5, 6 & 7 - demand management

Demand Management

2

Demand

• Planning as most important function of management

• Demand Management deals with both consumer needs and supplier coordination

• Purpose of demand management is to coordinate and control all resources to efficiently utilise systems

• Demands has to be forecasted to run businesses profitably

3

Forecasting

• Many business decisions depend on some sort of forecasting

• Forecasting is scientifically calculated guess, it forms the basis of planning

• Levels of forecasting - Short term (upto 1 yr) Medium term (1 to 3 yrs) and Long term (over 5 yrs)

• Extrinsic forecast & intrinsic forecast• Elements of forecasting

Internal factors (past, present and future) External factors (controllable & uncontrollable)

4

Methods of Forecasting

• Qualitative Techniques Market research Panel Consensus History Analogy Delphi Method

• Casual Methods Linear Regression Multiple Regression Input Output Analysis End use analysis

• Simulation – Monte Carlo Simulation

5

Methods of Forecasting . . contd

• Time Series Extrapolation – Used when past data is linear Moving Average – Used when data is cyclic

o Simple – Average of specified past period is consideredo Weighted – different weights are assigned to past data

Exponential Smoothing – weightage decreased exponentially

o Simple Exponential Smoothingo Trend adjusted o Seasonality considered

6

Forecasting programme for any company

• Observing, listing and studying external factors (cultural, social, political, technological) nationally & internationally

• Gather info on internal company policies (changes in design, quality, sales) & their effect on demand

• Analyse data to establish various relationships and their relative effects of each factors on final demand

• Create various scenarios assuming certain happenings in external environment & alternative internal policies

• Operationally apply the forecast by breaking it down on the number of product lines. Do Break Even analysis

• Regularly monitor forecast errors & update method

7

Prerequisites & Pitfalls in Forecasting

• Define the purpose of forecasting, this will help to decide the accuracy & type of technique to be chosen

• It should be combined effort organisationally• Forecasting technique will vary depending on the

Product Life Cycle and stage of the product New product development stage – Delphi, PDMT Steady state of PLC – Time series with trend & seasonality

• Quite often wrong things are forecasted• People go for minute forecasting of odd products• No timely tracking of forecasting

8

Range & Precision of Forecast

• Forecast may be in terms of ranges Higher range – low value, low turnover items in inventory Lower range – Capital intensive machineries

• It will also guide the company form its strategic posture

• Precision in forecasting is not as important as proper use of available data

• It is better to use the available data according to situational demands

9

Technology Forecasting

• It deals with estimation of future trends in technology• Helps making current decisions examining future choices• Guides wide range of long term planning process• Forecasting tool at micro level corporate planning also• Very effective for high range technology products as

gestation time to become productive is quite long• Exploratory technology forecasting – Predicting future

with present trends & capabilities• Normative Forecasting – Set goals & objectives of future

technology and take necessary current action

10

Uses of Technology Forecasting

In planning of future discoveries & technologies

Government IndividualsUniversitiesIndustry

Planning

Policy formation for the allocation of resources

Corporate Planning

Investment in production

Investment in research & development

Future Academic Roles

Selection of fertile areas of research

11

Selecting a forecasting method

• Choice depends on Purpose of forecasting Type and amount of data available Time horizon of forecast Degree of accuracy required Cost involved

12

Forecast Error Monitoring - MAD

•Mean Absolute Deviation (MAD)Absolute means the positive & negative signs are ignoredDeviation is difference between forecast & actuals

Period Forecast Demand Actual Demand Deviation

1 900 1000 100

2 1000 1100 100

3 1050 1000 -50

4 1010 960 -50

5 980 970 - 15

MAD = ∑I Deviation I = 315 = 63

N 5

13

Forecast Error Monitoring - RSFE

•Running sum of forecast errors (RSFE)This is algebraic sum of forecasting errors (deviation)

Period Forecast Demand Actual Demand Deviation

1 900 1000 100

2 1000 1100 100

3 1050 1000 -50

4 1010 960 -50

5 980 970 -15

RSFE = ∑Deviation = 85

14

Forecast Error Monitoring - Formulas

Mean Square Error (MSE) = ∑ (Deviation)²

N

Percentage Error (PE) = (Deviation / Demand) x 100

Mean Absolute Percentage Error = ∑ I PE I

N

Tracking Signal = RSFE

MAD

15

Forecast Error Monitoring . . contd

• RSFE is calculated to determine whether or not the forecast has positive or negative bias

