Demand Forecasting in a Supply Chain
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Demand Forecasting in a Supply Chain

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Demand Forecasting in a Supply Chain Demand Forecasting in a Supply Chain Presentation Transcript

  • Chapter 7 Demand Forecasting in a Supply Chain Supply Chain Management (3rd Edition) 7-
  • 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 Forecasting Forecast demand for the next four quarters.
  • Time Series Forecasting
  • Forecasting Methods
    • Static
    • Adaptive
      • Moving average
      • Simple exponential smoothing
      • Holt’s model ( with trend )
      • Winter’s model ( with trend and seasonality )
  • 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
  • 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)
    • F t+l = [L + ( t + l )T] S t+l
    • = forecast in period t for demand in period t + l
    • L = estimate of level for period 0
    • T = estimate of trend
    • S t = estimate of seasonal factor for period t
    • D t = actual demand in period t
    • F t = 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) Forecast demand for the next four quarters.
  • Time Series Forecasting (Figure 7.1)
  • 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
    • [D t-(p/2) + D t+(p/2) +  2D i ] / 2p for p even
    • D t = (sum is from i = t+1-(p/2) to t+1+(p/2))
    •  D i / p for p odd
    • (sum is from i = t-(p/2) to t+(p/2)), p/2 truncated to lower integer
  • Deseasonalizing Demand
    • 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
  • Deseasonalizing Demand
    • Then include trend
    • D t = L + t T
    • where D t = 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)
  • Estimating Seasonal Factors
    • Use the previous equation to calculate deseasonalized demand for each period
    • S t = D t / D t = seasonal factor for period t
    • In the example,
    • D 2 = 18439 + (524)(2) = 19487 D 2 = 13000
    • S 2 = 13000/19487 = 0.67
    • The seasonal factors for the other periods are calculated in the same manner
  • Estimating Seasonal Factors (Fig. 7.4)
  • Estimating Seasonal Factors
    • The 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
    • S i = [Sum (j=0 to r-1) S jp+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 Adaptive Forecasting
    • F t+1 = (L t + l T)S t+1 = forecast for period t+l in period t
    • L t = Estimate of level at the end of period t
    • T t = Estimate of trend at the end of period t
    • S t = Estimate of seasonal factor for period t
    • F t = Forecast of demand for period t (made period t -1 or earlier)
    • D t = Actual demand observed in period t
    • E t = Forecast error in period t
    • A t = Absolute deviation for period t = |E t |
    • MAD = Mean Absolute Deviation = average value of A t
  • General Steps in Adaptive Forecasting
    • Initialize: Compute initial estimates of level (L 0 ), trend (T 0 ), and seasonal factors (S 1 ,…,S p ). This is done as in static forecasting.
    • Forecast: Forecast demand for period t+ 1 using the general equation
    • Estimate error: Compute error E t+1 = F t+1 - D t+1
    • Modify estimates: Modify the estimates of level (L t +1 ), trend (T t +1 ), and seasonal factor (S t+p +1 ), given the error E t +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
    • L t = (D t + D t-1 + … + D t-N+1 ) / N
    • F t+1 = L t and F t+n = L t
    • After observing the demand for period t +1, revise the estimates as follows:
    • L t+1 = (D t+1 + D t + … + D t-N+2 ) / N
    • F t+2 = L t+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, L 0 , assumed to be the average of all historical data
    • L 0 = [Sum( i=1 to n )D i ]/n
    • Current forecast for all future periods is equal to the current estimate of the level and is given as follows:
    • F t+1 = L t and F t+n = L t
    • After observing demand Dt+1, revise the estimate of the level:
    • L t+1 =  D t+1 + (1-  )L t
    • L t+1 = Sum (n=0 to t+1) [  (1-  ) n D t+1-n ]
  • Simple Exponential Smoothing Example
    • From Tahoe Salt data, forecast demand for period 1 using exponential smoothing
    • L 0 = average of all 12 periods of data
    • = Sum (i=1 to 12) [D i ]/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:
    • D t = at + b
    • T 0 = a
    • L 0 = b
    • In period t, the forecast for future periods is expressed as follows:
    • F t+1 = L t + T t
    • F t+n = L t + nT t
  • Trend-Corrected Exponential Smoothing (Holt’s Model)
    • After observing demand for period t, revise the estimates for level and trend as follows:
    • L t+1 =  D t+1 + (1-  )(L t + T t )
    • T t+1 =  (L t+1 - L t ) + (1-  )T t
    •  = 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,
    • L 0 = 12015 (linear intercept)
    • T 0 = 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  = 0.1,  = 0.2
    • L1 =  D1 + (1-  )(L0+T0) = (0.1)(8000) + (0.9)(13564) = 13008
    • T1 =  (L1 - L0) + (1-  )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 (L 0 ), trend (T 0 ), seasonal factors (S 1 ,…,S p ) using procedure for static forecasting
    • In period t, the forecast for future periods is given by:
    • F t+1 = (L t +T t )(S t+1 ) and F t+n = (L t + nT t )S t+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:
    • L t+1 =  (D t+1 /S t+1 ) + (1-  )(L t +T t )
    • T t+1 =  (L t+1 - L t ) + (1-  )T t
    • S t+p+1 =  (D t+1 /L t+1 ) + (1-  )S t+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)
    • L 0 = 18439 T 0 = 524 S 1 =0.47, S 2 =0.68, S 3 =1.17, S 4 =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 = E t = F t - D t
    • Mean squared error (MSE)
    • MSE n = (Sum (t=1 to n) [E t 2 ])/n
    • Absolute deviation = A t = |E t |
    • Mean absolute deviation (MAD)
    • MAD n = (Sum (t=1 to n) [A t ])/n
    •  = 1.25MAD
  • Measures of Forecast Error
    • Mean absolute percentage error (MAPE)
    • MAPE n = (Sum (t=1 to n) [|E t / D t |100])/n
    • Bias
    • Shows whether the forecast consistently under- or overestimates demand; should fluctuate around 0
    • bias n = Sum (t=1 to n) [E t ]
    • Tracking signal
    • Should be within the range of + 6
    • Otherwise, possibly use a new forecasting method
    • TS t = bias / MAD t
  • 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?