【文章內(nèi)容簡介】 tify the 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 8/25/00 54 Components of an observation Observed demand (O) = Systematic ponent (S) + Random ponent (R) ? Multiplicative: S = L T seasonal factor ? Additive: S = L+T+ Seasonal factor ? Mixed: S = ( L+T) seasonal factor Level (current deseasonalized demand) Trend (growth or decline in demand) Seasonality (predictable seasonal fluctuation) 8/25/00 55 Time Series Forecasting Quart er Demand DtII, 1998 8000III, 1998 13000IV, 1998 23000I, 1999 34000II, 1999 10000III, 1999 18000IV, 1999 23000I, 2023 38000II, 2023 12023III, 2023 13000IV, 2023 32023I, 2023 41000Forecast demand for the next four quarters. 8/25/00 56 Time Series Forecasting 01 0 , 0 0 02 0 , 0 0 03 0 , 0 0 04 0 , 0 0 05 0 , 0 0 097,297,397,498,198,298,398,499,199,299,399,400,18/25/00 57 Forecasting methods ? Static ? Adaptive – Moving average – Simple exponential smoothing – Holt’s model (with trend) – Winter’s model (with trend and seasonality) 8/25/00 58 S = （ L+T） Seasonality L = Estimate of level for period 0。 T = Estimate of trend (per period)。 St = Estimate of seasonal factor for period t Dt = Actual demand observed in period t Ft = Forecast of demand for period t Ft+l = [ L + ( t + l ) T ] St+l Static Forecasting methods 8/25/00 59 ? ?? ?????????????????????????????2/2/)2/(1)2/(1)2/()2/(/2/2ptptiiptptiiptpttpDpDDDDFor p even For p odd P: periodicity Estimating Level: deseasonalized demand 8/25/00 60 8/2 2/24251)2/(1)2/(1)2/()2/(3????????????????????????????iiptptiiptptDDDpDDDDP = 4, t = 3 Example Excel File 8/25/00 61 tTLD t ??Linear Regression tt 524439,18 ??8/25/00 62 ttt DDS /?rSSrjijpi /10????????? ????Estimating Seasonal Factor Seasonal Cycles ? ? )(3/9511 ??????? SSSS ? ? )(3/10622 ??????? SSSS ? ? )(3/11733 ??????? SSSS ? ? )(3/12844 ??????? SSS8/25/00 63 ? ? 868,)52413439,18(13 1313 ?????? STLF ? ? 527,)52414439,18(14 1414 ?????? STLF ? ? 770,)52415439,18(151515 ?????? STL? ? 794,)52416439,18(16 1616 ?????? STLFForecast for the Next Four Quarters 8/25/00 64 Adaptive Forecasting methods 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 (for period t)。 Dt = Actual demand observed in period t。 Et = Forecast error observed in period t 。 At = Absolute deviation for period t = |Et |) ltttltSlTLF ?? ?? )(8/25/00 65 Initialize : L0 T0 S0； Forecast Estimate error Modify estimate ltltlt DFE ??? ??Four Steps 8/25/00 66 Systematic ponent = Level。 NDDDL Ntttt /)...( 11 ??? ???? tnttt LFLF ?? ?? ,112211 ,/)...( ?????? ????? ttNtttt LFNDDDLMoving Average 8/25/00 67 ???niiDnL101tnttt LFLF ?? ?? ,1 ttt LDL )1(11 ?? ??? ??nttnnt DL ????? ? ?? 1101 1( ）??Simple Exponential Smoothing Systematic ponent = Level。 8/25/00 68 batD t ?? ttntttt nTLFTLF ???? ?? ,1ttttttttTLLTTLDL)1()())(1(1111????????????????TrendCorrected Exponential Smoothing (Holt’s Model) Systematic ponent of demand = Level + trend。 8/25/00 69 Systematic ponent of demand = (Level+Trend) Seasonal factor ntttntttttSnTLFSTLF ???? ???? )( ,)( 11 111111111)1()/()1()())(1()/(?????????????????????tttpttttttttttSLDSTLLTTLSDL??????Trendand SeasonalityCorrected Exponential Smoothing (Winter’s Model) 8/25/00 70 Error measures tttDFE ?????????nitntnitnAnMADEAEnMSE11211tttnttnnt ttnMADbia sTSEbia snDEMAP EMAD???????? 。10011?8/25/00 71 Forecasting Method MAD MAPE(%) TS Range Moving average 9,719 49 Simple exponential smoothing 10,208 59 to Holt’s model 8,836 52 to Winter’s model 1,469 8 to 8/25/00 72 Aggregate Planning at Red Tomato Tools Mon t h D e m an d F ore c astJa n ua r y 1, 600F e br ua r y 3, 000Ma r c h 3, 200A pr i l 3, 800Ma y 2, 200Jun e 2, 2008/25/00 73 Fundamental tradeoffs in Aggregate Planning ? Capacity (regular time, over time, subcontract) ? Inventory ? Backlog / lost sales Basic Strategies ? Chase strategy ? Time flexibility from workforce or capacity ? Level strategy 8/25/00 74 Aggregate Planning It em C ost Mat er i al s $10/uni t I nv ent ory holdi ng cost $2/uni t / m onth Mar g i nal cost of a s t ock out $5/uni t / m onth H i r i ng and tr ai ni ng cost s $300 / w ork er L ay off cost $500 / w ork er L abor hours re quir ed 4/ unit R eg ul ar t i m e cost $4/hour O v er t i m e cost $6/hour C ost of subcont r act i ng $30/uni t 8/25/00 75 Aggregate Planning (Define Decision Variables) Wt Ht Lt Pt It St Ct Ot = Workforce size for month t, t = 1, ..., 6 = Number of employees hired at the beginning of month t = Number of employees laid off at the beginning of month t = Production in month t = Inventory at the end of month t = Number of units stocked out at the end of month t = Number of u