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© Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter3 MGMT 405, POM, 2010/11. Lec Notes Chapter 3: Forecasting Department of Business Administration FALL 20 10 - 2011 I see that you will get an A this semester.

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 2 Outline: What You Will Learn... List the elements of a good forecast. Outline the steps in the forecasting process. Describe at least three qualitative forecasting techniques and the advantages and disadvantages of each. Compare and contrast qualitative and quantitative approaches to forecasting. Briefly describe averaging techniques, trend and seasonal techniques, and regression analysis, and solve typical problems. Describe two measures of forecast accuracy. Describe two ways of evaluating and controlling forecasts. Identify the major factors to consider when choosing a forecasting technique

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 3 What is meant by Forecasting and Why? Forecasting is the process of estimating a variable, such as the sale of the firm at some future date. Forecasting is important to business firm, government, and non-profit organization as a method of reducing the risk and uncertainty inherent in most managerial decisions. A firm must decide how much of each product to produce, what price to charge, and how much to spend on advertising, and planning for the growth of the firm.

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 4 The aim of forecasting The aim of forecasting is to reduce the risk or uncertainty that the firm faces in its short-term operational decision making and in planning for its long term growth. Forecasting the demand and sales of the firm’s product usually begins with macroeconomic forecast of general level of economic activity for the economy as a whole or GNP.

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 5 The aim of forecasting The firm uses the macro-forecasts of general economic activity as inputs for their micro-forecasts of the industry’s and firm’s demand and sales. The firm’s demand and sales are usually forecasted on the basis of its historical market share and its planned marketing strategy (i.e., forecasting by product line and region). The firm uses long-term forecasts for the economy and the industry to forecast expenditure on plant and equipment to meet its long-term growth plan and strategy.

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 6 Forecasting Process Map Marketing Sales Product Management Management & Finance ExecutiveManagement Production & Inventory InventoryControl CausalFactors Statistical Model DemandHistory ConsensusProcess ConsensusForecast

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 7 AccountingCost/profit estimates FinanceCash flow and funding Human ResourcesHiring/recruiting/training MarketingPricing, promotion, strategy MISIT/IS systems, services OperationsSchedules, MRP, workloads Product/service designNew products and services Uses of Forecasts

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 8 Assumes causal system past ==> future Forecasts rarely perfect because of randomness Forecasts more accurate for groups vs. individuals Forecast accuracy decreases as time horizon increases I see that you will get an A this semester. Features of Forecasts

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 9 Elements of a Good Forecast Timely Accurate Reliable Meaningful Written Easy to use

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 10 Steps in the Forecasting Process Step 1 Determine purpose of forecast Step 2 Establish a time horizon Step 3 Select a forecasting technique Step 4 Obtain, clean and analyze data Step 5 Make the forecast Step 6 Monitor the forecast “The forecast”

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 11 Forecasting Techniques naïve methods highly complex approaches A wide variety of forecasting methods are available to management. These range from the most naïve methods that require little effort to highly complex approaches that are very costly in terms of time and effort such as econometric systems of simultaneous equations. Qualitative approaches (Judgmental forecasts)Quantitative approaches (Time- series forecasts) and Associative model forecasts). Mainly these techniques can break down into three parts: Qualitative approaches (Judgmental forecasts) and Quantitative approaches (Time- series forecasts) and Associative model forecasts).

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 12 Judgmental - uses subjective inputs such as opinion from consumer surveys, sales staff etc.. Time series - uses historical data assuming the future will be like the past Associative models - uses explanatory variables to predict the future Forecasting Techniques

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 13 Survey Techniques Some of the best-know surveys Planned Plant and Equipment Spending Expected Sales and Inventory Changes Consumers’ Expenditure Plans Opinion Polls Business Executives Sales Force Consumer Intentions Qualitative Forecasts or Judgmental Forecasts

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 14 What are qualitative forecast ? Qualitative forecast estimate variables at some future date using the results of surveys and opinion polls of business and consumer spending intentions. The rational is that many economic decisions are made well in advance of actual expenditures. For example, businesses usually plan to add to plant and equipment long before expenditures are actually incurred.

