Lecture Demand Fire Casting Jay
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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.
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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
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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)
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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
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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
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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
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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
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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.
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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
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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
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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
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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
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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
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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
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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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