【正文】 023 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。 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。 St = Estimate of seasonal factor for period t。 Dt = Actual demand 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。 8/25/00 68 batD t ?? ttntttt nTLFTLF ???? ?? ,1ttttttttTLLTTLDL)1()())(1(1111????????????????TrendCorrected Exponential Smoothing (Holt’s Model) Systematic ponent of demand = Level + trend。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 units subcontracted for month t = Number of overtime hours worked in month t, 8/25/00 76 Aggregate Planning (Define Objective Function)) ???????????????????????61616161616161613010526500300640ttttttttttttttttCPSIOLHWMi n8/25/00 77 Aggregate Planning (Define Constraints Linking Variables) ? Workforce size for each month is based on hiring and layoffs .80,6,... ,10,011???????????Wwh eretforLHWWorLHWWtttttttt8/25/00 78 Aggregate Planning (Constraints) ? Production for each month cannot exceed capacity .6,... ,1,0440,440??????tforPOWOWPtttttt8/25/00 79 Aggregate Planning (Constraints) ? Inventory balance for each month .500,0,000,1,6,... ,1,0,6001111?????????????????????IandSIwh eretforSISDCPISISDCPItttttttttttttt8/25/00 80 Aggregate Planning (Constraints) ? Over time for each month .6,... ,1,010,10????tforOWWOttttExcel File 8/25/00 81 Scenarios ? Increase in holding cost (from $2 to $6) ? Over time cost drops to $ per hour ? Increased demand fluctuation 8/25/00 82 Increased Demand Fluctuation Mon t h D e m an d F ore c astJa n ua r y 1, 000F e br ua r y 3, 000Ma r c h 3, 800A pr i l 4, 800Ma y 2, 000Jun e 1, 4008/25/00 83 Managing Predictable Variability ? Manage Supply – Manage capacity 187。Use of seasonal workforce 187。Use of dual facilitiesdedicated and flexible 187。Component monality 187。Batch size and cycle time 187。Short term discounts / Trade promotions – Stochastic variability of supply and demand 187。Evaluating safety inventory given desired service level ? Levers to improve performance 8/25/00 3/1/2023 S. Chopra/Inventory 97 Role of Inventory in the Supply