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1) Review Chapter 7 “Demand Forecasting in a Supply Chain power point slides for you will have to write up what you learned from this chapter. PLEASE EXEMPLIFY HIGH LEVEL ANALYSIS WITH YOUR WRITING (i.e. 3 Paragraphs Minimum)   2) Link for Ted Talk: This will be part of you participation points: (i.e. 3 Paragraphs Minimum): How supply chain transparency can help the planet | Markus Mutz  https://www.youtube.com/watch?v=ygxh6KR4BPk Supply Chain Management: Strategy, Planning, and Operation Seventh Edition Chapter 7 Demand Forecasting in a Supply Chain Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved If this PowerPoint presentation contains mathematical equations, you may need to check that your computer has the following installed: 1) MathType Plugin 2) Math Player (free versions available) 3) NVDA Reader (free versions available) 1 Learning Objectives 7.1 Understand the role of forecasting for both an enterprise and a supply chain. 7.2 Identify the components of a demand forecast and some basic approaches to forecasting. 7.3 Forecast demand using time-series methodologies given historical demand data in a supply chain. 7.4 Analyze demand forecasts to estimate forecast error. 7.5 Use Excel to build time-series forecasting models. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Role of Forecasting in a Supply Chain The basis for all planning decisions in a supply chain Used for both push and pull processes Production scheduling, inventory, aggregate planning Sales force allocation, promotions, new production introduction Plant/equipment investment, budgetary planning Workforce planning, hiring, layoffs All of these decisions are interrelated Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Characteristics of Forecasts Forecasts are always inaccurate and should thus include both the expected value of the forecast and a measure of forecast error Long-term forecasts are usually less accurate than short-term forecasts Aggregate forecasts are usually more accurate than disaggregate forecasts In general, the farther up the supply chain a company is, the greater is the distortion of information it receives Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Summary of Learning Objective 1 (1 of 2) Forecasting is a key input for virtually every design and planning decision made in a supply chain. It is important to recognize that all forecasts are likely to be wrong. Thus, an estimation of forecast error is essential to effectively use the forecast. Reducing the forecast horizon (by reducing the lead time of the associated decision) and aggregation are two effective approaches to decrease forecast error. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Summary of Learning Objective 1 (2 of 2) A relatively recent phenomenon, however, is to create collaborative forecasts for an entire supply chain and use these as the basis for decisions. Collaborative forecasting greatly increases the accuracy of forecasts and allows the supply chain to maximize its performance. Without collaboration, supply chain stages farther from demand will likely have poor forecasts that will lead to supply chain inefficiencies and a lack of responsiveness. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Components and Methods (1 of 2) Companies must identify the factors that influence future demand and then ascertain the relationship between these factors and future demand Past demand Lead time of product replenishment Planned advertising or marketing efforts Planned price discounts State of the economy Actions that competitors have taken Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Notes: Components and Methods (2 of 2) Qualitative Primarily subjective Rely on judgment Time Series Use historical demand only Best with stable demand Causal Relationship between demand and some other factor Simulation Imitate consumer choices that give rise to demand Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Notes: Components of An Observation Observed demand (O) = systematic component (S) + random component (R) Systematic component – expected value of demand Level (current deseasonalized demand) Trend (growth or decline in demand) Seasonality (predictable seasonal fluctuation) Random component – part of forecast that deviates from systematic part Forecast error – difference between forecast and actual demand Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Five Important Points in the Forecasting Process Understand the objective of forecasting. Integrate demand planning and forecasting throughout the supply chain. Identify the major factors that influence the demand forecast. Forecast at the appropriate level of aggregation. Establish performance and error measures for the forecast. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Notes: Summary of Learning Objective 2 Demand consists of a systematic and a random component. The systematic component measures the expected value of demand. The random component measures fluctuations in demand from the expected value. The systematic component consists of level, trend, and seasonality. Level measures the current de-seasonalized demand. Trend measures the current rate of growth or decline in demand. Seasonality indicates predictable seasonal fluctuations in demand. The goal of forecasting is to estimate the systematic component and the size (not direction) of the random component (in the form of a forecast error). Good forecasting requires a clear understanding of the objective of the forecast and should be integrated across the supply chain. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Time-Series Forecasting Methods Three ways to calculate the systematic component Multiplicative S = level × trend × seasonal factor Additive S = level + trend + seasonal factor Mixed S = (level + trend) × seasonal factor Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Static Methods Systematic component = (level+trend)×seasonal factor Where L = estimate of level at t = 0 T = estimate of trend St = estimate of seasonal factor for Period t Dt = actual demand observed in Period t Ft = forecast of demand for Period t Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Tahoe Salt (1 of 5) Table 7-1 Quarterly Demand for Tahoe Salt Year Quarter Period, t Demand, Dt 1 2 1 8,000 1 3 2 13,000 1 4 3 23,000 2 1 4 34,000 2 2 5 10,000 2 3 6 18,000 2 4 7 23,000 Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Tahoe Salt (2 of 5) Table 7-1 [continued] Year Quarter Period, t Demand, Dt 3 1 8 38,000 3 2 9 12,000 3 3 10 13,000 3 4 11 32,000 4 1 12 41,000 Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Tahoe Salt (3 of 5) Figure 7-1 Quarterly Demand at Tahoe Salt Deseasonalize demand and run linear regression to estimate level and trend. Estimate seasonal factors. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Estimate Level and Trend (1 of 2) Periodicity p = 4, t = 3 Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Notes: Estimate Level and Trend (2 of 2) Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Notes: Tahoe Salt (4 of 5) Figure 7-2 Excel Workbook with Deseasonalized Demand for Tahoe Salt Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Tahoe Salt (5 of 5) Figure 7-3 Deseasonalized Demand for Tahoe Salt A linear relationship exists between the deseasonalized demand and time based on the change in demand over time Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Estimating Seasonal Factors (1 of 3) Figure 7-4 Deseasonalized Demand and Seasonal Factors for Tahoe Salt Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Estimating Seasonal Factors (2 of 3) Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Estimating Seasonal Factors (3 of 3) Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Adaptive Forecasting (1 of 2) The estimates of level, trend, and seasonality are updated after each demand observation Estimates incorporate all new data that are observed Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Adaptive Forecasting (2 of 2) Where 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 = Ft – Dt = forecast error in Period t Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Steps in Adaptive Forecasting Initialize Compute initial estimates of level (L0), trend (T0), and seasonal factors (S1,…,Sp) Forecast Forecast demand for period t + 1 Estimate error Compute error Et+1 = Ft+1 – Dt+1 Modify estimates Modify the estimates of level (Lt+1), trend (Tt+1), and seasonal factor (St+p+1), given the error Et+1 Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Moving Average Used when demand has no observable trend or seasonality Systematic component of demand = level The level in period t is the average demand over the last N periods After observing the demand for period t + 1, revise the estimates Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Moving Average Example (1 of 2) A supermarket has experienced weekly demand of milk of D1 = 120, D2 = 127, D3 = 114, and D4 = 122 gallons over the past four weeks Forecast demand for Period 5 using a four-period moving average What is the forecast error if demand in Period 5 turns out to be 125 gallons? Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Moving Average Example (2 of 2) Forecast demand for Period 5 F5 = L4 = 120.75 gallons Error if demand in Period 5 = 125 gallons E5 = F5 – D5 = 120.75 – 125 = – 4.25 Revised demand Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Simple Exponential Smoothing (1 of 3) Used when demand has no observable trend or seasonality Systematic component of demand = level Initial estimate of level, L0, assumed to be the average of all historical data Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Simple Exponential Smoothing (2 of 3) Given data for Periods 1 to n Current forecast Revised forecast using smoothing constant (0 < α < 1) Thus Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Simple Exponential Smoothing (3 of 3) Supermarket data F1 = L0 = 120.75 E1 = F1−D1 = 120.75−120 = 0.75 L1 = αD1+(1−α)L0 = 0.1×120+0.9 ×120.75=120.68 Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Trend-Corrected Exponential Smoothing (Holt’s Model) (1 of 4) Appropriate when the demand is assumed to have a level and trend in the systematic component of demand but no seasonality Systematic component of demand = level + trend Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Trend-Corrected Exponential Smoothing (Holt’s Model) (2 of 4) Obtain initial estimate of level and trend by running a linear regression Dt = at + b T0 = a, L0 = b In Period t, the forecast for future periods is Ft+1 = Lt + Tt and Ft+n = Lt + nTt Revised estimates for Period t Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Trend-Corrected Exponential Smoothing (Holt’s Model) (3 of 4) Smartphone player demand D1 = 8,415, D2 = 8,732, D3 = 9,014, D4 = 9,808,D5 = 10,413, D6 = 11,961, α = 0.1, β = 0.2 Using regression analysis L0 = 7,367 and T0 = 673 Forecast for Period 1 F1 = L0 + T0 = 7,367 + 673 = 8,040 Period 1 error E1 = F1 – D1 = 8,040 – 8,415 = –375 Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Trend-Corrected Exponential Smoothing (Holt’s Model) (4 of 4) Revised estimate With new L1 F2 = L1 + T1 = 8,078 + 681 = 8,759 Continuing F7 = L6 + T6 = 11,399 + 673 = 12,072 Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Trend- and Seasonality-Corrected Exponential Smoothing (1 of 2) Appropriate when the systematic component of demand has a level, trend, and seasonal factor Systematic component = (level + trend) × seasonal factor Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Trend- and Seasonality-Corrected Exponential Smoothing (2 of 2) After observing demand for period t + 1, revise estimates for level, trend, and seasonal factors α = smoothing constant for level β = smoothing constant for trend γ = smoothing constant for seasonal factor Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Winter’s Model (1 of 3) L0 = 18,439 T0 = 524 S1= 0.47, S2 = 0.68, S3 = 1.17, S4 = 1.67 F1 = (L0 + T0)S1 = (18,439 + 524)(0.47) = 8,913 The observed demand for Period 1 = D1 = 8,000 Forecast error for Period 1 = E1 = F1 – D1 = 8,913 – 8,000 = 913 Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Winter’s Model (2 of 3) Assume α = 0.1, β = 0.2, γ = 0.1; revise estimates for level and trend for period 1 and for seasonal factor for Period 5 Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Winter’s Model (3 of 3) Forecast demand for Period 2 F2 = (L1 + T1)S2 = (18,769 + 485)(0.68) = 13,093 Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Time Series Models Forecasting Method Applicability Moving average No trend or seasonality Simple exponential smoothing No trend or seasonality Holt’s model Trend but no seasonality Winter’s model Trend and seasonality Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Summary of Learning Objective 3 Time-series methods for forecasting are categorized as static or adaptive. In static methods, the estimates of parameters are not updated as new demand is observed. Static methods include regression. In adaptive methods, the estimates are updated each time a new demand is observed. Adaptive methods include moving averages, simple exponential smoothing, Holt’s model, and Winter’s model. Moving averages and simple exponential smoothing are best used when demand displays neither trend nor seasonality. Holt’s model is best when demand displays a trend but no seasonality. Winter’s model is appropriate when demand displays both trend and seasonality. