168 175.5 = 190.82
7.50 177.50 9.50 2 168 = 44.75/8
175.5 = 7.50
5.59% 177.50 9.50
3 159 174.75 15.75 172.75 13.75 3 159 174.75 15.75 172.75 13.75
4 For 175
= .50 173.18 1.82 165.88 9.12 4 =
For 175 .50 173.18 1.82 165.88 9.12
5 190 173.36 16.64 170.44 19.56 5 190 173.36 16.64 170.44 19.56
6 = 1,561.91/8
205 175.02 = 195.24
29.98 180.22 24.78 6 205 = 54.05/8
175.02 =29.98
6.76% 180.22 24.78
7 180 178.02 1.98 192.61 12.61 7 180 178.02 1.98 192.61 12.61
8 182 178.22 3.78 186.30 4.30 8 182 178.22 3.78 186.30 4.30
82.45 98.62 82.45 98.62
MAD 10.31 12.33 MAD 10.31 12.33
MSE 190.82 195.24

COMPARISON OF FORECAST ERROR TREND PROJECTIONS

Rounded Absolute Rounded Absolute

Actual Forecast Deviation Forecast Deviation Fitting a trend line to historical data points
Tonnage with for with for
Quarter Unloaded  = .10  = .10  = .50  = .50 to project into the medium to long-range
1 180 175 5.00 175 5.00
2 168 175.5 7.50 177.50 9.50 Linear trends can be found using the least
3 159 174.75 15.75 172.75 13.75 squares technique
4 175 173.18 1.82 165.88 9.12
5 190 173.36 16.64 170.44 19.56 y^ = a + bx
6 205 175.02 29.98 180.22 24.78
7 180 178.02 1.98 192.61 12.61
where y^ = computed value of the variable to
8 182 178.22 3.78 186.30 4.30
be predicted (dependent variable)
82.45 98.62 a = y-axis intercept
MAD 10.31 12.33
MSE 190.82 195.24
b = slope of the regression line
MAPE 5.59% 6.76% x = the independent variable

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LEAST SQUARES METHOD LEAST SQUARES METHOD

Values of Dependent Variable

Values of Dependent Variable

Actual observation Deviation7 Actual observation Deviation7

(y value) (y value)

Deviation5 Deviation6 Deviation5 Deviation6

Deviation3 Deviation3 Least squares method

minimizes the sum of the
Deviation4 Deviation
squared errors (deviations)
4

Deviation1 Deviation1
(error) Deviation2 Deviation2
Trend line, y^ = a + bx Trend line, y^ = a + bx

Time period Figure 4.4

Time period Figure 4.4

LEAST SQUARES METHOD LEAST SQUARES EXAMPLE

Time Electrical Power
Equations to calculate the regression variables Year Period (x) Demand x2 xy
2001 1 74 1 74
2002 2 79 4 158
y^ = a + bx 2003 3 80 9 240
2004 4 90 16 360
2005 5 105 25 525
Sxy - nxy 2005 6 142 36 852
b= 2007 7 122 49 854
Sx2 - nx2 ∑x = 28 ∑y = 692 ∑x2 = 140 ∑xy = 3,063
x=4 y = 98.86

a = y - bx ∑xy - nxy 3,063 - (7)(4)(98.86)

b= = = 10.54
∑x2 - nx2 140 - (7)(42)

a = y - bx = 98.86 - 10.54(4) = 56.70

LEAST SQUARES EXAMPLE LEAST SQUARES EXAMPLE

Time Electrical Power
Year Period (x) Demand x2 xy 160 –
Trend line,
150 – y^ = 56.70 + 10.54x
1999 1 74 1 74
2000 2 79 4 158 140 –
Power demand

2001The trend
3 line is 80 9 240 130 –
2002 4 90 16 360 120 –
2003 ^
y = 56.70
5 + 10.54x
105 25 525 110 –
2004 6 142 36 852 100 –
2005 7 122 49 854 90 –
Sx = 28 Sy = 692 Sx2 = 140 Sxy = 3,063 80 –
x=4 y = 98.86 70 –
60 –
Sxy - nxy 3,063 - (7)(4)(98.86) 50 –
b= = = 10.54
Sx2 - nx2 140 - (7)(42) | | | | | | | | |
2001 2002 2003 2004 2005 2006 2007 2008 2009
a = y - bx = 98.86 - 10.54(4) = 56.70 Year

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LEAST SQUARES REQUIREMENTS ASSOCIATIVE FORECASTING

1. We always plot the data to insure a linear relationship
Used when changes in one or more
2. We do not predict time periods far beyond the database independent variables can be used to predict
the changes in the dependent variable
3. Deviations around the least squares line are assumed to be
random Most common technique is linear
regression analysis

