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© 2007 Pearson Education

Chapter 7

Demand Forecastingin a Supply Chain

Supply Chain Management

(3rd Edition)

7-1



© 2007 Pearson Education 7-2

Outline

The role of forecasting in a supply chain

Characteristics of forecasts

Components of forecasts and forecasting methodsBasic approach to demand forecasting

Time series forecasting methods

Measures of forecast error

Forecasting demand at Tahoe Salt

Forecasting in practice




Role of Forecasting

in a Supply Chain

The basis for all strategic and planning decisions

in a supply chain

Used for both push and pull processes

Examples:

± Production: scheduling, inventory, aggregate planning

± Marketing: sales force allocation, promotions, new

production introduction

± Finance: plant/equipment investment, budgetary

planning

± Personnel: workforce planning, hiring, layoffs

All of these decisions are interrelated




Characteristics of Forecasts

Forecasts are always wrong. Should include

expected value and measure of error.

Long-term forecasts are less accurate than short-

term forecasts (forecast horizon is important)

Aggregate forecasts are more accurate than

disaggregate forecasts




Forecasting Methods

Qualitative: primarily subjective; rely on

judgment and opinion

Time Series: use historical demand only

± Static

± Adaptive

Causal: use the relationship between demand and

some other factor to develop forecastSimulation

± Imitate consumer choices that give rise to demand

± Can combine time series and causal methods




Components of an Observation

O bserved demand (O) =

Systematic component (S) + Random component (R)

Level (current deseasonalized demand)

Trend (growth or decline in demand)

Seasonality (predictable seasonal fluctuation)

Systematic component: Expected value of demand

Random component: The part of the forecast that deviates

from the systematic component

Forecast error: difference between forecast and actual demand




Time Series Forecasting

Quarter Demand Dt

II, 1998 8000

III, 1998 13000

IV, 1998 23000

I, 1999 34000II, 1999 10000

III, 1999 18000

IV, 1999 23000

I, 2000 38000II, 2000 12000

III, 2000 13000

IV, 2000 32000

I, 2001 41000

F orecast demand for the

next four quarters.





0

10,000

20,000

30,000

40,000

50,000

9 7 , 2

9 7 , 3

9 7 , 4

9 8 , 1

9 8 , 2

9 8 , 3

9 8 , 4

9 9 , 1

9 9 , 2

9 9 , 3

9 9 , 4

0 0 , 1




Forecasting Methods

Static

Adaptive

± Moving average

± Simple exponential smoothing

± Holt¶s model (with trend)

± Winter¶s model (with trend and seasonality)




Basic Approach to

Demand Forecasting

Understand the objectives of forecasting

Integrate demand planning and forecasting

Identify major factors that influence the demandforecast

Understand and identify customer segments

Determine the appropriate forecasting technique

Establish performance and error measures for the

forecast




Time Series

Forecasting Methods

Goal is to predict systematic component of demand

± Multiplicative: (level)(trend)(seasonal factor)

± Additive: level + trend + seasonal factor

± Mixed: (level + trend)(seasonal factor)

Static methods

Adaptive forecasting




Static Methods

Assume a mixed model:

Systematic component = (level + trend)(seasonal factor)

Ft+l

= [L + (t + l )T]S t+l

= forecast in period t for demand in period t + l

L = estimate of level for period 0

T = estimate of trend

St = estimate of seasonal factor for period t

Dt = actual demand in period t

Ft = forecast of demand in period t




Static Methods

Estimating level and trend

Estimating seasonal factors




Estimating Level and Trend

Before estimating level and trend, demand data

must be deseasonalized

Deseasonalized demand = demand that would

have been observed in the absence of seasonal

fluctuations

Periodicity ( p)

± the number of periods after which the seasonal cyclerepeats itself

± for demand at Tahoe Salt (Table 7.1, Figure 7.1) p = 4





(Table 7.1)

Quarter Demand Dt

II, 1998 8000

III, 1998 13000

IV, 1998 23000

I, 1999 34000II, 1999 10000

III, 1999 18000

IV, 1999 23000

I, 2000 38000II, 2000 12000

III, 2000 13000

IV, 2000 32000

I, 2001 41000

F orecast demand for the

next four quarters.





