Demand Forecasting in a Supply Chain

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  • Demand Forecasting in a Supply Chain

    1. 1. Chapter 7 Demand Forecasting in a Supply Chain Supply Chain Management (3rd Edition) 7-
    2. 2. Outline <ul><li>The role of forecasting in a supply chain </li></ul><ul><li>Characteristics of forecasts </li></ul><ul><li>Components of forecasts and forecasting methods </li></ul><ul><li>Basic approach to demand forecasting </li></ul><ul><li>Time series forecasting methods </li></ul><ul><li>Measures of forecast error </li></ul><ul><li>Forecasting demand at Tahoe Salt </li></ul><ul><li>Forecasting in practice </li></ul>
    3. 3. Role of Forecasting in a Supply Chain <ul><li>The basis for all strategic and planning decisions in a supply chain </li></ul><ul><li>Used for both push and pull processes </li></ul><ul><li>Examples: </li></ul><ul><ul><li>Production: scheduling, inventory, aggregate planning </li></ul></ul><ul><ul><li>Marketing: sales force allocation, promotions, new production introduction </li></ul></ul><ul><ul><li>Finance: plant/equipment investment, budgetary planning </li></ul></ul><ul><ul><li>Personnel: workforce planning, hiring, layoffs </li></ul></ul><ul><li>All of these decisions are interrelated </li></ul>
    4. 4. Characteristics of Forecasts <ul><li>Forecasts are always wrong. Should include expected value and measure of error. </li></ul><ul><li>Long-term forecasts are less accurate than short-term forecasts (forecast horizon is important) </li></ul><ul><li>Aggregate forecasts are more accurate than disaggregate forecasts </li></ul>
    5. 5. Forecasting Methods <ul><li>Qualitative: primarily subjective; rely on judgment and opinion </li></ul><ul><li>Time Series: use historical demand only </li></ul><ul><ul><li>Static </li></ul></ul><ul><ul><li>Adaptive </li></ul></ul><ul><li>Causal: use the relationship between demand and some other factor to develop forecast </li></ul><ul><li>Simulation </li></ul><ul><ul><li>Imitate consumer choices that give rise to demand </li></ul></ul><ul><ul><li>Can combine time series and causal methods </li></ul></ul>
    6. 6. Components of an Observation <ul><li>Observed demand (O) = </li></ul><ul><li>Systematic component (S) + Random component (R) </li></ul>Level (current deseasonalized demand) Trend (growth or decline in demand) Seasonality (predictable seasonal fluctuation) <ul><li>Systematic component: Expected value of demand </li></ul><ul><li>Random component: The part of the forecast that deviates from the systematic component </li></ul><ul><li>Forecast error: difference between forecast and actual demand </li></ul>
    7. 7. Time Series Forecasting Forecast demand for the next four quarters.
    8. 8. Time Series Forecasting
    9. 9. Forecasting Methods <ul><li>Static </li></ul><ul><li>Adaptive </li></ul><ul><ul><li>Moving average </li></ul></ul><ul><ul><li>Simple exponential smoothing </li></ul></ul><ul><ul><li>Holt’s model ( with trend ) </li></ul></ul><ul><ul><li>Winter’s model ( with trend and seasonality ) </li></ul></ul>
    10. 10. Basic Approach to Demand Forecasting <ul><li>Understand the objectives of forecasting </li></ul><ul><li>Integrate demand planning and forecasting </li></ul><ul><li>Identify major factors that influence the demand forecast </li></ul><ul><li>Understand and identify customer segments </li></ul><ul><li>Determine the appropriate forecasting technique </li></ul><ul><li>Establish performance and error measures for the forecast </li></ul>
    11. 11. Time Series Forecasting Methods <ul><li>Goal is to predict systematic component of demand </li></ul><ul><ul><li>Multiplicative: (level)(trend)(seasonal factor) </li></ul></ul><ul><ul><li>Additive: level + trend + seasonal factor </li></ul></ul><ul><ul><li>Mixed: (level + trend)(seasonal factor) </li></ul></ul><ul><li>Static methods </li></ul><ul><li>Adaptive forecasting </li></ul>
    12. 12. Static Methods <ul><li>Assume a mixed model: </li></ul><ul><li>Systematic component = (level + trend)(seasonal factor) </li></ul><ul><li>F t+l = [L + ( t + l )T] S t+l </li></ul><ul><li>= forecast in period t for demand in period t + l </li></ul><ul><li>L = estimate of level for period 0 </li></ul><ul><li>T = estimate of trend </li></ul><ul><li>S t = estimate of seasonal factor for period t </li></ul><ul><li>D t = actual demand in period t </li></ul><ul><li>F t = forecast of demand in period t </li></ul>
    13. 13. Static Methods <ul><li>Estimating level and trend </li></ul><ul><li>Estimating seasonal factors </li></ul>
    14. 14. Estimating Level and Trend <ul><li>Before estimating level and trend, demand data must be deseasonalized </li></ul><ul><li>Deseasonalized demand = demand that would have been observed in the absence of seasonal fluctuations </li></ul><ul><li>Periodicity ( p ) </li></ul><ul><ul><li>the number of periods after which the seasonal cycle repeats itself </li></ul></ul><ul><ul><li>for demand at Tahoe Salt (Table 7.1, Figure 7.1) p = 4 </li></ul></ul>
    15. 15. Time Series Forecasting (Table 7.1) Forecast demand for the next four quarters.
