Demand Forecasting in a Supply Chain

© 2007 Pearson Education

Chapter 7Demand Forecasting

in 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 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


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 ForecastingQuarter Demand Dt

II, 1998 8000III, 1998 13000IV, 1998 23000I, 1999 34000II, 1999 10000III, 1999 18000IV, 1999 23000I, 2000 38000II, 2000 12000III, 2000 13000IV, 2000 32000I, 2001 41000

Forecast demand for thenext four quarters.


Time Series Forecasting

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


Forecasting Methods

Static Adaptive

– Moving average

– Simple exponential smoothing

– Holt’s model (with trend)

– Winter’s model (with trend and seasonality)


Basic Approach toDemand Forecasting

Understand the objectives of forecasting Integrate demand planning and forecasting Identify major factors that influence the demand

forecast 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]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


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


Time Series Forecasting (Table 7.1)

Quarter Demand Dt

II, 1998 8000III, 1998 13000IV, 1998 23000I, 1999 34000II, 1999 10000III, 1999 18000IV, 1999 23000I, 2000 38000II, 2000 12000III, 2000 13000IV, 2000 32000I, 2001 41000

Forecast demand for thenext four quarters.


Time Series Forecasting(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) + 2Di] / 2p for p even

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

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

an

d

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-bar1 8000 18963 0.42 = 8000/189632 13000 19487 0.67 = 13000/194873 23000 20011 1.15 = 23000/200114 34000 20535 1.66 = 34000/205355 10000 21059 0.47 = 10000/210596 18000 21583 0.83 = 18000/215837 23000 22107 1.04 = 23000/221078 38000 22631 1.68 = 38000/226319 12000 23155 0.52 = 12000/23155

10 13000 23679 0.55 = 13000/2367911 32000 24203 1.32 = 32000/2420312 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 forAdaptive Forecasting

Ft+1 = (Lt + lT)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 inAdaptive Forecasting

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 = Dt+1 + (1-)Lt

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


Simple Exponential Smoothing Example

From 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 = 0.1, revised estimate of level for period 1:

L1 = D1 + (1-)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 = Dt+1 + (1-)(Lt + Tt)

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

= smoothing constant for level

= 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 = 13564Observed demand for period 1 = D1 = 8000E1 = F1 - D1 = 13564 - 8000 = 5564Assume = 0.1, = 0.2L1 = D1 + (1-)(L0+T0) = (0.1)(8000) + (0.9)(13564) = 13008T1 = (L1 - L0) + (1-)T0 = (0.2)(13008 - 12015) + (0.8)(1549) = 1438F2 = L1 + T1 = 13008 + 1438 = 14446F5 = 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


Trend- and Seasonality-Corrected Exponential Smoothing (continued)After observing demand for period t+1, revise estimates for level, trend, and

seasonal factors as follows:

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

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

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

= smoothing constant for level

= smoothing constant for trend

= 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


Trend- and Seasonality-Corrected 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 = 0.1, =0.2, =0.1; revise estimates for level and trend for period 1 and for seasonal factor for period 5

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

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

S5 = (D1/L1)+(1-)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

= 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?

Demand Forecasting in a Supply Chain

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