Outline. Role of Forecasting. Characteristics of Forecasts. Logistics and Supply Chain Management. Demand Forecasting

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1 Logistics and Supply Chain Management Demand Forecasting 1 Outline The role of forecasting in a supply chain Characteristics ti of forecasts Components of forecasts and forecasting methods Basic approach to demand forecasting Time series forecasting methods Measures of forecast error Chopra and Meindl (2006) Supply Chain Management: Strategy, Planning and Operation. Prentice Hall Pearson Education Amir Samimi Civil Engineering Department, Sharif University of Technology Role of Forecasting Characteristics of Forecasts 2 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 3 Forecasts are always wrong. Should include expected value and measure of error. Long-term forecasts are less accurate than shortterm forecasts (forecast horizon is important) Aggregate forecasts are more accurate than disaggregate forecasts Bullwhip Effect: The farther up the supply chain a company is, the greater is the distortion of information it receives. 1

2 Factors Related to Demand Basic Steps to Demand Forecasting 4 Past demand Lead dtime of product Planned advertising or marketing efforts State of the economy Planned price discounts Actions that competitors have taken 5 Understand the objectives of forecasting Integrate t demand d planning and dforecasting Identify major factors that influence demand Identify customer segments Determine the appropriate forecasting technique Establish performance and error measures for the forecast Forecasting Methods Components of an Observation 6 1. Qualitative: primarily subjective; rely on judgment and opinion 2. Time Series: use historical demand only Static Adaptive 3. Causal: use the relationship between demand and some other factor to develop forecast 4. Simulation Imitate consumer choices that give rise to demand Can combine time series and causal methods 7 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 2

3 Time Series Forecasting Time Series Forecasting 8 Forecast demand for the next four quarters. 9 Quarter Demand D t II, III, IV, I, II, III, IV, I, II, III, IV, I, Forecasting Methods 50,000 40,000 30,000 20,000 10, ,2 97,3 97,4 98,1 98,2 98,3 98,4 99,1 99,2 99,3 99,4 00,1 Time Series Forecasting Methods 10 Static Adaptive Moving average Simple exponential smoothing Holt s model (with trend) Winter s model (with trend and seasonality) 11 Goal is to predict systematic component of demand Multiplicative: li (level)(trend)(seasonal l)(t l factor) Additive: level + trend + seasonal factor Mixed: (level + trend)(seasonal factor) Static methods Adaptive forecasting 3

4 Static Methods Static Methods 12 Assume a mixed model: Systematic ti component = (level l + trend)(seasonal factor) 13 Estimating level and trend Eti Estimating seasonal lfactors F t+l = [L + (t + l)t]s t+l = forecast in period t for demand in period t + l L = estimate t of flevel lfor period d0 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 Estimating Level and Trend Example: Tahoe Salt 14 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 =

5 Deseasonalizing Demand Deseasonalizing Demand For the example, p = 4 is even D3 = {D1 + D5 + Sum(i=2 to 4) [2Di]}/8 = { [(2)(13000)+(2)(23000)+(2)(34000)]}/8 = D4 = {D2 + D6 + Sum(i=3 to 5) [2Di]}/8 = { [(2)(23000)+(2)(34000)+(2)(10000)]/8 = Deseasonalizing Demand Demand for Tahoe Salt Then include trend: D t = L + tt D t = deseasonalized ddemand din period dt L = level (deseasonalized demand at period 0) T = trend (rate of growth of deseasonalized demand) Trend is determined by linear regression: Dependent variable: deseasonalized demand Independent variable: period In the example, L = 18,439 and T = 524 5

6 Estimating Seasonal Factors Estimating Seasonal Factors 20 Calculate deseasonalized demand for each period: S t = D t / D t = seasonal lfactor for period t In the example, D 2 = (524)(2) = D 2 = S 2 = 13000/19487 = 0.67 Other seasonal factors are calculated similarly 21 t Demand Deseasonalized Demand Seasonal Factor Estimating Seasonal Factors Estimating the Forecast 22 Overall seasonal factor: Averaging all of the factors for a season. 23 Forecast the next four periods: In the example: 3 seasonal cycles in the data and p=4: S1 = ( )/3 = 0.47 S2 = ( )/3 = 0.68 S3 = ( )/3 = 1.17 S4 = ( )/3 = 1.67 F 13 = (L+13T)S 1 = [18439+(13)(524)](0.47) = F 14 = (L+14T)S 2 = [18439+(14)(524)](0.68) = F 15 = (L+15T)S 3 = [18439+(15)(524)](1.17) = F 16 = (L+16T)S 4 = [18439+(16)(524)](1.67) )]( ) =

