Supply Chain Management Chapter 4 Demand forecasting in

  • Slides: 37
Download presentation

Supply Chain Management 第四章 供应链的需求预测 Chapter 4 Demand forecasting in a supply chain 7

Supply Chain Management 第四章 供应链的需求预测 Chapter 4 Demand forecasting in a supply chain 7 -2

Time Series Forecasting (Table 7. 1) 例:Natural. Gas. com Forecast demand for the next

Time Series Forecasting (Table 7. 1) 例:Natural. Gas. com Forecast demand for the next four quarters. 13

预测需求水平和需求趋势 n n 剔除季节影响后的需求Deseasonalized demand = demand that would have been observed in the

预测需求水平和需求趋势 n n 剔除季节影响后的需求Deseasonalized demand = demand that would have been observed in the absence of seasonal fluctuations 时期数Periodicity (p):在周期内包含的所有时期之 后,季节性周期将重复进行 for demand at Natural. Gas. com(Table 7. 1, Figure 7. 1) p =4 14

Deseasonalizing Demand 15

Deseasonalizing Demand 15

Deseasonalized demand Period t Demand D 1 8, 000 2 13, 000 3 23,

Deseasonalized demand Period t Demand D 1 8, 000 2 13, 000 3 23, 000 19, 750 4 34, 000 20, 650 5 10, 000 21, 250 6 18, 000 21, 750 7 23, 000 22, 500 8 38, 000 22, 125 9 12, 000 22, 625 10 13, 000 24, 125 11 32, 000 12 41, 000 16

剔除季节性影响后需求以一个固定比率变化,即剔除 季节性影响后的需求与时间t之间存在一个线性关 系 Dt = L + t. T where Dt = deseasonalized demand

剔除季节性影响后需求以一个固定比率变化,即剔除 季节性影响后的需求与时间t之间存在一个线性关 系 Dt = L + t. T where Dt = deseasonalized demand in period t L = level (deseasonalized demand at period 0) T = trend (rate of growth of deseasonalized demand) In the example, L = 18, 439 and T = 524 17

Time Series of Demand (Figure 7. 3) 18

Time Series of Demand (Figure 7. 3) 18

估计季节性系数 Use the previous equation to calculate deseasonalized demand for each period St =

估计季节性系数 Use the previous equation to calculate deseasonalized demand for each period St = Dt / Dt = seasonal factor for period t In the example, D 2 = 18439 + (524)(2) = 19487 D 2 = 13000 S 2 = 13000/19487 = 0. 67 19

Estimating Seasonal Factors (Fig. 7. 4) 20

Estimating Seasonal Factors (Fig. 7. 4) 20

预测季节性系数 The overall seasonal factor for a “season” is then obtained by averaging all

预测季节性系数 The overall seasonal factor for a “season” is then obtained by averaging all of the factors for a “season” n 如果数据中存在一个r的季节性循环,对所有pt+i, 1≤i≤p为形式的时期,定义 In the example, there are 3 seasonal cycles in the data and p=4, so S 1 = (0. 42+0. 47+0. 52)/3 = 0. 47 S 2 = (0. 67+0. 83+0. 55)/3 = 0. 68 S 3 = (1. 15+1. 04+1. 32)/3 = 1. 17 S 4 = (1. 66+1. 68+1. 66)/3 = 1. 67 21

预测 Using the original equation, we can forecast the next four periods of demand:

预测 Using the original equation, we can forecast the next four periods of demand: F 13 = (L+13 T)S 1 = [18439+(13)(524)](0. 47) = 11868 F 14 = (L+14 T)S 2 = [18439+(14)(524)](0. 68) = 17527 F 15 = (L+15 T)S 3 = [18439+(15)(524)](1. 17) = 30770 F 16 = (L+16 T)S 4 = [18439+(16)(524)](1. 67) = 44794 22

