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Supply Chain Management. Lecture 12. Outline. Today Chapter 7 Homework 3 Online tomorrow Due Friday February 26 before 5:00pm Next week Thursday Finish Chapter 7 (forecast error measures) Start with Chapter 8 Network design simulation assignment. Announcements. What?

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## Supply Chain Management

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**Supply Chain Management**Lecture 12**Outline**• Today • Chapter 7 • Homework 3 • Online tomorrow • Due Friday February 26 before 5:00pm • Next week Thursday • Finish Chapter 7 (forecast error measures) • Start with Chapter 8 • Network design simulation assignment**Announcements**• What? • Tour the Staples Fulfillment Center in Brighton, CO • Informal Lunch-and-Learn • Up to 20 students with a Operations Management major • When? • Weeks of March 15 or March 29 • There is a fair amount of time involved in the activity • Transit is close to an hour in each direction • Probably 2 hours onsite • Interested? • Let me know (email) by the end of this week**Time Series Forecasting**Observed demand = Systematic component + Random component L Level (current deseasonalized demand) T Trend (growth or decline in demand) S Seasonality (predictable seasonal fluctuation) The goal of any forecasting method is to predict the systematic component (Forecast) of demand and measure the size and variability of the random component (Forecast error)**Summary: N-Period Moving Average Method**• Estimate level • Take the average demand over the most recent N periods • Lt = (Dt + Dt-1 + … + Dt-N+1) / N • Forecast • Forecast for all future periods is based on the current estimate of level Lt • Ft+n = Lt Forecast Ft+n = Lt**Summary: Simple Exponential Smoothing Method**• Estimate level • The initial estimate of level L0 is the average of all historical data • L0 = (∑iDi)/ n • Revise the estimate of level for all periods using smoothing constant • Lt+1 = Dt+1 + (1 – )*Lt • Forecast • Forecast for future periods is • Ft+n = Lt Forecast Ft+n = Lt**Summary: Holt’s Method (Trend Corrected Exponential**Smoothing) • Estimate level and trend • The initial estimate of level L0 and trend T0 are obtained using linear regression • =INTERCEPT(known_y’s, known_x’s) • =LINEST(known_y’s, known_x’s) • Revise the estimates for all periods using smoothing constants and • Lt+1 = Dt+1 + (1 – )*(Lt + Tt) • Tt+1 = (Lt+1 – Lt) + (1 – )*Tt • Forecast • Forecast for future periods is • Ft+n = Lt + nTt Forecast Ft+n = Lt + nTt**Summary: Winter’s Model (Trend and Seasonality Corrected**Exp. Smoothing) • Estimate level, trend, and seasonality • The initial estimates of L0, T0, S1, S2, S3, and S4 are obtained from static forecasting procedure • Revise the estimates for all periods using smoothing constants , and • 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 • Forecast • Forecast for future periods is • Ft+n = (Lt + nTt)*St+n Forecast Ft+n = (Lt + nTt)St+n**Components of an Observation**Trend (T) Forecast(F) Ft+n = Lt + nTt Holt’s method is appropriate when demand is assumed to have a level and a trend**Example: Holt’s Method**• An electronics manufacturer has seen demand for its latest MP3 player increase over the last six months • 8415, 8732, 9014, 9808, 10413, 11961 Determine initial levelL0 = INTERCEPT(y’s, x’s)T0 = LINEST(y’s, x’s)**Example: Holt’s Method**• An electronics manufacturer has seen demand for its latest MP3 player increase over the last six months • 8415, 8732, 9014, 9808, 10413, 11961 Determine initial levelL0 = INTERCEPT(y’s, x’s)T0 = LINEST(y’s, x’s) Determine levelsLt+1 = Dt+1 + (1 – )*(Lt + Tt)Tt+1 = (Lt+1 – Lt) + (1 – )*Tt ForecastFt+n = Lt + nTt = 0.1, = 0.2**Example: Tahoe Salt**• Demand forecasting using Holt’s method**Components of an Observation**Seasonality (S) Forecast(F) Ft+n = (Lt + Tt)St+n**Example: Winter’s Model**• A theme park has seen the following attendance over the last eight quarters (in thousands) • 54, 87, 192, 130, 80, 124, 265, 171 Determine initial levelsL0 = From static forecastT0 = From static forecastSi,0 = From static forecast Determine levelsLt+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 ForecastFt+1 = (Lt + Tt)St+1**Example: Tahoe Salt**• Demand forecast using Winter’s method**Static**Dt: Actual demand L: Level T: Trend S: Seasonal factor Ft: Forecast Adaptive Dt: Actual demand Lt: Level Tt: Trend St: Seasonal factor Ft: Forecast Static Versus Adaptive Forecasting Methods**Components of an Observation**Seasonality (S) Forecast(F) Ft+n = (Lt + Tt)St+n**Determine deason. demandDt = L + Tt**Determine seasonal factorsSt = Dt / Dt Determine seasonal factorsSi =AVG(St) Example: Static Method • A theme park has seen the following attendance over the last eight quarters (in thousands) • 54, 87, 192, 130, 80, 124, 265, 171 Determine initial levelL = INTERCEPT(y’s, x’s)T = LINEST(y’s, x’s) ForecastFt = (L + T)Si**Static Forecasting Method**• Deseasonalize 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 • 12 months in a year • 7 days in a week • 4 quarters in a year • 3 months in a quarter**Periodicity p is odd**Periodicity p is even Deseasonalize demand**Example: Tahoe Salt**• Demand forecast using Static forecasting method**Summary: Static Forecasting Method**• Estimate level and trend • Deseasonalize the demand data • Estimate level L and trend T using linear regression • Obtain deasonalized demand Dt • Estimate seasonal factors • Estimate seasonal factors for each period St = Dt /Dt • Obtain seasonal factors Si = AVG(St) such that t is the same season as i • Forecast • Forecast for future periods is • Ft+n = (L + nT)*St+n Forecast Ft+n = (L + nT)St+n**Forecast**Forecast error Time Series Forecasting Observed demand = Systematic component + Random component L Level (current deseasonalized demand) T Trend (growth or decline in demand) S Seasonality (predictable seasonal fluctuation) The goal of any forecasting method is to predict the systematic component (Forecast) of demand and measure the size and variability of the random component (Forecast error)**1) Characteristics of Forecasts**• Forecasts are always wrong! • Forecasts should include an expected value and a measure of error (or demand uncertainty) • Forecast 1: sales are expected to range between 100 and 1,900 units • Forecast 2: sales are expected to range between 900 and 1,100 units

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