• MAD indicates the volume or amplitude of deviation from actuals

• Both the bias and amplitude of forecast errors are important

• It is important to monitor MAD & Tracking signal for any modifications to be made in original forecasting model

• A good forecast should have approximately as much positive as negative deviation

16

Problem

Forecast Demand

100 110

90 85

80 88

85 95

75 65

85 80

65 52

Table shows actual & forecasted demand. Calculate:

- MAD

- MSE

- MAPE

- Tracking Signal

17

Problem

Forecast Demand Deviation

100 110 10

90 85 -5

80 88 8

85 95 10

75 65 -10

85 80 -5

65 52 -13

18

Problem

Forecast Demand Deviation (Deviation)²

100 110 10 100

90 85 -5 25

80 88 8 64

85 95 10 100

75 65 -10 100

85 80 -5 25

65 52 -13 169

19

Problem

Forecast Demand Deviation (Deviation)² Percentage Error

100 110 10 100 9.09

90 85 -5 25 -5.88

80 88 8 64 9.09

85 95 10 100 10.52

75 65 -10 100 -15.38

85 80 -5 25 -6.25

65 52 -13 169 -25

20

Problem

MAD =∑ I Deviation I = 61 = 8.71

N 7

MSE = ∑ (Deviation)² = 583 = 83.29

7 7

MAPE = ∑ I PE I = 81.23 = 11.6%

N 7

Tracking Signal = RSFE = -5 = -0.57

MAD 8.71

21

Practice Problem

Forecast Demand

150 160

125 130

130 135

145 150

180 160

170 165

165 145

155 150

155 155

150 160

150 165

160 160

Table shows actual & forecasted demand. Calculate:

- MAD

- MSE

- MAPE

- Tracking Signal

22

Simple Moving Average - Formula

( MA ) t = Dt + Dt-1 + Dt-2 + . . . . Dt-n+1

n

( MA ) t = ( f ) t+1

Where; MA = Moving Average

f = Moving Avg Forecast

t = time

23

Problem – Simple Moving Average Method

Month Demand (D)

Jan 450

Feb 440

Mar 460

Apr 510

May 520

Jun 495

Jul 475

Aug 560

Sep 510

Oct 520

Nov 540

Dec 550

Forecast using 3 month and 6 month moving average and determine which is a better forecast

24


Month Demand (D) Moving Average

(3 mth)

Jan 450 -

Feb 440 -

Mar 460 450

Apr 510 470

May 520 497

Jun 495 508

Jul 475 497

Aug 560 510

Sep 510 515

Oct 520 530

Nov 540 523

Dec 550 537

25


Month Demand (D) Moving Average (3 mth)

Moving Average Forecast (f)(3 mth)

Jan 450 - -

Feb 440 - -

Mar 460 450 -

Apr 510 470 450

May 520 497 470

Jun 495 508 497

Jul 475 497 508

Aug 560 510 497

Sep 510 515 510

Oct 520 530 515

Nov 540 523 530

Dec 550 537 523

26


Month Demand (D) Moving Average (3 mth)

Moving Average Forecast (f)(3 mth)

Deviation

Jan 450 - - -

Feb 440 - - -

Mar 460 450 - -

Apr 510 470 450 60

May 520 497 470 50

Jun 495 508 497 -2

Jul 475 497 508 -33

Aug 560 510 497 63

Sep 510 515 510 0

Oct 520 530 515 5

Nov 540 523 530 10

Dec 550 537 523 27

27


Month Demand (D) MA (3 mth) F (3 mth) Deviation

Jan 450 - - -

Feb 440 - - -

Mar 460 450 - -

Apr 510 470 450 60

May 520 497 470 50

Jun 495 508 497 -2

Jul 475 497 508 -33

Aug 560 510 497 63

Sep 510 515 510 0

Oct 520 530 515 5

Nov 540 523 530 10

Dec 550 537 523 27

MAD = ∑I Deviation I

N

MAD = 250 / 9

MAD = 27.78

RSFE = ∑ Deviation

RSFE = 180

Tracking Signal = RSFE / MAD

= 6.48

28



(6 mth)