    16. 16. Time Series Forecasting (Figure 7.1)
    17. 17. Estimating Level and Trend <ul><li>Before estimating level and trend, demand data must be deseasonalized </li></ul><ul><li>Deseasonalized demand = demand that would have been observed in the absence of seasonal fluctuations </li></ul><ul><li>Periodicity ( p ) </li></ul><ul><ul><li>the number of periods after which the seasonal cycle repeats itself </li></ul></ul><ul><ul><li>for demand at Tahoe Salt (Table 7.1, Figure 7.1) p = 4 </li></ul></ul>
    18. 18. Deseasonalizing Demand <ul><li> [D t-(p/2) + D t+(p/2) +  2D i ] / 2p for p even </li></ul><ul><li>D t = (sum is from i = t+1-(p/2) to t+1+(p/2)) </li></ul><ul><li>  D i / p for p odd </li></ul><ul><li> (sum is from i = t-(p/2) to t+(p/2)), p/2 truncated to lower integer </li></ul>
    19. 19. Deseasonalizing Demand <ul><li>For the example, p = 4 is even </li></ul><ul><li>For t = 3: </li></ul><ul><li>D3 = {D1 + D5 + Sum(i=2 to 4) [2Di]}/8 </li></ul><ul><li>= {8000+10000+[(2)(13000)+(2)(23000)+(2)(34000)]}/8 </li></ul><ul><li>= 19750 </li></ul><ul><li>D4 = {D2 + D6 + Sum(i=3 to 5) [2Di]}/8 </li></ul><ul><li>= {13000+18000+[(2)(23000)+(2)(34000)+(2)(10000)]/8 </li></ul><ul><li>= 20625 </li></ul>
    20. 20. Deseasonalizing Demand <ul><li>Then include trend </li></ul><ul><li>D t = L + t T </li></ul><ul><li>where D t = deseasonalized demand in period t </li></ul><ul><li>L = level (deseasonalized demand at period 0) </li></ul><ul><li>T = trend (rate of growth of deseasonalized demand) </li></ul><ul><li>Trend is determined by linear regression using deseasonalized demand as the dependent variable and period as the independent variable (can be done in Excel) </li></ul><ul><li>In the example, L = 18,439 and T = 524 </li></ul>
    21. 21. Time Series of Demand (Figure 7.3)
    22. 22. Estimating Seasonal Factors <ul><li>Use the previous equation to calculate deseasonalized demand for each period </li></ul><ul><li>S t = D t / D t = seasonal factor for period t </li></ul><ul><li>In the example, </li></ul><ul><li>D 2 = 18439 + (524)(2) = 19487 D 2 = 13000 </li></ul><ul><li>S 2 = 13000/19487 = 0.67 </li></ul><ul><li>The seasonal factors for the other periods are calculated in the same manner </li></ul>
    23. 23. Estimating Seasonal Factors (Fig. 7.4)
    24. 24. Estimating Seasonal Factors <ul><li>The overall seasonal factor for a “season” is then obtained by averaging all of the factors for a “season” </li></ul><ul><li>If there are r seasonal cycles, for all periods of the form pt+i , 1 < i<p , the seasonal factor for season i is </li></ul><ul><li>S i = [Sum (j=0 to r-1) S jp+i ]/ r </li></ul><ul><li>In the example, there are 3 seasonal cycles in the data and p=4, so </li></ul><ul><li>S1 = (0.42+0.47+0.52)/3 = 0.47 </li></ul><ul><li>S2 = (0.67+0.83+0.55)/3 = 0.68 </li></ul><ul><li>S3 = (1.15+1.04+1.32)/3 = 1.17 </li></ul><ul><li>S4 = (1.66+1.68+1.66)/3 = 1.67 </li></ul>
    25. 25. Estimating the Forecast <ul><li>Using the original equation, we can forecast the next four periods of demand: </li></ul><ul><li>F13 = (L+13T)S1 = [18439+(13)(524)](0.47) = 11868 </li></ul><ul><li>F14 = (L+14T)S2 = [18439+(14)(524)](0.68) = 17527 </li></ul><ul><li>F15 = (L+15T)S3 = [18439+(15)(524)](1.17) = 30770 </li></ul><ul><li>F16 = (L+16T)S4 = [18439+(16)(524)](1.67) = 44794 </li></ul>
