Supply Chain Management-L6a-Demand Forecasting

8/6/2019 Supply Chain Management-L6a-Demand Forecasting

1/44

Demand Forecasting

in a Supply Chain


2/44

Chapter 7

Demand Forecasting

in a Supply Chain

Supply Chain Management

(3rd Edition)

7-2


3/44

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


4/44

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, newproduction introduction

Finance: plant/equipment investment, budgetaryplanning

Personnel: workforce planning, hiring, layoffs

All of these decisions are interrelated


5/44

Characteristics of Forecasts

Forecasts are always wrong. Should include

expected value and measure of error.

Long-term forecasts are less accurate thanshort-term forecasts (forecast horizon is

important)

Aggregate forecasts are more accurate thandisaggregate forecasts


6/44

Forecasting Methods

Qualitative: primarily subjective; rely on judgmentand opinion

Time Series: use historical demand only

Static Adaptive

Causal: use the relationship between demand andsome other factor to develop forecast

Simulation Imitate consumer choices that give rise to demand Can combine time series and causal methods


7/44

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


8/44

Time Series Forecasting

Q uarter D em and D tII, 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 13000IV , 2000 32000

I, 2001 41000

Forecast demand for the

next four quarters.


9/44


0

10,000

20,000

30,000

40,000

50,000

97,

297,

397,

498,

198,2

98,3

98,

499,

199,2

99,3

99,

400,

1


10/44

Forecasting Methods

Static

Adaptive

Moving average Simple exponential smoothing

Holts model (with trend)

W

inters model (w

ith trend and seasonality)


11/44

Basic Approach to

Demand 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 forecastingtechnique

Establish performance and error measures forthe forecast


12/44

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


13/44

Static Methods

Assume a mixed model:

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

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

= forecast in period tfor 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


14/44

Static Methods

Estimating level and trend

Estimating seasonal factors


15/44

Estimating Level and Trend

Before estimating level and trend, demanddata must be deseasonalized

Deseasonalized demand = demand that would

have been observed in the absence ofseasonal fluctuations

Periodicity (p)

the number of periods after which the seasonalcycle repeats itself

for demand at Tahoe Salt (Table 1, Figure 1) p = 4


16/44


(Table 1)Quarter Dem and D tII, 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.


17/44


(Figure 1)

0

10,000

20,000

30,000

40,000

50,000

97,

297,

397,

498,

198,2

98,3

98,

499,

199,2

99,3

99,

400,

1


18/44

Estimating Level and Trend

Before estimating level and trend, demanddata must be deseasonalized

Deseasonalized demand = demand that would

have been observed in the absence ofseasonal fluctuations

Periodicity (p)

the number of periods after which the seasonalcycle repeats itself

for demand at Tahoe Salt (Table 1, Figure 1) p = 4


19/44

Deseasonalizing Demand

[Dt-(p/2) + Dt+(p/2) + 7 2Di] / 2p forp evenDt = (sum is from i = t+1-(p/2) to t+1+(p/2))

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


20/44


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


21/44


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 usingdeseasonalized demand as the dependent variable andperiod as the independent variable (can be done in

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


22/44

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

Deman Dt

Dt-bar


23/44

Estimating Seasonal Factors

Use the previous equation to calculatedeseasonalized demand for each period

St= D

t/ D

t= 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 arecalculated in the same manner


24/44


(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


25/44


The overall seasonal factor for a season is then obtained byaveraging all of the factors for a season

If there are r seasonal cycles, for all periods of the form pt+i,1


26/44

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


27/44

Adaptive Forecasting

The estimates of level, trend, and seasonalityare adjusted after each demand observation

General steps in adaptive forecasting

Moving average Simple exponential smoothing

Trend-corrected exponential smoothing(Holts model)

Trend- and seasonality-corrected exponentialsmoothing (Winters model)


28/44

Basic Formula for


Ft+1 = (Lt+ lT)St+1 = forecast for period t+lin 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


29/44

General Steps in


Initialize: Compute initial estimates of level (L0), trend(T0), and seasonal factors (S1,,Sp). This is done as instatic 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


30/44

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 levelLt = (Dt + Dt-1 + + Dt-N+1) / N

Ft+1 = Lt and Ft+n = LtAfter observing the demand for period t+1, revise the estimates asfollows:

Lt+1 = (Dt+1 + Dt + + Dt-N+2) / NFt+2 = Lt+1


31/44

Moving Average Example

From Tahoe Salt example (Table 7.1)

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


32/44

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 allhistorical data

L0 = [Sum(i=1 to n)Di]/nCurrent forecast for all future periods is equal to the currentestimate of the level and is given as follows:

Ft+1 = Ltand Ft+n = LtAfter observing demand Dt+1, revise the estimate of the level:

Lt+1 = EDt+1 + (1-E)LtLt+1 = Sum(n=0 to t+1)[E(1-E)

nDt+1-n ]


33/44

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 = 8000Forecast 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 = 20675Note that the estimate of level for period 1 is lower than in period 0


34/44

Trend-Corrected Exponential

Smoothing (Holts 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


35/44

Trend-Corrected Exponential

Smoothing (Holts 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 levelF = smoothing constant for trend

Example: Tahoe Salt demand data. Forecast demand for period 1 usingHolts model (trend corrected exponential smoothing)

Using linear regression,

L0 = 12015 (linear intercept)

T0 = 1549 (linear slope)


36/44

Holts 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 = 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)

= 1438

F2 = L1 + T1 = 13008 + 1438 = 14446

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


37/44

Trend- and Seasonality-Corrected

Exponential Smoothing Appropriate when the systematic component of

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

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

Assume periodicity p

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


38/44

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

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

E = smoothing constant for levelF = smoothing constant for trend

K = smoothing constant for seasonal factor

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

Initial estimates of level, trend, and seasonal factors are obtained as inthe static forecasting case


39/44

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 E = 0.1,F=0.2, K=0.1; revise estimates for level and trend forperiod 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) = 485

S5 = 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


40/44

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

W = 1.25MAD


41/44

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- oroverestimates 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


42/44

7-42

Forecasting Demand at Tahoe Salt

Moving average

Simple exponential smoothing

Trend-corrected exponential smoothing Trend- and seasonality-corrected

exponential smoothing


43/44

7-43

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


44/44

7-44

Summary of Learning Objectives

What are the roles of forecasting for anenterprise and a supply chain?

What are the components of a demandforecast?

How is demand forecast given historical datausing time series methodologies?

How is a demand forecast analyzed to estimateforecast error?

Supply Chain Management-L6a-Demand Forecasting

Documents

Transcript of Supply Chain Management-L6a-Demand Forecasting