Jan 450 -

Feb 440 -

Mar 460 -

Apr 510 -

May 520 -

Jun 495 479

Jul 475 483

Aug 560 503

Sep 510 512

Oct 520 513

Nov 540 517

Dec 550 526

29



(6 mth)

Moving Average Forecast(6 mth)

Jan 450 - -

Feb 440 - -

Mar 460 - -

Apr 510 - -

May 520 - -

Jun 495 479 -

Jul 475 483 479

Aug 560 503 483

Sep 510 512 503

Oct 520 513 512

Nov 540 517 513

Dec 550 526 517

30



(6 mth)

Moving Average Forecast(6 mth)

Deviation

Jan 450 - - -

Feb 440 - - -

Mar 460 - - -

Apr 510 - - -

May 520 - - -

Jun 495 479 - -

Jul 475 483 479 -4

Aug 560 503 483 77

Sep 510 512 503 7

Oct 520 513 512 8

Nov 540 517 513 27

Dec 550 526 517 33

31


Month Demand (D) MA (6mth)

F (6mth) Deviation

Jan 450 - - -

Feb 440 - - -

Mar 460 - - -

Apr 510 - - -

May 520 - - -

Jun 495 479 - -

Jul 475 483 479 -4

Aug 560 503 483 77

Sep 510 512 503 7

Oct 520 513 512 8

Nov 540 517 513 27

Dec 550 526 517 33

MAD = ∑I Deviation I

N

MAD = 156 / 6

MAD = 26

RSFE = ∑ Deviation

RSFE = 148

Tracking Signal = RSFE / MAD

= 5.7

32


• Since Tracking Signal of 6 month moving average is more closer to zero it is a better forecasting technique

33

Weighted Moving Average - Formula

• Weighted Moving Average

= ∑ Ct Dt

Where,

Ct = Fraction used as weight for period t

0 ≤ Ct ≤1

t = 1

n

34

Problem – Weighted Moving Average

Month Demand (D) Moving

Average

(3 mth)

Moving Average Forecast

(3 mth)

Jan 450 - -

Feb 440 - -

Mar 460 450 -

Apr 510 470 450

May 520 497 470

Jun 495 508 497

Jul 475 497 508

Aug 560 510 497

Sep 510 515 510

Oct 520 530 515

Nov 540 523 530

Dec 550 537 523

Since it is a 3 month moving average, assume values of:

C1 = 0.25

C2 = 0.25

C3 = 0.5

35


Month Demand (D) MA

(3 mth)

MA Forecast

(3 mth)

3 mnth WMA

Jan 450 - - -

Feb 440 - - -

Mar 460 450 - 453

Apr 510 470 450 480

May 520 497 470 503

Jun 495 508 497 505

Jul 475 497 508 491

Aug 560 510 497 523

Sep 510 515 510 514

Oct 520 530 515 528

Nov 540 523 530 528

Dec 550 537 523 541

36


Month Demand (D) MA

(3 mth)

MA Forecast

(3 mth)

3 mnth WMA

3 mnth WMA forecast

Jan 450 - - - -

Feb 440 - - - -

Mar 460 450 - 453 -

Apr 510 470 450 480 453

May 520 497 470 503 480

Jun 495 508 497 505 503

Jul 475 497 508 491 505

Aug 560 510 497 523 491

Sep 510 515 510 514 523

Oct 520 530 515 528 514

Nov 540 523 530 528 528

Dec 550 537 523 541 528

37

Practice Problem

Month Demand (D)

Jan 125

Feb 135

Mar 130

Apr 120

May 115

Jun 140

Jul 135

Aug 110

Sep 120

Oct 120

Nov 140

Dec 145

Use Simple Moving Average and Weighted Moving average method for 2 months. Forecast and compare two methods. Assume appropriate values