We apply this technique just as we did

in the time series example

ASSOCIATIVE FORECASTING ASSOCIATIVE FORECASTING EXAMPLE

Forecasting an outcome based on Sales Local Payroll

($ millions), y ($ billions), x
predictor variables using the least squares
2.0 1
technique 3.0 3
y^ = a + bx 2.5 4 4.0 –
2.0 2
2.0 1 3.0 –
where y^ = computed value of the variable to

Sales
3.5 7
be predicted (dependent variable) 2.0 –
a = y-axis intercept
b = slope of the regression line 1.0 –
x = the independent variable though to | | | | | | |
predict the value of the dependent 0 1 2 3 4 5 6 7
variable Area payroll

ASSOCIATIVE FORECASTING EXAMPLE ASSOCIATIVE FORECASTING EXAMPLE

Sales, y Payroll, x x2 xy
2.0 1 1 2.0 y^ = 1.75 + .25x Sales = 1.75 + .25(payroll)
3.0 3 9 9.0
2.5 4 16 10.0
If payroll next year
2.0 2 4 4.0 4.0 –
2.0 1 1 2.0
is estimated to be
$6 billion, then: 3.25
3.5 7 49 24.5 3.0 –
Sales

∑y = 15.0 ∑x = 18 ∑x2 = 80 ∑xy = 51.5

2.0 –
Sales = 1.75 + .25(6)
∑xy - nxy 51.5 - (6)(3)(2.5) Sales = $3,250,000 1.0 –
x = ∑x/6 = 18/6 = 3 b=
∑x2 - nx2
= 80 - (6)(32)
= .25
| | | | | | |
y = ∑y/6 = 15/6 = 2.5 a = y - bx = 2.5 - (.25)(3) = 1.75 0 1 2 3 4 5 6 7
Area payroll

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FORECASTING IN THE SERVICE SECTOR FAST FOOD RESTAURANT FORECAST

 Presents unusual challenges 20% –

Percentage of sales
 Special need for short term records
15% –
 Needs differ greatly as function of industry and product
 Holidays and other calendar events
10% –
 Unusual events
5% –

11-12 1-2 3-4 5-6 7-8 9-10

12-1 2-3 4-5 6-7 8-9 10-11
(Lunchtime) (Dinnertime)
Hour of day

Exponential smoothing is used to forecast automobile battery sales. Two value of
FEDEX CALL CENTER FORECAST are examined,   0.8 and   0.5. Evaluate the accuracy of each smoothing constant.
Which is preferable? (Assume the forecast for January was 22 batteries.) Actual sales
are given below:
12% –

10% – Month Actual Battery Sales Forecast

8% –
January 20 22
6% –
February 21
4% – March 15
2% –
April 14
0% – May 13
2 4 6 8 10 12 2 4 6 8 10 12
A.M. P.M.
Hour of day June 16

PROBLEM 1 PROBLEM 2
 The Yearly demand for three years (quarterly) is given in the table below. Extract the trend component
 The monthly demand for units delivered by a company is as per the table below: of the given data and predict the future demand for next year. monthly demand for units delivered by a
 Use the exponential smoothing method to forecast the number of units for February- company is as per the table below:
Year Quarter Actual Demand (Y) X X*Y X*X
November. The initial forecast for January was 90 units. Do a comparison for α = 0.2
and α = 0.8 . Month Units Forecast Forecast 1 1 360 1 360 1
0.2 0.8 1 2 438 2 876 4
January 100 1 3 359 3 1078 9
February 95 1 4 406 4
March 105 2 1 393 5
April 110 2 2 465 6
May 100 2 3 387 7
June 130 2 4 464 8
July 90 3 1 505 9
August 110 3 2 618 10
September 100 3 3 443 11
October 140 3 4 540 12
November

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Year Sales (Units)

A manufacturer of critical components has the data of 18 months of demand and
forecast as below: Compute the measures of forecast accuracy and comment on
2001 100 the usefulness of the forecasting system
2002 110 Period Demand Forecast Period Demand Forecast
2003 122 1 120 109 10 109 104
2 114 118 11 123 110
2004 130 3 130 132 12 119 119
4 124 110 13 130 124
2005 139 5 97 110 14 125 110
2006 152 6 95 105 15 119 90
7 100 98 16 120 95
2007 164 8 110 95 17 90 75
9 109 104 18 95 65
USE THE SALES DATA GIVEN BELOW TO DETERMINE: PROBLEM 4
(A) THE LEAST SQUARES TREND LINE
(B) THE PREDICTED VALUE FOR 2008 SALES.

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