BYDR. JAYASHREE DUBEY

IIFM, BHOPAL

Demand Forecastingin a Supply Chain

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SOME NEWS

American Airlines placed order for 460 aircrafts Bajaj stopped production of Scooters Airtel acquired Zain telecom to foray in African

market Tata targeting export market for Nano Maruti Suzuki to set up its third facility near

Sanand Woodland upto 50% off Tata power to increase its capacity Malvinder Mohan Singh sold Ranbaxy and

entered into Hospitals/ Health insurance etc.

LEARNING OBJECTIVES

Difference between forecasting & predictions The role of forecasting in a supply chain Characteristics of forecasts Pattern of demand Forecasting methods Basic approach to demand forecasting Time series forecasting methods Measures of forecast error Forecast control system Forecasting demand at Tahoe Salt/ Specialty

packaging Forecasting in practice

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DIFFERENCE BETWEEN FORECASTING & PREDICTIONS

Forecasting : Objective, scientific, free from bias, reproducible, error analysis possible

Predictions : Subjective, Intuitive & Bias

ROLE OF FORECASTING IN A SUPPLY CHAIN Input for all strategic and planning decisions in a

supply chain (Operational, Marketing & Financial Decisions)

Long term Planning: Plant expansion & New product

Medium term: Manpower planning, Inventory & Aggregate planning

Short term: Production planning & Scheduling Other Decisions:

Marketing: sales force allocation, promotions, new production introduction

Finance: plant/equipment investment, budgetary planning

Used for both push and pull processes All of these decisions are interrelated

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OBJECTIVES

Reduce Inventory Improve customer service Level Save on transportation and distribution Reduce over all SCM cost Effective promotional activity

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CHARACTERISTICS OF FORECASTS

Forecasts are always wrong. Should include expected value and measure of error. (65% accurate)

Long-term forecasts are less accurate than short-term forecasts (forecast time horizon is important)

Aggregate forecasts are more accurate than disaggregate forecasts

Forecasting error is high at upstream enterprise

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DEMAND PATTERN

Constant (Mature markets) Linear trend (Decreasing/ increasing) (Scooters/

land line/ 3G/ internet penetration) Cyclic & Seasonal Seasonal with growth

Abnormal demand Pattern (Due to external factors)

Transient impulseSudden rise (news of the world)Sudden fall (housing infrastructure/ cars/

blackberry)

FORECASTING METHODS Qualitative (Subjective or intuitive methods): rely on

judgment (opinion poll, Interview, Delphi) (KOL) Methods based on averaging of past data: Moving average

& Exponential smoothening Regression model on historical data: Trend extrapolation

D= a+bt, fitting straight line Causal: use the relationship between demand and some

other factor to develop forecast (what if) (Situational analysis-Marketing plans) (Factors like, rain, GDP, PCI, Govt. policies, Marketing plans)

Time Series: use historical demand only Static Adaptive

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

Replenishment (CPFR) (K- mart)7-9

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 forecasting

technique Establish performance and error measures for

the forecast

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QUALITATIVE

Subjective or intuitive methods rely on judgment of knowledgeable person (Educated Guess)

Methods: opinion poll, Interview, Delphi: KOL, May move towards

divergent view points Delphi story- Saint used to stay in

slopes of Mount Parnassus in Greece

Subjective bias

MOVING AVERAGE & EXPONENTIAL SMOOTHENING K period Moving average: Average of most recent N

periods. Lt = (Dt + Dt-1 + … + Dt-N+1) / N

Forecast lag a trend in increasing or decreasing trend and goes out of phase and shows smoothened demand pattern in cyclic trend . Thus result in error

Impact of no. of data Exponential smoothening: If impact of recent

data is more as compared to old data. Weighted averageLt+1 = Dt+1 + (1-)Lt (is generally between 0.01 to 0.3 or

Difference: MA takes only some data point & ES takes all the data points

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) / NFt+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