38

Simple Exponential Smoothing - Formula

Ft = F t-1 + α(Dt - Ft-1) OR α (Dt) + (1 – α ) Ft-1

ft = Ft-1

Where,

F = Simple Exponential average

f = Forecast for time t

D = Demand

α = Smoothing constant between 0 to 1

39

Problem – Simple Exponential Smoothing

Month Demand

Jan 97

Feb 93

Mar 110

Apr 98

May 104

Jun 103

Jul 99

Aug 108

Sep 106

Oct 94

Nov 109

Dec 95

A firm uses exponential smoothing method for forecasting. Try α = 0.1 & F0 = 100

40


Month Demand Exponential Avg (Ft)

100

Jan 97 99.7

Feb 93 99.03

Mar 110 100.73

Apr 98 99.91

May 104 100.32

Jun 103 100.60

Jul 99 100.44

Aug 108 101.20

Sep 106 101.68

Oct 94 82.11

Nov 109 84.8

Dec 95 85.82

41


Month Demand Exponential Avg (Ft)

Forecast (ft)

100

Jan 97 99.7 100

Feb 93 99.03 99.7

Mar 110 100.73 99.03

Apr 98 99.91 100.73

May 104 100.32 99.91

Jun 103 100.60 100.32

Jul 99 100.44 100.60

Aug 108 101.20 100.44

Sep 106 101.68 101.20

Oct 94 82.11 101.68

Nov 109 84.8 82.11

Dec 95 85.82 84.8

42

Practice Problem

• A firm uses exponential smoothing method for forecasting, with α = 0.2

The forecast for month of March was 500 units but actual demand turned out to be 460. Forecast demand in April.

ft = F t-1 i.e f APR = F MAR

Ft = α (Dt) + (1 – α ) Ft-1

FMAR = α (DMAR) + (1 – α ) FFEB

F MAR = 0.2 (460) + (1-0.2) 500

F MAR = 492

43

Practice Problem

Month Demand

Jan 122

Feb 127

Mar 125

Apr 126

May 139

Jun 127

Jul 134

Aug 128

Sep 134

Oct 136

Nov 132

Dec 131

Given in table is the data for 1994. F0 = 150. Try α = 0.1 and 0.3, which is a better value?

44

Exponential Smoothing with Trend (Winter’s)

Ft = α (Dt) + (1 – α ) (Ft-1 + Tt-1)

Tt = β (Ft – Ft-1) + (1 – β) Tt-1

ft = Ft-1 + Tt-1

Where,

F = Winters Exponential average

f = Forecast for time t

D = Demand

α = Smoothing constant between 0 to 1

T = Trend estimate at time t

Β = Averaging fraction

45

Problem – Exponential smoothing with trend

Month Demand

Jan 460

Feb 510

Mar 520

Apr 495

May 475

Jun 560

Jul 510

Aug 520

Sep 540

Oct 550

Nov 555

Dec 569

Calculate forecast with:

α = 0.2

β = 0.2

F0 = 480

T0 = 9

46


Month Demand Winter’s exp avg (Ft)

Trend (Tt)

480 9

Jan 460 483.20 7.84

Feb 510 494.83 8.60

Mar 520 506.74 9.26

Apr 495 511.80 8.42

May 475 511.18 6.61

Jun 560 526.23 8.30

Jul 510 529.62 7.32

Aug 520 533.55 6.64

Sep 540 540.16 6.63

Oct 550 547.43 6.76

Nov 555 554.35 6.79

Dec 569 562.72 7.11

47


Month Demand Winter’s exp avg (Ft)

Trend (Tt) Winter’s Forecast (ft)

480 9

Jan 460 483.20 7.84 489.00

Feb 510 494.83 8.60 491.04

Mar 520 506.74 9.26 503.43

Apr 495 511.80 8.42 516.00

May 475 511.18 6.61 520.22

Jun 560 526.23 8.30 517.79

Jul 510 529.62 7.32 534.53

Aug 520 533.55 6.64 536.94

Sep 540 540.16 6.63 540.20

Oct 550 547.43 6.76 546.79

Nov 555 554.35 6.79 554.19

Dec 569 562.72 7.11 561.15

48

Practice problem

Month Demand

Jan 128

Feb 136

Mar 137

Apr 141

May 157

Jun 148

Jul 158

Aug 155

Sep 164

Oct 169

Nov 168

Dec 160

Given data is for year 1994. Calculate forecast with:

α = 0.2

β = 0.05

F0 = 130

T0 = 0

49

Exponential smoothing with seasonality

Ft = α Dt + (1-α) Ft-1

It-m

It = γ Dt + (1-γ) It-m

Ft

ft+1 = Ft x It+1-m

Where;

It-m = Index calculated m=12 months ago for monthly forecast, m=4 quarters ago for quarterly forecast

γ = smoothing constant, normally ≤ 0.05

50

Prob - Exponential smoothing with seasonality

Month 1993 1994

Jan 80 100

Feb 75 85

Mar 80 90

Apr 90 110

May 115 131

Jun 110 120

Jul 100 110

Aug 90 110

Sep 85 95

Oct 75 85

Nov 75 85

Dec 80 80

The table shows demand data of 1993 & 1994. Forecast for the year 1995.

Other data:

α = 0.1 , γ = 0.05 , FDEC94 = 94

Next Step: Calculate average demand of 1993 & 1994 and average monthly demand

Demand

51


Month 1993 1994 Average Demand

Jan 80 100 90

Feb 75 85 80

Mar 80 90 85

Apr 90 110 100

May 115 131 123

Jun 110 120 115

Jul 100 110 105

Aug 90 110 100

Sep 85 95 90

Oct 75 85 80

Nov 75 85 80

Dec 80 80 80

Demand

Avg Monthly Demand = 1128 / 12

= 94

Next Step: Calculate Seasonal Index It = Dt / Ft

52


Month 1993 1994 Average Demand

Seasonality Index (It)

Jan 80 100 90 0.957

Feb 75 85 80 0.851

Mar 80 90 85 0.904

Apr 90 110 100 1.064

May 115 131 123 1.309

Jun 110 120 115 1.223

Jul 100 110 105 1.117

Aug 90 110 100 1.064

Sep 85 95 90 0.957

Oct 75 85 80 0.851

Nov 75 85 80 0.851

Dec 80 80 80 0.851

Demand

The demand for 1995 is given as:

53


Month Seasonality Index (It-m)

Demand

(Dt) 1995

Jan 0.957 95

Feb 0.851 75

Mar 0.904 90

Apr 1.064 105

May 1.309 120

Jun 1.223 117

Jul 1.117 102

Aug 1.064 98

Sep 0.957 95

Oct 0.851 75

Nov 0.851 85

Dec 0.851 75

Next Step: Calculate Ft for 1995 using formula

Ft = α Dt + (1-α) Ft-1

It-m

54



Demand

(Dt) 1995

Average

(Ft)

Jan 0.957 95 94.50

Feb 0.851 75 93.86

Mar 0.904 90 94.43

Apr 1.064 105 94.86

May 1.309 120 94.54

Jun 1.223 117 94.65

Jul 1.117 102 94.32

Aug 1.064 98 94.10

Sep 0.957 95 94.62

Oct 0.851 75 93.37

Nov 0.851 85 94.56

Dec 0.851 75 93.91

Next Step: Calculate Forecast values for 1995 using formula:

ft+1 = Ft x It+1-m

55



Demand

(Dt) 1995

Average

(Ft)

Forecast

(ft)

Jan 0.957 95 94.50 89.96

Feb 0.851 75 93.86 80.42

Mar 0.904 90 94.43 84.45

Apr 1.064 105 94.86 100.47

May 1.309 120 94.54 124.17

Jun 1.223 117 94.65 115.62

Jul 1.117 102 94.32 105.72

Aug 1.064 98 94.10 100.36

Sep 0.957 95 94.62 90.05

Oct 0.851 75 93.37 80.52

Nov 0.851 85 94.56 79.97

Dec 0.851 75 93.91 80.47

Next Step: Calculate It using formula


Ft

56



Demand

(Dt) 1995

Average

(Ft)

Forecast

(ft)

New Seasonality Index (It)