适应性预测法 Ft+l = (Lt + l. Tt )St+l = forecast for period t+l in

适应性预测法 Ft+l = (Lt + l. Tt )St+l = forecast for period t+l in period t Lt = Estimate of level at the end of period t Tt = Estimate of trend at the end of period t St = Estimate of seasonal factor for period t Ft = Forecast of demand for period t (made period t-1 or earlier) Dt = Actual demand observed in period t Et = Forecast error in period t At = Absolute deviation for period t = |Et| MAD = Mean Absolute Deviation = average value of At 23

适应法预测步骤 n n n 初始化: Compute initial estimates of level (L 0), trend (T

适应法预测步骤 n n n 初始化: Compute initial estimates of level (L 0), trend (T 0), and seasonal factors (S 1, …, Sp). This is done as in static forecasting. 预测: Forecast demand for period t+1 using the general equation Ft+l = (Lt + l. Tt )St+l. 估计误差: Compute error Et+1 = Ft+1 - Dt+1 修正预测值: Modify the estimates of level (Lt+1), trend (Tt+1), and seasonal factor (St+p+1), given the error Et+1 in the forecast Repeat steps 2, 3, and 4 for each subsequent period 24

Moving Average Example From Natural. Gas. com example (Table 7. 1) At the end

Moving Average Example From Natural. Gas. com example (Table 7. 1) At the end of period 4, what is the forecast demand for periods 5 through 8 using a 4 -period moving average? L 4 = (D 4+D 3+D 2+D 1)/4 = (34000+23000+13000+8000)/4 = 19500 F 5 = 19500 = F 6 = F 7 = F 8 Observe demand in period 5 to be D 5 = 10000 Forecast error in period 5, E 5 = F 5 - D 5 = 19500 - 10000 = 9500 Revise estimate of level in period 5: L 5 = (D 5+D 4+D 3+D 2)/4 = (10000+34000+23000+13000)/4 = 20000 F 6 = L 5 = 20000 = F 7 = F 8 26

Simple Exponential Smoothing Example From Natural. Gas. com example, forecast demand for period 1

Simple Exponential Smoothing Example From Natural. Gas. com example, forecast demand for period 1 using exponential smoothing L 0 = average of all 12 periods of data = Sum(i=1 to 12)[Di]/12 = 22083 F 1 = L 0 = 22083 Observed demand for period 1 = D 1 = 8000 Forecast error for period 1, E 1, is as follows: E 1 = F 1 - D 1 = 22083 - 8000 = 14083 Assuming α = 0. 1, revised estimate of level for period 1: L 1 = αD 1 + (1 -α)L 0 = (0. 1)(8000) + (0. 9)(22083) = 20675 F 2 = L 1 = 20675 Note that the estimate of level for period 1 is lower than in period 0 28

需求趋势修正后的指数平滑法Trend-Corrected Exponential Smoothing (Holt’s Model) 系统需求有需求水平和需求趋势没有季节性变动 系统成分=需求水平+需求趋势 n Obtain initial estimate of level and

需求趋势修正后的指数平滑法Trend-Corrected Exponential Smoothing (Holt’s Model) 系统需求有需求水平和需求趋势没有季节性变动 系统成分=需求水平+需求趋势 n Obtain initial estimate of level and trend by running a linear regression of the following form: Dt = at + b T 0 = a L 0 = b In period t, the forecast for future periods is expressed as follows: Ft+1 = Lt + Tt Ft+n = Lt + n. Tt 观测到t+1期需求后,修正 Lt+1 = Dt+1 + (1 - )(Lt + Tt) Tt+1 = b(Lt+1 - Lt) + (1 -b)Tt α为需求水平的平滑系数,0< α<1 β为需求趋势的平滑系数,0< β<1。 n 29

Trend-Corrected Exponential Smoothing Example: Tahoe Salt demand data. Forecast demand for period 1 using