    26. 26. Adaptive Forecasting <ul><li>The estimates of level, trend, and seasonality are adjusted after each demand observation </li></ul><ul><li>General steps in adaptive forecasting </li></ul><ul><li>Moving average </li></ul><ul><li>Simple exponential smoothing </li></ul><ul><li>Trend-corrected exponential smoothing (Holt’s model) </li></ul><ul><li>Trend- and seasonality-corrected exponential smoothing (Winter’s model) </li></ul>
    27. 27. Basic Formula for Adaptive Forecasting <ul><li>F t+1 = (L t + l T)S t+1 = forecast for period t+l in period t </li></ul><ul><li>L t = Estimate of level at the end of period t </li></ul><ul><li>T t = Estimate of trend at the end of period t </li></ul><ul><li>S t = Estimate of seasonal factor for period t </li></ul><ul><li>F t = Forecast of demand for period t (made period t -1 or earlier) </li></ul><ul><li>D t = Actual demand observed in period t </li></ul><ul><li>E t = Forecast error in period t </li></ul><ul><li>A t = Absolute deviation for period t = |E t | </li></ul><ul><li>MAD = Mean Absolute Deviation = average value of A t </li></ul>
    28. 28. General Steps in Adaptive Forecasting <ul><li>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. </li></ul><ul><li>Forecast: Forecast demand for period t+ 1 using the general equation </li></ul><ul><li>Estimate error: Compute error E t+1 = F t+1 - D t+1 </li></ul><ul><li>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 </li></ul><ul><li>Repeat steps 2, 3, and 4 for each subsequent period </li></ul>
    29. 29. Moving Average <ul><li>Used when demand has no observable trend or seasonality </li></ul><ul><li>Systematic component of demand = level </li></ul><ul><li>The level in period t is the average demand over the last N periods (the N-period moving average) </li></ul><ul><li>Current forecast for all future periods is the same and is based on the current estimate of the level </li></ul><ul><li>L t = (D t + D t-1 + … + D t-N+1 ) / N </li></ul><ul><li>F t+1 = L t and F t+n = L t </li></ul><ul><li>After observing the demand for period t +1, revise the estimates as follows: </li></ul><ul><li>L t+1 = (D t+1 + D t + … + D t-N+2 ) / N </li></ul><ul><li>F t+2 = L t+1 </li></ul>
    30. 30. Moving Average Example <ul><li>From Tahoe Salt example (Table 7.1) </li></ul><ul><li>At the end of period 4, what is the forecast demand for periods 5 through 8 using a 4-period moving average? </li></ul><ul><li>L4 = (D4+D3+D2+D1)/4 = (34000+23000+13000+8000)/4 = 19500 </li></ul><ul><li>F5 = 19500 = F6 = F7 = F8 </li></ul><ul><li>Observe demand in period 5 to be D5 = 10000 </li></ul><ul><li>Forecast error in period 5, E5 = F5 - D5 = 19500 - 10000 = 9500 </li></ul><ul><li>Revise estimate of level in period 5: </li></ul><ul><li>L5 = (D5+D4+D3+D2)/4 = (10000+34000+23000+13000)/4 = 20000 </li></ul><ul><li>F6 = L5 = 20000 </li></ul>
    31. 31. Simple Exponential Smoothing <ul><li>Used when demand has no observable trend or seasonality </li></ul><ul><li>Systematic component of demand = level </li></ul><ul><li>Initial estimate of level, L 0 , assumed to be the average of all historical data </li></ul><ul><li>L 0 = [Sum( i=1 to n )D i ]/n </li></ul><ul><li>Current forecast for all future periods is equal to the current estimate of the level and is given as follows: </li></ul><ul><li>F t+1 = L t and F t+n = L t </li></ul><ul><li>After observing demand Dt+1, revise the estimate of the level: </li></ul><ul><li>L t+1 =  D t+1 + (1-  )L t </li></ul><ul><li>L t+1 = Sum (n=0 to t+1) [  (1-  ) n D t+1-n ] </li></ul>