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 15 Surveys and opinion pools are often used to make short-term forecasts when quantitative data are not available Usually based on judgments about causal factors that underlie the demand of particular products or services Do not require a demand history for the product or service, therefore are useful for new products/services Approaches vary in sophistication from scientifically conducted surveys to intuitive hunches about future events The approach/method that is appropriate depends on a product’s life cycle stage Qualitative Forecasts or Judgmental Forecasts

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 16 Polls can also be very useful in supplementing quantitative forecasts, anticipating changes in consumer tastes or business expectations about future economic conditions, and forecasting the demand for a new product. Firms conduct opinion polls for economic activities based on the results of published surveys of expenditure plans of businesses, consumers and governments. Qualitative Forecasts or Judgmental Forecasts

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 17 lSurvey Techniques– The rationale for forecasting based on surveys of economic intentions is that many economic decisions are made in advance of actual expenditures (Ex: Consumer’s decisions to purchase houses, automobiles, TV sets, furniture, vocation, education etc. are made months or years in advance of actual purchases) lOpinion Polls– The firm’s sales are strongly dependent on the level of economic activity and sales for the industry as a whole, but also on the policies adopted by the firm. The firm can forecast its sales by pooling experts within and outside the firm. Qualitative Forecasts or Judgmental Forecasts

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 18 lExecutive Polling- Firm can poll its top management from its sales, production, finance for the firm during the next quarter or year. lBandwagon effect (opinions of some experts might be overshadowed by some dominant personality in their midst). lDelphi Method – experts are polled separately, and then feedback is provided without identifying the expert responsible for a particular opinion. Qualitative Forecasts or Judgmental Forecasts

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 19 Consumers intentions polling- Consumers intentions polling- Firms selling automobiles, furniture, etc. can pool a sample of potential buyers on their purchasing intentions. By using results of the poll a firm can forecast its sales for different levels of consumer’s future income. Sales force polling – Sales force polling – Forecast of the firm’s sales in each region and for each product line, it is based on the opinion of the firm’s sales force in the field (people working closer to the market and their opinion about future sales can provide essential information to top management). Qualitative Forecasts or Judgmental Forecasts

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 20 Based on the assumption, the “forces” that generated the past demand will generate the future demand, i.e., history will tend to repeat itself. Analysis of the past demand pattern provides a good basis for forecasting future demand. Majority of quantitative approaches fall in the category of time series analysis. Quantitative Forecasting Approaches

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 21 Time Series Analysis A time series (naive forecasting) is a set of numbers where the order or sequence of the numbers is important, i.e., historical demand Attempts to forecasts future values of the time series by examining past observations of the data only. The assumption is that the time series will continue to move as in the past Analysis of the time series identifies patterns Once the patterns are identified, they can be used to develop a forecast

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 22 Forecast Horizon Short term Up to a year Medium term One to five years Long term More than five years

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 23 Reasons for Fluctuations in Time Series Data Secular Trend are noted by an upward or downward sloping line- long-term movement in data (e.g. Population shift, changing income and cultural changes). Cycle fluctuations is a data pattern that may cover several years before it repeats itself- wavelike variations of more than one year’s duration (e.g. Economic, political and agricultural conditions). Seasonality is a data pattern that repeats itself over the period of one year or less- short-term regular variations in data (e.g. Weekly or daily restaurant and supermarket experiences). Irregular variations caused by unusual circumstances (e.g. Severe weather conditions, strikes or major changes in a product or service). Random influences (noise) or variations results from random variation or unexplained causes. (e.g. residuals)

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 24 Forecast Variations Trend Irregular variatio n Seasonal variations 90 89 88 Cycles

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 25 Stable time series data F(t) = A(t-1) Seasonal variations F(t) = A(t-n) Data with trends F(t) = A(t-1) + (A(t-1) – A(t-2)) Uses for Naïve Forecasts

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 26 Techniques for Averaging Moving average Weighted moving average Exponential smoothing

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 27 Moving Averages Moving average – A technique that averages a number of recent actual values, updated as new values become available. F t = MA n = n A t-n + … A t-2 + A t-1 F t = WMA n = w n A t-n + … w n-1 A t-2 + w 1 A t-1 Weighted moving average – More recent values in a series are given more weight in computing the forecast. n n=total amount of number of weights n= number of period

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 28 Simple Moving Average Actual MA3 MA5 F t = MA n = n A t-n + … A t-2 + A t-1

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 29 Simple Moving Average An averaging period (AP) is given or selected The forecast for the next period is the arithmetic average of the AP most recent actual demands It is called a “simple” average because each period used to compute the average is equally weighted It is called “moving” because as new demand data becomes available, the oldest data is not used By increasing the AP, the forecast is less responsive to fluctuations in demand (low impulse response and high noise dampening) By decreasing the AP, the forecast is more responsive to fluctuations in demand (high impulse response and low noise dampening)