7 Adaptive Forecasting Basic Formulas 24 The estimates of level, trend, and seasonality are adjusted after each demand observation Moving average Simple exponential smoothing Trend-corrected exponential smoothing (Holt s model) Trend- and seasonality-corrected exponential smoothing (Winter s model) 25 F t+1 = (L t + lt)s t+1 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 = At Actual ldemand dobserved din period idtt 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 Moving Average 26 Initialize Compute initial estimates of level (L 0 ), trend (T 0 )and ), seasonal factors (S 1,,S p ). As in static forecasting. Forecast Forecast demand for period t+1 Estimate error 27 Used when demand has no observable trend or seasonality Systematic component of demand = level Level in period t is the average over last N periods Current forecast for all future periods is the same: L t = (D t + D t D t-n+1 ) / N 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 F t+1 = L t and F t+n = L t After observing the demand for period t+1, revise: L t+1 = (D t+1 + D t + + D t-n+2 ) / N F t+2 = L t+1 7

8 Example Simple Exponential Smoothing 28 In the Tahoe Salt example, what is the forecast demand for periods 5 through 8 using a 4-period moving average? L4 = (D4+D3+D2+D1)/4 = ( )/4 = F5 = = F6 = F7 = F8 Observe demand in period 5 to be D5 = Forecast error in period 5: E5 = = 9500 Revise estimate of level in period 5: L5 = (D5+D4+D3+D2)/4 = F6 = L5 = Used when demand has no observable trend or seasonality Systematic component of demand = level Initial estimate of level average of all demand data: L 0 = [Sum( i=1 to n )D i ]/n Current forecast current estimate of the level: F t+n = L t Revise, after observing demand D t+1 L t+1 = D t+1 + (1- )L t : Smoothing constant Example Holt s Model 30 Tahoe Salt data Forecast tdemand dusing exponential smoothing: Period 1: L 0 = average of all periods = Sum (i=1 to 12) [D i ]/12 = F 1 = L 0 = Observed demand for period 1 = D 1 = 8000 Forecast error for period 1: E 1 = F 1 -D 1 = Assuming = 0.1, revised the estimates: L 1 = D 1 + (1- )L 0 = (0.1)(8000) + (0.9)(22083) = F 2 = L 1 = Trend-Corrected Exponential Smoothing When demand d is assumed to have 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: F t+1 = L t + T t F t+n = L t + nt t 8

9 Holt s Model Example 32 Revise the estimates after observing demand for period t: 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 33 Forecast Tahoe Salt demand using Holt s model Using linear regression, L 0 = (linear intercept) T 0 = 1549 (linear slope) Forecast for period 1: F 1 = L 0 + T 0 = = Observed demand for period 1 = D 1 = 8000 E 1 = F 1 - D 1 = = 5564 Assume = 0.1, = 0.2 L 1 = D 1 + (1- )(L 0 +T 0 ) = (0.1)(8000) + (0.9)(13564) = T 1 = (L 1 L 0 ) + (1- )T 0 = (0.2)( ) + (0.8)(1549) = 1438 F 1 = L 1 + T 1 = = F 5 = L 1 + 4T 1 = (4)(1438) = Winter s Model Winter s Model 34 Trend- and Seasonality-Corrected Exponential Smoothing Systematic component of demand is assumed to have a level, trend, and seasonal factor Systematic component = (level + trend)(seasonal factor) 35 Revise estimates Observing demand d for period t+1, L t+1 = (D t+1 /S t+1 ) + (1- )(L t +T t ) = smoothing constant for level Assume periodicity p Obtain initial estimates using procedure for static forecasting Forecast in period t: T t+1 = (L t+1 - L t ) + (1- )T t = smoothing constant for trend S t+p+1 = (D t+1 /L t+1 ) + (1- )S t+1 = smoothing constant for seasonal factor F t+1 = (L t +T t )(S t+1 ) and F t+n = (L t + nt t )S t+n 9

10 Example Measures of Forecast Error 36 Forecast Tahoe Salt demand using Winter s model. Initial estimates: es: L 0 = 18439, T 0 = 524 S 1 =0.47, S 2 =0.68, S 3 =1.17, S 4 =1.67 F 1 = (L 0 + T 0 )S 1 = ( )(0.47) = 8913 Forecast error D 1 = 8000 E 1 = F 1 -D 1 = = 913 Revise estimates, assume = 0.1, =0.2, =0.1 L 1 = (D 1 /S 1 )+(1- )(L 0 +T 0 ) = (0.1)(8000/0.47)+(0.9)( )=18769 T 1 = (L 1 -L 0 )+(1- )T 0 = (0.2)( )+(0.8)(524) = 485 S 5 = (D 1 /L 1 )+(1- )S 1 = (0.1)(8000/18769)+(0.9)(0.47) = 0.47 F 2 = (L 1 +T 1 )S 2 = ( )(0.68) = Forecast error = E t = F t -D t Mean squared error (MSE) MSE n = (Sum (t=1 to n) [E t2 ])/n Absolute deviation = A t = E t Mean absolute deviation (MAD) MAD n = (Sum (t=1 to n) [A t ])/n Measures of Forecast Error Homework 3 38 Mean absolute percentage error (MAPE) MAPE n = (Sum (t=1 to n) [ E t /D 100])/ t 100])/n Bias Consistently under- or overestimate demand bias n = Sum (t=1 to n) [E t ] 39 Exercises: 2 3 Due on 3 November. Chapter 7 Tracking signal TS t = bias / MAD t Should be within the range of +6 Otherwise, possibly use a new forecasting method 10