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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 = F8Observe demand in period 5 to be D5 = 10000Forecast error in period 5, E5 = F5 - D5 = 19500 - 10000 = 9500Revise estimate of level in period 5:L5 = (D5+D4+D3+D2)/4 = (10000+34000+23000+13000)/4 =

20000F6 = L5 = 20000

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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 = Dt+1 + (1-)Lt

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

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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 = 22083F1 = L0 = 22083Observed demand for period 1 = D1 = 8000Forecast error for period 1, E1, is as follows:E1 = F1 - D1 = 22083 - 8000 = 14083Assuming = 0.1, revised estimate of level for period 1:L1 = D1 + (1-)L0 = (0.1)(8000) + (0.9)(22083) = 20675F2 = L1 = 20675Note that the estimate of level for period 1 is lower than in

period 0

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COMPONENTS OF AN OBSERVATION

Observed demand (O) =Systematic component (S) + Random component (R)

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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

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Forecast demand for thenext four quarters.

TIME SERIES FORECASTING

0

10,000

20,000

30,000

40,000

50,000

97,297,397,498,198,298,398,499,199,299,399,400,1

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FORECASTING METHODS

Static Adaptive

Moving average Simple exponential smoothing Holt’s model (with trend) Winter’s model (with trend and seasonality)

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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

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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 + lL = estimate of level for period 0T = estimate of trendSt = estimate of seasonal factor for period t

Dt = actual demand in period t

Ft = forecast of demand in period t

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STATIC METHODS

Estimating level and trend Estimating seasonal factors

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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

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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

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DESEASONALIZING DEMAND

For the example, p = 4 is evenFor t = 3:D3 = {D1 + D5 + Sum(i=2 to 4) [2Di]}/8= {8000+10000+[(2)(13000)+(2)(23000)+(2)

(34000)]}/8= 19750D4 = {D2 + D6 + Sum(i=3 to 5) [2Di]}/8= {13000+18000+[(2)(23000)+(2)(34000)+(2)

(10000)]/8= 20625

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DESEASONALIZING DEMANDThen include trendDt = L + tT

where Dt = deseasonalized demand in period tL = 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 = 5247-27

TIME SERIES OF DEMAND

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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 periodSt = 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

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ESTIMATING SEASONAL FACTORS (FIG. 7.4)

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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, soS1 = (0.42+0.47+0.52)/3 = 0.47S2 = (0.67+0.83+0.55)/3 = 0.68S3 = (1.15+1.04+1.32)/3 = 1.17S4 = (1.66+1.68+1.66)/3 = 1.67

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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) = 11868F14 = (L+14T)S2 = [18439+(14)(524)](0.68) = 17527F15 = (L+15T)S3 = [18439+(15)(524)](1.17) = 30770F16 = (L+16T)S4 = [18439+(16)(524)](1.67) = 44794

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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)

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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 7-34

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 period7-35

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 trendExample: 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)

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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 + bT0 = aL0 = bIn period t, the forecast for future periods is expressed as follows:Ft+1 = Lt + Tt Ft+n = Lt + nTt

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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

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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

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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 factorExample: 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

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TREND- AND SEASONALITY-CORRECTED EXPONENTIAL SMOOTHING EXAMPLE (CONTINUED)

L0 = 18439 T0 = 524 S1=0.47, S2=0.68, S3=1.17, S4=1.67F1 = (L0 + T0)S1 = (18439+524)(0.47) = 8913The observed demand for period 1 = D1 = 8000Forecast error for period 1 = E1 = F1-D1 = 8913 - 8000 = 913Assume = 0.1, =0.2, =0.1; revise estimates for level and

trend for period 1 and for seasonal factor for period 5L1 = (D1/S1)+(1-)(L0+T0) = (0.1)(8000/0.47)+(0.9)

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

F2 = (L1+T1)S2 = (18769 + 485)(0.68) = 130937-41

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

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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 0biasn = 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

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FORECASTING DEMAND AT TAHOE SALT

Moving average Simple exponential smoothing Trend-corrected exponential smoothing Trend- and seasonality-corrected exponential

smoothing

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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 Range forecasting- Motorola

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