Trend-Corrected Exponential Smoothing Example: Tahoe Salt demand data. 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) Forecast for period 1: F 1 = L 0 + T 0 = 12015 + 1549 = 13564 Observed demand for period 1 = D 1 = 8000 E 1 = F 1 - D 1 = 13564 - 8000 = 5564 Assume = 0. 1, = 0. 2 L 1 = D 1 + (1 - )(L 0+T 0) = (0. 1)(8000) + (0. 9)(13564) = 13008 T 1 = (L 1 - L 0) + (1 - )T 0 = (0. 2)(13008 - 12015) + (0. 8)(1549) = 1438 F 2 = L 1 + T 1 = 13008 + 1438 = 14446 F 5 = L 1 + 4 T 1 = 13008 + (4)(1438) = 18760 30

需求趋势和季节性需求修正后的指数平滑法 Trend- and Seasonality-Corrected Exponential Smoothing (Winter Model) n 系统需求有需求水平、需求趋势和季节性变动 系统需求=(需求水平+需求趋势)×季节性需 求 n Assume

需求趋势和季节性需求修正后的指数平滑法 Trend- and Seasonality-Corrected Exponential Smoothing (Winter Model) n 系统需求有需求水平、需求趋势和季节性变动 系统需求=(需求水平+需求趋势)×季节性需 求 n Assume periodicity p n Obtain initial estimates of level (L 0), trend (T 0), seasonal factors (S 1, …, Sp) using procedure for static forecasting n In period t, the forecast for future periods is given by: Ft+1 = (Lt+Tt)(St+1) and Ft+n = (Lt + n. Tt)St+n 31

Trend- and Seasonality-Corrected Exponential Smoothing (continued) After observing demand for period t+1, revise estimates

Trend- and Seasonality-Corrected Exponential Smoothing (continued) After observing demand for period t+1, revise estimates for level, trend, and seasonal factors as follows: Lt+1 = (Dt+1/St+1) + (1 - )(Lt+Tt) Tt+1 = (Lt+1 - Lt) + (1 - )Tt St+p+1 = (Dt+1/Lt+1) + (1 - )St+1 a 为需求水平的平滑系数,0< <1 b 为需求趋势的平滑系数,0< <1 g为季节性需求的平滑系数,0< <1 32

Trend- and Seasonality-Corrected Exponential Smoothing Example: Tahoe Salt data. Forecast demand for period 1

Trend- and Seasonality-Corrected Exponential Smoothing Example: Tahoe Salt data. 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 F 1 = (L 0 + T 0)S 1 = (18439+524)(0. 47) = 8913 The observed demand for period 1 = D 1 = 8000 Forecast error for period 1 = E 1 = F 1 -D 1 = 8913 - 8000 = 913 Assume a = 0. 1, b=0. 2, g=0. 1; revise estimates for level and trend for period 1 and for seasonal factor for period 5 L 1 = a(D 1/S 1)+(1 -a)(L 0+T 0) = 0. 1)(8000/0. 47)+(0. 9)(18439+524)=18769 T 1 = b(L 1 -L 0)+(1 -b)T 0 = (0. 2)(18769 -18439)+(0. 8)(524) = 485 S 5 = g(D 1/L 1)+(1 -g)S 1 = (0. 1)(8000/18769)+(0. 9)(0. 47) = 0. 47 F 2 = (L 1+T 1)S 2 = (18769 + 485)(0. 68) = 13093 33

7. 5 预测误差的度量 n 一个好的预测方法应该反映系统需求部分而不是随机需求部分。 随机需求部分会以预测误差的形式表现出来。 t期的预测误差Forecast error = Et = Ft - Dt

7. 5 预测误差的度量 n 一个好的预测方法应该反映系统需求部分而不是随机需求部分。 随机需求部分会以预测误差的形式表现出来。 t期的预测误差Forecast error = Et = Ft - Dt n 平均方差Mean squared error (MSE) n 绝对离差Absolute deviation = At = |Et| n 平均绝对离差Mean absolute deviation (MAD) When the random component is normally distributed = 1. 25 MAD 34

37

37