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Measures of Forecast Error (1 of 2) Forecast errors contain valuable information and must be analyzed for two reasons: Managers use error analysis to determine whether the current forecasting method is predicting the systematic component of demand accurately All contingency plans must account for forecast error Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Measures of Forecast Error (2 of 2) Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Summary of Learning Objective 4 Forecast error measures the random component of demand. This measure is important because it reveals how inaccurate a forecast is likely to be and what contingencies a firm may have to plan for. The M S E, M A D, and M A P E are used to estimate the size of the fore- cast error. The bias and T S are used to estimate if the forecast consistently over- or under- forecasts or if demand has deviated significantly from historical norms. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Selecting the Best Smoothing Constant (1 of 2) Figure 7-5 Selecting Smoothing Constant by Minimizing M S E Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Selecting the Best Smoothing Constant (2 of 2) Figure 7-6 Selecting Smoothing Constant by Minimizing M A D Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Forecasting Demand at Tahoe Salt (1 of 10) Moving average Simple exponential smoothing Trend-corrected exponential smoothing Trend- and seasonality-corrected exponential smoothing Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Forecasting Demand at Tahoe Salt (2 of 10) Figure 7-7 Tahoe Salt Forecasts Using Four-Period Moving Average Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Forecasting Demand at Tahoe Salt (3 of 10) Moving average L12 = 24,500 F13 = F14 = F15 = F16 = L12 = 24,500 σ = 1.25 × 9,719 = 12,148 Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Forecasting Demand at Tahoe Salt (4 of 10) Figure 7-8 Tahoe Salt Forecasts Using Simple Exponential Smoothing Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Forecasting Demand at Tahoe Salt (5 of 10) Simple exponential smoothing α = 0.1 L0 = 22,083 L12 = 23,490 F13 = F14 = F15 = F16 = L12 = 23,490 σ = 1.25 × 10,208 = 12,761 Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Forecasting Demand at Tahoe Salt (6 of 10) Figure 7-9 Trend-Corrected Exponential Smoothing Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Forecasting Demand at Tahoe Salt (7 of 10) Trend-Corrected Exponential Smoothing L0 = 12,015 and T0 = 1,549 L12 = 30,443 and T12 = 1,541 F13 = L12 + T12 = 30,443 + 1,541 = 31,984 F14 = L12 + 2T12 = 30,443 + 2 × 1,541 = 33,525 F15 = L12 + 3T12 = 30,443 + 3 × 1,541 = 35,066 F16 = L12 + 4T12 = 30,443 + 4 × 1,541 = 36,607 σ = 1.25 × 8,836 = 11,045 Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Forecasting Demand at Tahoe Salt (8 of 10) Figure 7-10 Trend- and Seasonality-Corrected Exponential Smoothing Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Forecasting Demand at Tahoe Salt (9 of 10) Trend- and Seasonality-Corrected L0 = 18,439 T0 =524 L12 = 24,791 T12 = 532 S1 = 0.47 S2 = 0.68 S3 = 1.17 S4 = 1.67 F13 = (L12 + T12)S13 = (24,791 + 532)0.47 = 11,902 F14 = (L12 + 2T12)S13 = (24,791 + 2 × 532)0.68 = 17,581 F15 = (L12 + 3T12)S13 = (24,791 + 3 × 532)1.17 = 30,873 F16 = (L12 + 4T12)S13 = (24,791 + 4 × 532)1.67 = 44,955 σ = 1.25 × 1,469 = 1,836 Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Forecasting Demand at Tahoe Salt (10 of 10) Table 7-2 Error Estimates for Tahoe Salt Forecasting Forecasting Method M A D M A P E (\%) T S Range Four-period moving average 9,719 49 –1.52 to 2.21 Simple exponential smoothing 10,208 59 –1.38 to 2.15 Holt’s model 8,836 52 –2.15 to 2.00 Winter’s model 1,469 8 –2.74 to 4.00 Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved The Role of Software Tools in Forecasting Software is important Large amounts of data Frequency of forecasts Importance of high-quality results Can forecast demand by products and markets Real time updates help firms respond quickly to changes in marketplace Facilitates demand planning Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Summary of Learning Objective 5 Given the repetitive nature of time-series forecasting methods, they can easily be modeled in Microsoft Excel with simple formulae that are copied across rows or columns. For regular forecasting at companies, however, it may be more effective to select among a wide variety of software packages available today. