Chapter 7Demand Forecastingin 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. 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 ObservationObserved 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) Winter’s model (with trend and seasonality)

Basic Approach toDemand 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 + lL = estimate of level for period 0T = estimate of trendSt = estimate of seasonal factor for period tDt = actual demand in period tFt = 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 p = 4

Deseasonalizing Demand

[Dt-(p/2) + Dt+(p/2) ]/2p + Di] / p for p evenDt = (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 DemandFor 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 Deseasonalized Demand

Deseasonalizing DemandThen include trendDt = L + tTwhere 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 = 524 Deseasonalized Demand Deseasonalizing DemandThen include trendDt = L + tTwhere 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 = 524 Time Series of Demand Estimating Seasonal Factors

Use the previous equation to calculate deseasonalized demand for each periodSt = Dt / Dt = seasonal factor for period tIn the example, D2 = 18439 + (524)(2) = 19487 D2 = 13000S2 = 13000/19487 = 0.67The seasonal factors for the other periods are calculated in the same manner

Estimating Seasonal Factors Estimating Seasonal Factors 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 = 1.17

S4 = (1.66+1.68+1.66)/3 = 1.67 Estimating the ForecastUsing 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) = 44794Error: 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)[Et2])/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 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 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

Case 1: TahoeSaltIn 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