University:
Massachusetts Institute of Technology
Course:
15.501/516 | Accounting
Academic year:

2023
Views:

100

Pages:

31
Author:

flippernwq3

The Art of Forecasting Costs of Forecasting IBM continues to struggle with shortages in the Think Pad line. WSJ 5/2/94 IBM sells out new Aptiva PC. Shortage may cost millions… WSJ 10/7/94 Dell … stock plunges. Dell…was sharply off in its forecast of demand… WSJ 8/93 Liz Claiborne said … earnings decline is consequence of [unanticipated] excess inventories. WSJ 7/15/93 Toyota believes it can save $100M/3a … [with] accurate ordering and inventory management. “It’s unbelievable the number of (after market) parts that are thrown away each year.” Automotive News 2/26/01 Store Mark-Downs % of Dollar Sales 26% 22% 18% 14% 10% 6% 1970 1975 1980 1985 1990 Forecasting Basics… Forecasts are usually wrong Forecasts should contain error measure. Aggregate Forecasts are more accurate The longer the horizon, the lower the accuracy Common Sense Compatibility Include other known Information Basic Taxonomy Qualitative (subjective) Expertise Based Delphi Method The “Sage” Sales Force Customer Surveys Long Term Complex Scenarios Quantitative (objective) Causal Models Y=f(X1, X2, …, Xn) Time Series Models Yt =f(Yt-1, Yt-2,…, Yt-n) Causal Models Use Data other than the Series predicted Principal Tool: Regression Analysis Y = a0 + a1X1 + a2X2+ … anXn Estimates ai to minimize “Sum of Least Squares” Y X Time Series Models Prediction based exclusively on previously observed Values General Idea: Detect Patterns! Short Term Demand Prediction Prevalent Tool In Operations Time Series Patterns Random Trend Linear (default) or Nonlinear Seasonality No Pattern Repetition at Fixed Intervals Cyclic Long Term Economy The Basic Concept ∞ Ft = ∑ a n Dt − n n =1 Ft : Forecast for Period t , made in Period t-1 Di : Observed Demand in Period i < t a i : Weights associated with Period i Question: How to assign Weights? Stationary Series Moving Averages & Exponential Smoothing Moving Averages Dt −1 + Dt −1 + ... + Dt − N 1 N Ft = ∑ Dt − n = N n =1 N a i = N1 for i < N , a i = 0 elsewhere Simple Average of Last N Periods No Pattern Large N ⇒ Stability up Small N ⇒ Responsiveness up Exponential Smoothing Ft = a ⋅ Dt −1 + (1 − a ) ⋅ Ft −1 = Ft −1 − a ⋅ (Ft −1 − Dt −1 ) = Ft −1 − a ⋅ et −1 New Forecast = Weighted Average of et −1 ≅ The last Error Last Demand and Last Forecast Small a ⇒ Stability up Large a ⇒ Responsiveness up Moving Average vs. Exponential Smoothing Commonalities Stationary Process 1 Parameter (a or N) Lag behind Trend Differences ES: All past data MA: Last N periods ES: Less data Outliers washed out Last Forecast * Demand MA: Last N data Trends Exponential Smoothing with Linear Trend Regression Analysis Exponential Smoothing with Linear Trend Ft +1 = St + Gt St = a ⋅ Dt + (1 − a ) ⋅ [St −1 + Gt −1 ] = Ft Gt = b ⋅ (St − St −1 ) + (1 − b ) ⋅ Gt −1 Ft +τ = St + τ ⋅ Gt St ≅ The “Intercept” or “Status Quo” Gt ≅ The “Trend” Regression Analysis Sum of Least Squares Min Sum of 2 Y a0 Y = a0 + a1*X X Regression in Excel “Formal Regression Analysis” 1. 2. 3. 4. 5. Tools, Data Analysis, Regression Input Y Range: Dependent Variable Input X Range: Independent Variable Specify where you want Output Output is Table with Regression Statistics Trend Tool =Trend(y-range,x-range,x-value) Output: Trend Estimate for “x-value” Y-range: Observed Data (Demand) X-range: Independent Variable (Time) X-value: Value (Date) for which to estimate Y (Demand) Non Linear Trend Regression Same Procedure as Linear Regression Difference: Change Time to 2 Time ln(Time) etc.. Seasonal Patterns Basic Idea: Assign Weights cn to the N Periods Σc n = N Adjust Forecast by Weights Caution: A Season is the time until a Pattern repeats I.e. a week is a Season with 7 Periods A year is a Season with 4 Periods… Error Measures Mean Absolute Deviation MAD MAD = 1 n ∑ F −D t i =1 t Mean Square Deviation MSD MSD = n Bias = n 1 n ∑ F −D t i =1 n 1 n ∑ (F − D ) i =1 t t t 2 How to choose the right forecasting technique? Chambers, Mullick & Smith Demand Demand and Product Life Cycles Product Development Steady State Introduction Growth Decline Time Demand Predictions are dependent on Life Cycle Decisions Made During PLC Product Development Development Effort Market Entry Product Specs Product Introduction facility size supply chain design Analysis delphi / expert Comparisons QFD Analysis market tests consumer survey life cycle analysis Decision Made During PLC Growth capacity expansion statistical tech production planning promotions Steady State production planning inventory models Analysis Causal Models Simulation Analysis time series causal models Next Week Monday Voluntary Lead-Offs Download Inventory Problems from SloanSpace in Handouts folder Sale of SKU 367890, a seasonal product PREDICTED Sales OBSERVED ACTUAL Feb Apr Jun Aug Oct Dec Demand Random Patterns Time Demand Increasing Linear Trend Time Demand Curve Linear Trend Time Demand Seasonal & Linear Trend Time