    32. 32. Simple Exponential Smoothing Example <ul><li>From Tahoe Salt data, forecast demand for period 1 using exponential smoothing </li></ul><ul><li>L 0 = average of all 12 periods of data </li></ul><ul><li>= Sum (i=1 to 12) [D i ]/12 = 22083 </li></ul><ul><li>F1 = L0 = 22083 </li></ul><ul><li>Observed demand for period 1 = D1 = 8000 </li></ul><ul><li>Forecast error for period 1, E1, is as follows: </li></ul><ul><li>E1 = F1 - D1 = 22083 - 8000 = 14083 </li></ul><ul><li>Assuming  = 0.1, revised estimate of level for period 1: </li></ul><ul><li>L1 =  D1 + (1-  )L0 = (0.1)(8000) + (0.9)(22083) = 20675 </li></ul><ul><li>F2 = L1 = 20675 </li></ul><ul><li>Note that the estimate of level for period 1 is lower than in period 0 </li></ul>
    33. 33. Trend-Corrected Exponential Smoothing (Holt’s Model) <ul><li>Appropriate when the demand is assumed to have a level and trend in the systematic component of demand but no seasonality </li></ul><ul><li>Obtain initial estimate of level and trend by running a linear regression of the following form: </li></ul><ul><li>D t = at + b </li></ul><ul><li>T 0 = a </li></ul><ul><li>L 0 = b </li></ul><ul><li>In period t, the forecast for future periods is expressed as follows: </li></ul><ul><li>F t+1 = L t + T t </li></ul><ul><li>F t+n = L t + nT t </li></ul>
    34. 34. Trend-Corrected Exponential Smoothing (Holt’s Model) <ul><li>After observing demand for period t, revise the estimates for level and trend as follows: </li></ul><ul><li>L t+1 =  D t+1 + (1-  )(L t + T t ) </li></ul><ul><li>T t+1 =  (L t+1 - L t ) + (1-  )T t </li></ul><ul><li> = smoothing constant for level </li></ul><ul><li> = smoothing constant for trend </li></ul><ul><li>Example: Tahoe Salt demand data. Forecast demand for period 1 using Holt’s model (trend corrected exponential smoothing) </li></ul><ul><li>Using linear regression, </li></ul><ul><li>L 0 = 12015 (linear intercept) </li></ul><ul><li>T 0 = 1549 (linear slope) </li></ul>
    35. 35. Holt’s Model Example (continued) <ul><li>Forecast for period 1: </li></ul><ul><li>F1 = L0 + T0 = 12015 + 1549 = 13564 </li></ul><ul><li>Observed demand for period 1 = D1 = 8000 </li></ul><ul><li>E1 = F1 - D1 = 13564 - 8000 = 5564 </li></ul><ul><li>Assume  = 0.1,  = 0.2 </li></ul><ul><li>L1 =  D1 + (1-  )(L0+T0) = (0.1)(8000) + (0.9)(13564) = 13008 </li></ul><ul><li>T1 =  (L1 - L0) + (1-  )T0 = (0.2)(13008 - 12015) + (0.8)(1549) </li></ul><ul><li>= 1438 </li></ul><ul><li>F2 = L1 + T1 = 13008 + 1438 = 14446 </li></ul><ul><li>F5 = L1 + 4T1 = 13008 + (4)(1438) = 18760 </li></ul>
    36. 36. Trend- and Seasonality-Corrected Exponential Smoothing <ul><li>Appropriate when the systematic component of demand is assumed to have a level, trend, and seasonal factor </li></ul><ul><li>Systematic component = (level+trend)(seasonal factor) </li></ul><ul><li>Assume periodicity p </li></ul><ul><li>Obtain initial estimates of level (L 0 ), trend (T 0 ), seasonal factors (S 1 ,…,S p ) using procedure for static forecasting </li></ul><ul><li>In period t, the forecast for future periods is given by: </li></ul><ul><li>F t+1 = (L t +T t )(S t+1 ) and F t+n = (L t + nT t )S t+n </li></ul>
