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# Chapter 7

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### Chapter 7

1. 1.  Chapter 7 Demand Forecasting in a Supply Chain  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 rarely perfect because of randomness.
2. 2.  Beside the average, we also need a measure of variations– Standard deviation.  Forecasts are more accurate for groups of items than for individuals.  Forecast accuracy decreases as time horizon increases.  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)  Example: Tahoe Salt  Tahoe Salt Scattered Graph  Forecasting Methods  Static  Adaptive  Moving average  Simple exponential smoothing  Holt’s model (with trend)
3. 3.  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) 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
4. 4.  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 p = 4  Deseasonalizing Demand [Dt-(p/2) + Dt+(p/2) ]/2p +  Di] / p 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  Time Series Forecasting  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  Deseasonalized Demand  Deseasonalizing Demand Then include trend Dt = L + tT where Dt = deseasonalized demand in period t
5. 5. 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  Deseasonalized Demand  Deseasonalizing Demand 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  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  Estimating Seasonal Factors  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 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
6. 6. 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 Error: difference between predicted value and actual value  Mean Absolute Deviation (MAD)  Mean Square Error (MSE)  Mean Absolute Percentage Error (MAPE)  Tracking Signal (TS)    Measures of Forecast Error  Forecast error = Et = Ft - Dt  Mean squared error (MSE) MSEn = (Sum(t=1 to n)[Et 2 ])/n  Absolute deviation = At = |Et|  Mean absolute deviation (MAD) MADn = (Sum(t=1 to n)[At])/n  = 1.25MAD  = Standard Deviation of forecast  Measures of Forecast Error
7. 7.  Mean absolute percentage error (MAPE) MAPEn = (Sum(t=1 to n)[100|Et/ Dt|])/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  Case 1: TahoeSalt In a very well designed excel work book, repeat the computations explained in this lecture. Also compute MSE, MAD, MPE, and TS for all possible periods