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved Copyright Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved ++ =++ [()] tltl FLtlTS 184 Chapter 7 • Demand Forecasting in a Supply Chain We now describe one method for estimating the three parameters L, T, and S. As an example, consider the demand for rock salt used primarily to melt snow. This salt is produced by a firm called Tahoe Salt, which sells its salt through a variety of independent retailers around the Lake Tahoe area of the Sierra Nevada Mountains. In the past, Tahoe Salt has relied on estimates of demand from a sample of its retailers, but the company has noticed that these retailers always overestimate their purchases, leaving Tahoe (and even some retailers) stuck with excess inventory. After meeting with its retailers, Tahoe has decided to produce a collaborative forecast. Tahoe Salt wants to work with the retailers to create a more accurate forecast based on the actual retail sales of their salt. Quarterly retail demand data for the past three years are shown in Table 7-1 and charted in Figure 7-1. In Figure 7-1, observe that demand for salt is seasonal, increasing from the second quarter of a given year to the first quarter of the following year. The second quarter of each year has the lowest demand. Each cycle lasts four quarters, and the demand pattern repeats every year. There is also a growth trend in the demand, with sales growing over the past three years. The company estimates that growth will continue in the coming year at historical rates. We now describe how each of the three parameters—level, trend, and seasonal factors—may be estimated. The following two steps are necessary to making this estimation: 1. Deseasonalize demand and run linear regression to estimate level and trend. 2. Estimate seasonal factors. 40,000 30,000 20,000 10,000 0 50,000 1, 2 1, 3 1, 4 2, 1 2, 2 Period D em an d 2, 3 2, 4 3, 1 3, 2 3, 3 3, 4 4, 1 FIGURE 7-1 Quarterly Demand at Tahoe Salt Table 7-1 Quarterly Demand for Tahoe Salt Year Quarter Period, t Demand, Dt 1 2 1 8,000 1 3 2 13,000 1 4 3 23,000 2 1 4 34,000 2 2 5 10,000 2 3 6 18,000 2 4 7 23,000 3 1 8 38,000 3 2 9 12,000 3 3 10 13,000 3 4 11 32,000 4 1 12 41,000 M07_CHOP3952_05_SE_C07.QXD 10/22/11 6:54 PM Page 184 – – – – – – æö + ç÷ èø æöæö + ç÷ç÷ æö èøèø =+ ç÷ èø éù + êú ëû éù = êú ëû ì éù ï êú ++ ï êú ï êú ëû ï ï = í ï ï ï ï ï î å å p t i pp tt p it t p t i p it DDD pp D D pp 1 2 22 1 2 (1) 2 (1) 2 2 (2) for even for odd – – – æö + ç÷ èø æöæö + ç÷ç÷ æö èøèø =+ ç÷ èø éù êú ++ êú êú ëû = å p t i pp tt p it t DDD D p 1 2 22 1 2 2 (2) = ++ = å i i DDD 4 15 2 2 8 UFERNCL Figure 7-2 =+ tt DLT 186 Chapter 7 • Demand Forecasting in a Supply Chain 40,000 30,000 20,000 10,000 0 50,000 1 2 3 4 5 6 7 8 9 10 11 12 Actual Demand Deseasonalized Demand Period D em an d FIGURE 7-3 Deseasonalized Demand for Tahoe Salt Note that in Equation 7.3, represents deseasonalized demand and not the actual demand in Period t, L represents the level or deseasonalized demand at Period 0, and T represents the rate of growth of deseasonalized demand or trend. We can estimate the values of L and T for the deseasonalized demand using linear regression with deseasonalized demand (see Figure 7-2) as the dependent variable and time as the independent variable. Such a regression can be run using Microsoft Excel (Data | Data Analysis | Regression). This sequence of commands opens the Regression dialog box in Excel. For the Tahoe Salt workbook in Figure 7-2, in the resulting dialog box, we enter and click the OK button. A new sheet containing the results of the regression opens up. This new sheet contains estimates for both the initial level L and the trend T. The initial level, L, is obtained as the intercept coefficient, and the trend, T, is obtained as the X variable coefficient (or the slope) from the sheet containing the regression results. For the Tahoe Salt example, we obtain L ! 18,439 and T ! 