(Figure 7.1)

0

10,000

20,000

30,000

40,000

50,000

9 7 , 2

9 7 , 3

9 7 , 4

9 8 , 1

9 8 , 2

9 8 , 3

9 8 , 4

9 9 , 1

9 9 , 2

9 9 , 3

9 9 , 4

0 0 , 1




Estimating Level and Trend

Before estimating level and trend, demand data

must be deseasonalized

Deseasonalized demand = demand that would

have been observed in the absence of seasonal

fluctuations

Periodicity ( p)

± the number of periods after which the seasonal cyclerepeats itself

± for demand at Tahoe Salt (Table 7.1, Figure 7.1) p = 4




Deseasonalizing Demand

[Dt-(p/2)

+ Dt+(p/2)

+ 7 2Di

] / 2p for p even

Dt = (sum is from i = t+1-(p/2) to t+1+(p/2))

7 Di / p for p odd

(sum is from i = t-(p/2) to t+(p/2)), p/2 truncated to lower integer





For the example, p = 4 is even

For t = 3:

D3 = {D1 + D5 + Sum(i=2 to 4) [2Di]}/8

= {8000+10000+[(2)(13000)+(2)(23000)+(2)(34000)]}/8

= 19750

D4 = {D2 + D6 + Sum(i=3 to 5) [2Di]}/8

= {13000+18000+[(2)(23000)+(2)(34000)+(2)(10000)]/8

= 20625





Then include trend

Dt = L + t T

where Dt = deseasonalized demand in period t

L = level (deseasonalized demand at period 0)

T = trend (rate of growth of deseasonalized demand)

Trend is determined by linear regression using

deseasonalized demand as the dependent variable and period as the independent variable (can be done in

Excel)

In the example, L = 18,439 and T = 524




Time Series of Demand

(Figure 7.3)

0

10000

20000

30000

40000

50000

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

Period

D e m a n Dt

Dt-bar




Estimating Seasonal Factors

Use the previous equation to calculate deseasonalized

demand for each period

St

= Dt

/ Dt

= seasonal factor for period t

In the example,

D2 = 18439 + (524)(2) = 19487 D2 = 13000

S2 = 13000/19487 = 0.67

The seasonal factors for the other periods are

calculated in the same manner




Estimating Seasonal Factors

(Fig. 7.4)

t Dt Dt-bar S-bar

1 8000 18963 0.42 = 8000/18963

2 13000 19487 0.67 = 13000/19487

3 23000 20011 1.15 = 23000/20011

4 34000 20535 1.66 = 34000/20535

5 10000 21059 0.47 = 10000/210596 18000 21583 0.83 = 18000/21583

7 23000 22107 1.04 = 23000/22107

8 38000 22631 1.68 = 38000/22631

9 12000 23155 0.52 = 12000/23155

10 13000 23679 0.55 = 13000/23679

11 32000 24203 1.32 = 32000/24203

12 41000 24727 1.66 = 41000/24727




Estimating Seasonal FactorsThe overall seasonal factor for a ³season´ is then obtained

by averaging all of the factors for a ³season´

If there are r seasonal cycles, for all periods of the form

pt+i, 1<i< p, the seasonal factor for season i isSi = [Sum(j=0 to r-1) S j p+i]/r

In the example, there are 3 seasonal cycles in the data and

p=4, so

S1 = (0.42+0.47+0.52)/3 = 0.47

S2 = (0.67+0.83+0.55)/3 = 0.68

S3 = (1.15+1.04+1.32)/3 = 1.17

S4 = (1.66+1.68+1.66)/3 = 1.67




Estimating the Forecast

Using the original equation, we can forecast the next

four periods of demand:

F13 = (L+13T)S1 = [18439+(13)(524)](0.47) = 11868

F14 = (L+14T)S2 = [18439+(14)(524)](0.68) = 17527

F15 = (L+15T)S3 = [18439+(15)(524)](1.17) = 30770

F16 = (L+16T)S4 = [18439+(16)(524)](1.67) = 44794




Adaptive Forecasting

The estimates of level, trend, and seasonality are

adjusted after each demand observation

General steps in adaptive forecasting

Moving average

Simple exponential smoothing

Trend-corrected exponential smoothing (Holt¶s

model)Trend- and seasonality-corrected exponential

smoothing (Winter¶s model)