Jan 0.957 95 94.50 89.96 0.959

Feb 0.851 75 93.86 80.42 0.848

Mar 0.904 90 94.43 84.45 0.906

Apr 1.064 105 94.86 100.47 1.066

May 1.309 120 94.54 124.17 1.307

Jun 1.223 117 94.65 115.62 1.224

Jul 1.117 102 94.32 105.72 1.115

Aug 1.064 98 94.10 100.36 1.063

Sep 0.957 95 94.62 90.05 0.959

Oct 0.851 75 93.37 80.52 0.849

Nov 0.851 85 94.56 79.97 0.853

Dec 0.851 75 93.91 80.47 0.848

57

Practice Problem

Month 2003 2004 2005

Jan 120 130 145

Feb 115 121 127

Mar 117 125 132

Apr 122 122 127

May 125 122 118

Jun 127 120 115

Jul 125 125 128

Aug 122 130 135

Sep 120 133 140

Oct 115 130 140

Nov 117 127 135

Dec 120 127 130

The table shows demand data of 2003, 2004 & 2005. Forecast for the year 2005.

Other data:

α = 0.2 , γ = 0.05 , F0 = 130

Demand

58

Exponential smoothing with seasonality & trend (Winter’s complete model)

Ft = α Dt + (1-α) (Ft-1 + Tt-1)

It-m

Tt = β (Ft – Ft-1) + (1 – β) Tt-1


Ft

ft+1 = (Ft + Tt) x It+1-m

Consider values of α = 0.2, β = 0.05 and γ = 0.01

59

Prob – Smoothing with trend & seasonality

MonthDemand

‘95Seasonality

Index ‘95Demand

‘96

Jan 95 0.959 80

Feb 75 0.848 85

Mar 90 0.906 90

Apr 105 1.066 95

May 120 1.307 100

Jun 117 1.224 100

Jul 102 1.115 95

Aug 98 1.063 95

Sep 95 0.959 90

Oct 75 0.849 95

Nov 85 0.853 85

Dec 75 0.848 80

Forecast the demand for 1996 where:

F0 = 80

T0 = 4.5

α = 0.2

β = 0.05

γ = 0.01

Step 1: Calculate smoothing average and trend for each month of 1996

60


Month Demand

‘95

It-m Demand

‘96

Average

Ft

Trend

Tt

80 4.5

Jan 95 0.959 80 84.284 4.489

Feb 75 0.848 85 91.066 4.604

Mar 90 0.906 90 96.403 4.641

Apr 105 1.066 95 98.659 4.521

May 120 1.307 100 97.846 4.255

Jun 117 1.224 100 98.020 4.051

Jul 102 1.115 95 98.697 3.882

Aug 98 1.063 95 99.937 3.750

Sep 95 0.959 90 101.719 3.651

Oct 75 0.849 95 106.676 3.717

Nov 85 0.853 85 108.243 3.609

Dec 75 0.848 80 108.350 3.434

Now do forecasting for 1996 and calculate new seasonal index

61


Month Demand

‘95

It-m Demand

‘96

Average

Ft

Trend

Tt

Forecast’96 (ft)

New Index (It)

80 4.5

Jan 95 0.959 80 84.284 4.489 81.036 0.959

Feb 75 0.848 85 91.066 4.604 75.280 0.849

Mar 90 0.906 90 96.403 4.641 86.677 0.906

Apr 105 1.066 95 98.659 4.521 107.713 1.065

May 120 1.307 100 97.846 4.255 134.856 1.304

Jun 117 1.224 100 98.020 4.051 124.971 1.222

Jul 102 1.115 95 98.697 3.882 113.809 1.113

Aug 98 1.063 95 99.937 3.750 109.041 1.062

Sep 95 0.959 90 101.719 3.651 99.436 0.958

Oct 75 0.849 95 106.676 3.717 89.460 0.849

Nov 85 0.853 85 108.243 3.609 94.165 0.852

Dec 75 0.848 80 108.350 3.434 94.851 0.847

62

Problem – Smoothing with trend & seasonality

1992 1993 1994

Quarter 1 146 192 272

Quarter 2 96 127 155

Quarter 3 59 79 98

Quarter 4 133 186 219

Estimate forecast for 1995 using winter’s complete model with α = 0.2 , β = 0.1 and γ = 0.05

63


Ft = α Dt + (1-α) (Ft-1 + Tt-1)

It-m

Tt = β (Ft – Ft-1) + (1 – β) Tt-1


Ft

ft+1 = (Ft + Tt) x It+1-m

Here, F0, T0 and It-m (i.e I -3) are unknown.

Lets calculate it first.