524. For this example, deseasonalized demand for any Period t is thus given by (7.4) Note that it is not appropriate to run a linear regression between the original demand data and time to estimate level and trend because the original demand data are not linear and the resulting linear regression will not be accurate. The demand must be deseasonalized before we run the linear regression. ESTIMATING SEASONAL FACTORS We can now obtain deseasonalized demand for each period using Equation 7.4. The seasonal factor for Period t is the ratio of actual demand Dt to deseasonalized demand and is given as (7.5) For the Tahoe Salt example, the deseasonalized demand estimated using Equation 7.4 and the seasonal factors estimated using Equation 7.5 are shown in Figure 7-4. Given the periodicity, p, we obtain the seasonal factor for a given period by averaging seasonal factors that correspond to similar periods. For example, if we have a periodicity of p ! 4, Periods 1, 5, and 9 have similar seasonal factors. The seasonal factor for these periods is obtained -St = Di -Dt -Dt St -Dt = 18,439 + 524t -Dt Input X Range: A4: A11 Input Y Range: C4: C11 -Dt M07_CHOP3952_05_SE_C07.QXD 10/22/11 6:54 PM Page 186 = i t t D S D – + = = å r jpi j i S S r 1 0 ++ ++ === ++ ++ === ++ ++ === ++ ++ === SSS S SSS S SSS S SSS S 159 1 2610 2 3711 3 4812 4 () (0.420.470.52) 0.47 33 () (0.670.830.55) 0.68 33 () (1.151.041.32) 1.17 33 () (1.661.681.66) 1.67 33 =+=+´= =+=+´= =+=+´= =+=+´= FLTS FLTS FLTS FLTS 1313 1414 1515 1616 (13)(18,43913524)0.4711,868 (14)(18,43914524)0.6817,527 (15)(18,43915524)1.1730,770 (16)(18,43916524)1.6744,794 = tttt FLlTS +1+1 (+) - ++ +++ = == tttN t tttnt DDD L FLFL 1–+1 1 … N     and     () , -+ + +++ == tttN ttt DDD LFL N +12 +12+1 ( … ) ( ) +++ = +++ == DDDD L 4321 4    122 114 127 1 ( 20   12 ) 4 4 0.75 ( ) +++ = +++ == DDDD L 5432 5 125 122 114 127   () 4 4 122 = = å n i i LD n 0 1 1 ++ == tttnt FLFL 1 and – aa ++ =+ ttt LDL 11 (1) – – –– aaa ++ = =+ å t nt ttn n LDD 1 111 0 (1)(1) = == å i i D L 4 0 1 120.75 4 ( ) ( ) ( ) ( ) a bb ++ + =+-+ =-+- tttt tttt LD αLT TLLT 11 +11 1 1 ( ) ( ) ( ) ( ) ( ) aa bb =+-+ =´+´= =-+- =´-+´= LDLT TLLT 1100 1100 1 0.18,4150.98,0408,078 1 0.28,0787,3670.8673681 =+=+ tttttt FLTSFLlTS +1tt+1+l+l   and ( )    () ( ) ( ) ( ) ( ) ( ) aa bb gg + + + + + + æö =+-+ ç÷ èø =-+- æö =+- ç÷ èø t ttt t tttt t tpt t D LLT S TLLT D SS L 1 +1 1 +11 1 ++11 1 1 1 1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) aa b gg æö =+-+ ç÷ èø éù æö éù =´+´+= ç÷ êú ëû èø ëû =-+- éù =´-+´= ëû æö =+- ç÷ èø éù æö =´+´= ç÷ êú èø ëû D LLT S TLL βT D SS L 1 100 1 1100 1 51 1 1 8,000 0.10.918,43952418,769 0.47 1 0.218,76918,4390.8524485 1 8,000 0.10.90.470.47 18,769 – = ttt EFD = = = == s= å å n nt t n ttnt t MSEE n AEMADA n MAD 2 1 1 1 1 1.25 = = = = å å n t t t n n nt t t t t E D MAPE n biasE bias TS MAD 1 1 100 – – a r a rar == + t t t t –1 –1 Declining a 1 p 1 lha 196 Chapter 7 • Demand Forecasting in a Supply Chain as shown in Figure 7-5. The forecast shown in Figure 7-5 uses the resulting ! ! 0.54 and gives MSE ! 2,460, MAD ! 42.5 and MAPE ! 2.1 percent. The smoothing constant can also be selected using Solver by minimizing the MAD or the MAPE at the end of 10 periods. In Figure 7-6, we show the results from minimizing MAD (cell G13). The forecasts and errors with the resulting ! ! 0.32 are shown in Figure 7-6. In this case, the MSE increases to 2,570 (compared to 2,460 in Figure 7-5) while the MAD decreases to 39.2 (compared to 42.5 in Figure 7-5) and the MAPE decreases to 2.0 percent (compared to 2.1 percent in Figure 7-5). The major difference between the two forecasts is in period 9 (the period with the largest error shown in cell D11), where minimizing MSE picks a smoothing constant that reduces large errors, while minimizing MAD picks a smoothing constant that gives equal weight to reducing all errors even if large errors get somewhat larger. FIGURE 7-5 Selecting Smoothing Constant by Minimizing MSE M07_CHOP3952_05_SE_C07.QXD 10/22/11 6:54 PM Page 196 Chapter 7 • Demand Forecasting in a Supply Chain 197 In general, it is not a good idea to use smoothing constants much larger than 0.2 for extended periods of time. A larger smoothing constant may be justified for a short period of time when demand is in transition. It should, however, generally be avoided for extended periods of time. 7.8 FORECASTING DEMAND AT TAHOE SALT Recall the Tahoe Salt example earlier in the chapter …