    37. 37. Trend- and Seasonality-Corrected Exponential Smoothing (continued) <ul><li>After observing demand for period t+1, revise estimates for level, trend, and seasonal factors as follows: </li></ul><ul><li>L t+1 =  (D t+1 /S t+1 ) + (1-  )(L t +T t ) </li></ul><ul><li>T t+1 =  (L t+1 - L t ) + (1-  )T t </li></ul><ul><li>S t+p+1 =  (D t+1 /L t+1 ) + (1-  )S t+1 </li></ul><ul><li> = smoothing constant for level </li></ul><ul><li> = smoothing constant for trend </li></ul><ul><li> = smoothing constant for seasonal factor </li></ul><ul><li>Example: Tahoe Salt data. Forecast demand for period 1 using Winter’s model. </li></ul><ul><li>Initial estimates of level, trend, and seasonal factors are obtained as in the static forecasting case </li></ul>
    38. 38. Trend- and Seasonality-Corrected Exponential Smoothing Example (continued) <ul><li>L 0 = 18439 T 0 = 524 S 1 =0.47, S 2 =0.68, S 3 =1.17, S 4 =1.67 </li></ul><ul><li>F1 = (L0 + T0)S1 = (18439+524)(0.47) = 8913 </li></ul><ul><li>The observed demand for period 1 = D1 = 8000 </li></ul><ul><li>Forecast error for period 1 = E1 = F1-D1 = 8913 - 8000 = 913 </li></ul><ul><li>Assume  = 0.1,  =0.2,  =0.1; revise estimates for level and trend for period 1 and for seasonal factor for period 5 </li></ul><ul><li>L1 =  (D1/S1)+(1-  )(L0+T0) = (0.1)(8000/0.47)+(0.9)(18439+524)=18769 </li></ul><ul><li>T1 =  (L1-L0)+(1-  )T0 = (0.2)(18769-18439)+(0.8)(524) = 485 </li></ul><ul><li>S5 =  (D1/L1)+(1-  )S1 = (0.1)(8000/18769)+(0.9)(0.47) = 0.47 </li></ul><ul><li>F2 = (L1+T1)S2 = (18769 + 485)(0.68) = 13093 </li></ul>
    39. 39. Measures of Forecast Error <ul><li>Forecast error = E t = F t - D t </li></ul><ul><li>Mean squared error (MSE) </li></ul><ul><li>MSE n = (Sum (t=1 to n) [E t 2 ])/n </li></ul><ul><li>Absolute deviation = A t = |E t | </li></ul><ul><li>Mean absolute deviation (MAD) </li></ul><ul><li>MAD n = (Sum (t=1 to n) [A t ])/n </li></ul><ul><li> = 1.25MAD </li></ul>
    40. 40. Measures of Forecast Error <ul><li>Mean absolute percentage error (MAPE) </li></ul><ul><li>MAPE n = (Sum (t=1 to n) [|E t / D t |100])/n </li></ul><ul><li>Bias </li></ul><ul><li>Shows whether the forecast consistently under- or overestimates demand; should fluctuate around 0 </li></ul><ul><li>bias n = Sum (t=1 to n) [E t ] </li></ul><ul><li>Tracking signal </li></ul><ul><li>Should be within the range of + 6 </li></ul><ul><li>Otherwise, possibly use a new forecasting method </li></ul><ul><li>TS t = bias / MAD t </li></ul>
    41. 41. Forecasting Demand at Tahoe Salt <ul><li>Moving average </li></ul><ul><li>Simple exponential smoothing </li></ul><ul><li>Trend-corrected exponential smoothing </li></ul><ul><li>Trend- and seasonality-corrected exponential smoothing </li></ul>
    42. 42. Forecasting in Practice <ul><li>Collaborate in building forecasts </li></ul><ul><li>The value of data depends on where you are in the supply chain </li></ul><ul><li>Be sure to distinguish between demand and sales </li></ul>
    43. 43. Summary of Learning Objectives <ul><li>What are the roles of forecasting for an enterprise and a supply chain? </li></ul><ul><li>What are the components of a demand forecast? </li></ul><ul><li>How is demand forecast given historical data using time series methodologies? </li></ul><ul><li>How is a demand forecast analyzed to estimate forecast error? </li></ul>

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