Basic Formula for


Ft+1 = (Lt + l T)St+1 = forecast for period t+l in period t

Lt = Estimate of level at the end of period t

Tt = Estimate of trend at the end of period t

St = Estimate of seasonal factor for period t

Ft = Forecast of demand for period t (made period t -1 or

earlier)

Dt = Actual demand observed in period t Et = Forecast error in period t

At = Absolute deviation for period t = |Et |

MAD = Mean Absolute Deviation = average value of At




General Steps in


Initialize: Compute initial estimates of level (L0), trend

(T0), and seasonal factors (S1,«,S p). This is done as

in static forecasting.

Forecast: Forecast demand for period t+1 using thegeneral equation

Estimate error: Compute error Et+1 = Ft+1- Dt+1

Modify estimates: Modify the estimates of level (Lt +1),trend (Tt +1), and seasonal factor (St+ p+1), given the

error Et +1 in the forecast

Repeat steps 2, 3, and 4 for each subsequent period




Moving Average

Used when demand has no observable trend or seasonality

Systematic component of demand = level

The level in period t is the average demand over the last N

periods (the N-period moving average)

Current forecast for all future periods is the same and is based

on the current estimate of the level

Lt = (Dt + Dt-1 + « + Dt-N+1) / N

Ft+1 = Lt and Ft+n = Lt

After observing the demand for period t +1, revise the

estimates as follows:

Lt+1 = (Dt+1 + Dt + « + Dt-N+2) / N

Ft+2 = Lt+1




Moving Average Example

From Tahoe Salt example (Table 7.1)

At the end of period 4, what is the forecast demand for periods 5

through 8 using a 4-period moving average?

L4 = (D4+D3+D2+D1)/4 = (34000+23000+13000+8000)/4 = 19500F5 = 19500 = F6 = F7 = F8

O bserve demand in period 5 to be D5 = 10000

Forecast error in period 5, E5 = F5 - D5 = 19500 - 10000 = 9500

Revise estimate of level in period 5:L5 = (D5+D4+D3+D2)/4 = (10000+34000+23000+13000)/4 =

20000

F6 = L5 = 20000




Simple Exponential Smoothing

Used when demand has no observable trend or seasonality

Systematic component of demand = level

Initial estimate of level, L0, assumed to be the average of all

historical dataL0 = [Sum(i=1 to n)Di]/n

Current forecast for all future periods is equal to the current

estimate of the level and is given as follows:

Ft+1 = Lt and Ft+n = Lt

After observing demand Dt+1, revise the estimate of the level:

Lt+1 = EDt+1 + (1-E)Lt

Lt+1 = Sum(n=0 to t+1)[E(1-E)nDt+1-n ]




Simple Exponential Smoothing

ExampleFrom Tahoe Salt data, forecast demand for period 1 using

exponential smoothing

L0 = average of all 12 periods of data

= Sum(i=1 to 12)[Di]/12 = 22083

F1 = L0 = 22083

O bserved demand for period 1 = D1 = 8000

Forecast error for period 1, E1, is as follows:

E1 = F1 - D1 = 22083 - 8000 = 14083

Assuming E = 0.1, revised estimate of level for period 1:

L1 = ED1 + (1-E)L0 = (0.1)(8000) + (0.9)(22083) = 20675

F2 = L1 = 20675

Note that the estimate of level for period 1 is lower than in period 0




Trend-Corrected Exponential

Smoothing (Holt¶s Model)

Appropriate when the demand is assumed to have a level and

trend in the systematic component of demand but no seasonality

O btain initial estimate of level and trend by running a linear

regression of the following form:Dt = at + b

T0 = a

L0 = b

In period t, the forecast for future periods is expressed as follows:Ft+1 = Lt + Tt

Ft+n = Lt + nTt




Trend-Corrected Exponential

Smoothing (Holt¶s Model)

After observing demand for period t, revise the estimates for level

and trend as follows:

Lt+1 = EDt+1 + (1-E)(Lt + Tt)

Tt+1 = F(Lt+1 - Lt) + (1- F)Tt

E = smoothing constant for level

F = smoothing constant for trend

Example: Tahoe Salt demand data. Forecast demand for period 1

using Holt¶s model (trend corrected exponential smoothing)Using linear regression,