64


F0 = D – T0 (2.5) for quarterly data

And

F0 = D – T0 (6.5) for monthly data

Lets Calculate D for year 1992 and 1993

D1992 = 108.5 and D1993 = 146

Here we see the upward trend movement from 1992 to 1993 is

= 146 – 108.5 = 37.5, hence quarterly movement (T0) = 9.38So, F0 = 108.5 – 9.38 (2.5) = 85.05

65


Now, lets calculate the trend line sales estimate for 1992 & 1993

1992 Q1 = F0 + T0(1) = 85.05 + 9.38 = 94.43

1992 Q2 = F0 + T0(2) = 85.05 + 9.38 (2) = 103.81 and so on

1992 1993

Quarter 1 94.43 131.95

Quarter 2 103.81 141.33

Quarter 3 113.19 150.71

Quarter 4 122.57 160.09

From these trend estimates (table) we can develop initial seasonal indices as:

Index = Demand / Estimate

66


Index for Q1 of 1992 = 146 / 94.43 = 1.55

Q2 of 1992 = 96 / 103.81 = 0.92 and so on

1992 1993

Quarter 1 1.55 1.46

Quarter 2 0.92 0.90

Quarter 3 0.52 0.52

Quarter 4 1.09 1.13

Lets check our indices are correct or not

To check, take average of indices for 1992 and 1993 and calculate ∑ average

67


1992 1993 Average

Quarter 1 1.55 1.46 1.51

Quarter 2 0.92 0.90 0.91

Quarter 3 0.52 0.52 0.52

Quarter 4 1.09 1.13 1.13

∑ Average 4.07

∑ Average = 4.07. It should have been 4, so there is a mistake in calculated indices.

Lets introduce a correction factor and recalculate the indices

68


Correction factor = (4 / 4.07) = 0.983. Now recalculate the indices

1992 1993 Average I t-m

Quarter 1 1.55 1.46 1.51 1.51 x 0.983 = 1.48

Quarter 2 0.92 0.90 0.91 0.91 x 0.983 = 0.89

Quarter 3 0.52 0.52 0.52 0.52 x 0.983 = 0.51

Quarter 4 1.09 1.13 1.13 1.13 x 0.983 = 1.11

Now we have values of all the unknowns F0, T0 and It-m (i.e I-3) and we can calculate Ft, Tt, It and also forecast for 1995

69


F1 = 0.2 (146 / 1.48) + (1 – 0.8)(85.05 + 9.38) = 95.27

T1 = 0.1 (95.27 – 85.05) + (1 – 0.1) 9.38 = 9.46

I1 = 0.05 (146 / 95.27) + (1 – 0.05) 1.48 = 1.48

. . . And so on till the value of F12, T12 and I12

70


Ft Tt It

0 85.05 9.38 1.11

1 95.27 9.46 1.48

2 105.36 9.53 0.89

3 115.05 9.54 0.51

4 123.64 9.45 1.11

5 132.37 9.38 1.48

6 141.90 9.39 0.89

7 152.01 9.46 0.51

8 162.74 9.59 1.11

9 174.60 9.82 1.48

10 182.31 9.61 0.90

11 191.92 9.61 0.52

12 199.92 9.48 1.11Lets forecast for 1995

71


Forecast for Q1 of 1995

= f13 = (199.92 + 9.48) * 1.49 = 312


= f14 = (199.92 + (2 x 9.48)) * 0.90 = 197


= f15 = (199.92 + (3 x 9.48)) * 0.52 = 119


= f16 = (199.92 + (4 x 9.48)) * 1.11 = 264

72

Practice Problem

Month Demand’ 93 Forecast ‘93 Demand ‘94

Jan 97 100 78

Feb 93 100 0

Mar 110 100 55

Apr 98 100 75

May 130 102 87

Jun 133 104 0

Jul 129 106 73

Aug 138 108 0

Sep 136 110 0

Oct 124 112 0

Nov 139 114 0

Dec 125 116 53

Calculate Winter’s trend ratio and seasonality index.

What is the forecast for Q1 of 1995?

5, 6 & 7 - demand management

Documents

purpose of forecasting

forecasting short term

external factors cultural

demandanalyse data

estimation of future

high range technology

yr medium term

proper use of available