Objectives of Chapters 7,8 - Al Akhawayn UniversityA.Berrado/MGT5309/MGT5309_ch07.pdf · Objectives...

© 2007 Pearson Education 7-1

Objectives of Chapters 7,8

�Planning Demand and Supply in a SC: (Ch7, 8, 9)

– Ch7� Describes methodologies that can be used to forecast future demand based on historical data.

– Ch8� Describes the aggregate planning methodology used to plan production, distribution and allocate resources for the near future, by making trade-offs among capacity, inventory and backlogged orders across the entire SC.

– Ch9� Describes how pricing and promotions can be planned to manage customer demand in coordination with production and distribution.

© 2007 Pearson Education

Chapter 7Demand Forecasting

in a Supply Chain

Supply Chain Management(3rd Edition)

7-2


Outline

�The role of forecasting in a supply chain

�Characteristics of forecasts

�Components of forecasts and forecasting methods

�Basic 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

�The farther up the SC an enterprise is, the larger is the forecast error �importance of collaborative forecasting


Components of Forecast

�To forecast demand, companies must first identify the factors that influence future demand and ascertain the relationship between these factors and future demand.

�Objective and subjective factors:

– Past demand

– Lead time of product

– Planned advertising or marketing efforts

– State of the economy

– Planned price discounts

– Actions that competitors have taken

– Human input


Four Types of 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 forecast

�Simulation

– Imitate consumer choices that give rise to demand

– Can combine time series and causal methods


Components of an Observation

Observed 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 34000

II, 1999 10000

III, 1999 18000

IV, 1999 23000

I, 2000 38000

II, 2000 12000

III, 2000 13000

IV, 2000 32000

I, 2001 41000

Forecast demand for the

next four quarters.



0

10,000

20,000

30,000

40,000

50,000

97,2

97,3

97,4

98,1

98,2

98,3

98,4

99,1

99,2

99,3

99,4

00,1


Basic Approach to

Demand Forecasting

�Understand the objectives of forecasting

� Integrate demand planning and forecasting

�Understand and identify customer segments

� Identify major demand, supply and product related factors

that influence the demand forecast

�Determine the appropriate forecasting technique for

demand along three dimensions: the geographic areas,

product groups, and customer groups

�Establish performance and error measures for the forecast


Time Series

Forecasting Methods

� Goal is to predict systematic component of demand and estimate the random component.

� The systematic component contains a level, a trend and a seasonal factor and make take a variety of forms:

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

– Additive: level + trend + seasonal factor

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

� Static

� Adaptive

– Moving average

– Simple exponential smoothing

– Holt’s model (with trend)

– Winter’s model (with trend and seasonality)


Static Methods

�Assume a mixed model:

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

Ft+l = [L + (t + l)T]St+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



(Table 7.1)

Quarter Demand Dt

II, 1998 8000

III, 1998 13000

IV, 1998 23000

I, 1999 34000

II, 1999 10000

III, 1999 18000

IV, 1999 23000

I, 2000 38000

II, 2000 12000

III, 2000 13000

IV, 2000 32000

I, 2001 41000

Forecast demand for the

next four quarters.



(Figure 7.1)

0

10,000

20,000

30,000

40,000

50,000

97,2

97,3

97,4

98,1

98,2

98,3

98,4

99,1

99,2

99,3

99,4

00,1


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 cycle

repeats itself

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


Deseasonalizing Demand

[Dt-(p/2) + Dt+(p/2) + Σ 2Di] / 2p for p even

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

Σ 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 + tT

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

Dem

and

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 = 10000/21059

6 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 “season” is then obtained

by averaging all of the factors for a “season”

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

pt+i, 1<i<p, the seasonal factor for season i is

Si = [Sum(j=0 to r-1) Sjp+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 + lTt)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,…,Sp). This is done as

in static forecasting.

�Forecast: Forecast demand for period t+1 using the

general 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 = 19500

F5 = 19500 = F6 = F7 = F8

Observe 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 data

L0 = [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 = αDt+1 + (1-α)Lt

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


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

Observed demand for period 1 = D1 = 8000

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

E1 = F1 - D1 = 22083 - 8000 = 14083

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

L1 = αD1 + (1-α)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

�Obtain 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 = αDt+1 + (1-α)(Lt + Tt)

Tt+1 = β(Lt+1 - Lt) + (1-β)Tt

α = smoothing constant for level

β = 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

Observed demand for period 1 = D1 = 8000

E1 = F1 - D1 = 13564 - 8000 = 5564

Assume α = 0.1, β = 0.2

L1 = αD1 + (1-α)(L0+T0) = (0.1)(8000) + (0.9)(13564) = 13008

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

= 1438

F2 = 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

�Obtain initial estimates of level (L0), trend (T0),

seasonal factors (S1,…,Sp) 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 = α(Dt+1/St+1) + (1-α)(Lt+Tt)

Tt+1 = β(Lt+1 - Lt) + (1-β)Tt

St+p+1 = γ(Dt+1/Lt+1) + (1-γ)St+1

α = smoothing constant for level

β = smoothing constant for trend

γ = 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 α = 0.1, β=0.2, γ=0.1; revise estimates for level and trend

for period 1 and for seasonal factor for period 5

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

T1 = β(L1-L0)+(1-β)T0 = (0.2)(18769-18439)+(0.8)(524) = 485

S5 = γ(D1/L1)+(1-γ)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)[Et2])/n

�Absolute deviation = At = |Et|

�Mean absolute deviation (MAD)

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

σ = 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 = biast / 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?

Objectives of Chapters 7,8 - Al Akhawayn UniversityA.Berrado/MGT5309/MGT5309_ch07.pdf · Objectives...

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