L0 = 12015 (linear intercept)

T0 = 1549 (linear slope)




Holt¶s Model Example (continued)

Forecast for period 1:

F1 = L0 + T0 = 12015 + 1549 = 13564

O bserved demand for period 1 = D1 = 8000

E1 = F1 - D1 = 13564 - 8000 = 5564Assume E = 0.1, F = 0.2

L1 = ED1 + (1-E)(L0+T0) = (0.1)(8000) + (0.9)(13564) = 13008

T1 = F(L1 - L0) + (1- F)T0 = (0.2)(13008 - 12015) + (0.8)(1549)

= 1438F2 = L1 + T1 = 13008 + 1438 = 14446

F5 = L1 + 4T1 = 13008 + (4)(1438) = 18760




Trend- and Seasonality-Corrected

Exponential Smoothing

Appropriate when the systematic component of

demand is assumed to have a level, trend, and seasonal

factor

Systematic component = (level+trend)(seasonal factor)Assume periodicity p

O btain initial estimates of level (L0), trend (T0),

seasonal factors (S1

,«,S p

) using procedure for static

forecasting

In period t, the forecast for future periods is given by:

Ft+1 = (Lt+Tt)(St+1) and Ft+n = (Lt + nTt)St+n





Exponential Smoothing (continued)

After observing demand for period t+1, revise estimates for level,

trend, and seasonal factors as follows:

Lt+1 = E(Dt+1/St+1) + (1-E)(Lt+Tt)

Tt+1 = F(Lt+1 - Lt) + (1- F)Tt

St+p+1 = K(Dt+1/Lt+1) + (1-K)St+1

E = smoothing constant for level

F = smoothing constant for trend

K = smoothing constant for seasonal factor Example: Tahoe Salt data. Forecast demand for period 1 using

Winter¶s model.

Initial estimates of level, trend, and seasonal factors are obtained

as in the static forecasting case





Exponential Smoothing Example (continued)

L0 = 18439 T0 = 524 S1=0.47, S2=0.68, S3=1.17, S4=1.67

F1 = (L0 + T0)S1 = (18439+524)(0.47) = 8913

The observed demand for period 1 = D1 = 8000

Forecast error for period 1 = E1 = F1-D1 = 8913 - 8000 = 913

Assume E = 0.1, F=0.2, K=0.1; revise estimates for level and trend

for period 1 and for seasonal factor for period 5

L1 = E(D1/S1)+(1-E)(L0+T0) = (0.1)(8000/0.47)+(0.9)(18439+524)=18769

T1 = F(L1-L0)+(1- F)T0 = (0.2)(18769-18439)+(0.8)(524) = 485S5 = K(D1/L1)+(1-K)S1 = (0.1)(8000/18769)+(0.9)(0.47) = 0.47

F2 = (L1+T1)S2 = (18769 + 485)(0.68) = 13093




Measures of Forecast Error

Forecast error = Et = Ft - Dt

Mean squared error (MSE)

MSEn

= (Sum(t=1 to n)

[Et

2])/n

Absolute deviation = At = |Et|

Mean absolute deviation (MAD)

MADn = (Sum(t=1 to n)[At])/n

W = 1.25MAD




Measures of Forecast Error

Mean absolute percentage error (MAPE)

MAPEn = (Sum(t=1 to n)[|Et/ Dt|100])/n

Bias

Shows whether the forecast consistently under- or

overestimates demand; should fluctuate around 0

biasn = Sum(t=1 to n)[Et]

Tracking signal

Should be within the range of +6

Otherwise, possibly use a new forecasting method

TSt = bias / MADt




Forecasting Demand at Tahoe Salt

Moving average

Simple exponential smoothing

Trend-corrected exponential smoothing

Trend- and seasonality-corrected exponential

smoothing




Forecasting in Practice

Collaborate in building forecasts

The value of data depends on where you are in the

supply chain

Be sure to distinguish between demand and sales




Summary of Learning Objectives

What are the roles of forecasting for an enterprise and

a supply chain?

What are the components of a demand forecast?

How is demand forecast given historical data using

time series methodologies?

How is a demand forecast analyzed to estimate

forecast error?

chopra3 ppt ch07

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