1. Chapter 7 Demand Forecasting in a Supply Chain Supply Chain Management 7-1

2. 7-2 Role of Forecasting in a Supply Chain uThe basis for all strategic and planning decisions in a supply chain uUsed for both push and pull processes uExamples: –Production: scheduling, inventory, aggregate planning –Marketing: sales force allocation, promotions, new production introduction –Finance: plant/equipment investment, budgetary planning –Personnel: workforce planning, hiring, layoffs uAll of these decisions are interrelated

3. 7-3 Characteristics of Forecasts uForecasts are always wrong. Should include expected value and measure of error. uLong-term forecasts are less accurate than short- term forecasts (forecast horizon is important) uAggregate forecasts are more accurate than disaggregate forecasts

4. 7-4 Forecasting Methods uQualitative: primarily subjective; rely on judgment and opinion uTime Series: use historical demand only –Static –Adaptive uCausal: use the relationship between demand and some other factor to develop forecast uSimulation –Imitate consumer choices that give rise to demand –Can combine time series and causal methods

5. 7-5 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

6. 7-6 Time Series Forecasting Forecast demand for the next four quarters.

7. 7-7 Time Series Forecasting

8. 7-8 Time Series Forecasting Methods uGoal is to predict systematic component of demand –Multiplicative: (level)(trend)(seasonal factor) –Additive: level + trend + seasonal factor –Mixed: (level + trend)(seasonal factor) uStatic methods uAdaptive forecasting –Moving average –Simple exponential smoothing –Holt’s model (with trend) –Winter’s model (with trend and seasonality)

9. 7-9 Static Methods uAssume 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

10. 7-10 Static Methods uEstimating level and trend uEstimating seasonal factors

11. 7-11 Time Series Forecasting Forecast demand for the next four quarters.

12. 7-12 Time Series Forecasting

13. 7-13 Estimating Level and Trend uDeseasonalize the Demand –Deseasonalized demand: Demand that would have been observed in the absence of seasonal fluctuations uPeriodicity (p) –the number of periods after which the seasonal cycle repeats itself –In our example: p = 4

14. 7-14 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-1)/2] to t+[(p-1)/2]

15. 7-15 Deseasonalizing Demand For the example, p = 4 is even For t = 3: D3 = (D1 + D5 + 2D2+2D3+2D4)/8 = {8000+10000+[(2)(13000)+(2)(23000)+(2)(34000)]}/8 = 19750 D4 = {D2 + D6 + 2D3+2D4+2D5}/8 = {13000+18000+[(2)(23000)+(2)(34000)+(2)(10000)]/8 = 20625

16. 7-16 Deseasonalized Demand

17. 7-17 Time Series of Demand

18. 7-18 Deseasonalizing Demand Then include trend D t = L + tT 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

19. 7-19 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

20. 7-20 Estimating Seasonal Factors

21. 7-21 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

22. 7-22 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

23. 7-23 Adaptive Forecasting uThe estimates of level, trend, and seasonality are adjusted after each demand observation uMoving average uSimple exponential smoothing uTrend-corrected exponential smoothing (Holt’s model) uTrend- and seasonality-corrected exponential smoothing (Winter’s model)

24. 7-24 Basic Formula for Adaptive Forecasting F t+1 = (L t + lT 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 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

25. 7-25 General Steps in Adaptive Forecasting uInitialize: Compute initial estimates of level (L 0 ), trend (T 0 ), and seasonal factors (S 1,…,S p ). This is done as in static forecasting. uForecast: Forecast demand for period t+1 using the general equation uEstimate error: Compute error E t+1 = F t+1 - D t+1 uModify 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 uRepeat steps 2, 3, and 4 for each subsequent period

26. 7-26 Moving Average uUsed when demand has no observable trend or seasonality uSystematic component of demand = level uThe level in period t is the average demand over the last N periods (the N-period moving average) uCurrent 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

27. 7-27 Moving Average Example Ex: 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

28. 7-28 Simple Exponential Smoothing uUsed when demand has no observable trend or seasonality uSystematic component of demand = level uInitial 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 D t+1, revise the estimate of the level: L t+1 =  D t+1 + (1-  )L t

29. 7-29 Simple Exponential Smoothing Example Ex: 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

30. 7-30 Trend-Corrected Exponential Smoothing (Holt’s Model) uAppropriate when the demand is assumed to have a level and trend in the systematic component of demand but no seasonality uObtain initial estimate of level and trend by running a linear regression of the following form: D t = b + at L 0 = b T 0 = a 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

31. 7-31 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: 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)

32. 7-32 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

33. 7-33 Trend- and Seasonality-Corrected Exponential Smoothing uAppropriate when the systematic component of demand is assumed to have a level, trend, and seasonal factor uSystematic component = (level+trend)(seasonal factor) uAssume periodicity p uObtain initial estimates of level (L 0 ), trend (T 0 ), seasonal factors (S 1,…,S p ) using procedure for static forecasting uIn 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

34. 7-34 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

35. 7-35 Trend- and Seasonality-Corrected Exponential Smoothing Example Example: 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: 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

36. 7-36 Measures of Forecast Error uForecast error = E t = F t - D t uMean squared error (MSE) MSE n = (Sum (t=1 to n) [E t 2 ])/n uAbsolute deviation = A t = |E t | uMean absolute deviation (MAD) MAD n = (Sum (t=1 to n) [A t ])/n uMean absolute percentage error (MAPE) MAPE n = 100*(Sum (t=1 to n) |E t / D t |)/n uBias = Sum (t=1 to n) [E t ] Shows whether the forecast consistently under- or overestimates demand; should fluctuate around 0 uTracking Signal = Bias / MAD Should be within the range of +6. Otherwise, possibly use a new forecasting method

37. 7-37 Forecasting in Practice uCollaborate in building forecasts uThe value of data depends on where you are in the supply chain uBe sure to distinguish between demand and sales