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 30 Exponential Smoothing Premise--The most recent observations might have the highest predictive value. Therefore, we should give more weight to the more recent time periods when forecasting. Weighted averaging method based on previous forecast plus a percentage of the forecast error A-F is the error term, is the % feedback F t = F t-1 + ( A t-1 - F t-1 ) F t = forecast for period t F t-1 = forecast for the previous period smoothing constant A t-1 = actual data for the previous period

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 31 Exponential Smoothing Forecasts The weights used to compute the forecast (moving average) are exponentially distributed. The forecast is the sum of the old forecast and a portion (a) of the forecast error (A t-1 - F t-1 ). The smoothing constant, , must be between 0.0 and 1.0. A large provides a high impulse response forecast. A small provides a low impulse response forecast.

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 32 Example-Moving Average Central Call Center (CCC) wishes to forecast the number of incoming calls it receives in a day from the customers of one of its clients, BMI. CCC schedules the appropriate number of telephone operators based on projected call volumes. CCC believes that the most recent 12 days of call volumes (shown on the next slide) are representative of the near future call volumes.

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 33 Moving Average Use the moving average method with an AP = 3 days to develop a forecast of the call volume in Day 13 (The 3 most recent demands) compute a three-period average forecast given scenario above: F13 = (168 + 198 + 159)/3 = 175.0 calls Example-Moving Average

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 34 Example-Weighted Moving Average Weighted Moving Average (Central Call Center ) Use the weighted moving average method with an AP = 3 days and weights of.1 (for oldest datum),.3, and.6 to develop a forecast of the call volume in Day 13. compute a weighted average forecast given scenario above: F13 =.1(168) +.3(198) +.6(159) = 171.6 calls Note: The WMA forecast is lower than the MA forecast because Day 13’s relatively low call volume carries almost twice as much weight in the WMA (.60) as it does in the MA (.33). 1

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 35 Example-Exponential Smoothing Exponential Smoothing ( Exponential Smoothing (Central Call Center) Suppose a smoothing constant value of.25 is used and the exponential smoothing forecast for Day 11 was 180.76 calls. Suppose a smoothing constant value of.25 is used and the exponential smoothing forecast for Day 11 was 180.76 calls. what is the exponential smoothing forecast for Day 13? what is the exponential smoothing forecast for Day 13? F12 = 180.76 +.25(198 – 180.76) = 185.07 F12 = 180.76 +.25(198 – 180.76) = 185.07 F13 = 185.07 +.25(159 – 185.07) = 178.55 F13 = 185.07 +.25(159 – 185.07) = 178.55

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 36 Example 2-Exponential Smoothing Exponential Smoothing (Actual Exponential Smoothing (Actual Demand forecasting ) Suppose a smoothing constant value of.10 is used and the exponential smoothing forecast for the previous period was 42 units (actual demand was 40 units). Suppose a smoothing constant value of.10 is used and the exponential smoothing forecast for the previous period was 42 units (actual demand was 40 units). what is the exponential smoothing forecast for the next periods? what is the exponential smoothing forecast for the next periods? F3 = 42 +.10(40 – 42) = 41.8 F3 = 42 +.10(40 – 42) = 41.8 F4 = 41.8 +.10(43 – 41.8) = 41.92 F4 = 41.8 +.10(43 – 41.8) = 41.92

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 37 .1 .4 Actual Example 2-Exponential Smoothing Graphical presentation

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 38 Trend Projection The simplest form of time series is projecting the past trend by fitting a straight line to the data either visually or more precisely by regression analysis. Linear regression analysis establishes a relationship between a dependent variable and one or more independent variables. In simple linear regression analysis there is only one independent variable. If the data is a time series, the independent variable is the time period. The dependent variable is whatever we wish to forecast.

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 39 Linear Trend Equation Ft = Forecast for period t t = Specified number of time periods a = Value of Ft at t = 0 b = Slope of the line F t = a + bt 0 1 2 3 4 5 t FtFt

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 40 Trend Projection Linear Trend: S t = S 0 + b t b = Growth per time period Constant Growth Rate S t = S 0 (1 + g) t g = Growth rate Estimation of Growth Rate ln S t = ln S 0 + t ln (1 + g)

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 41 Trend Projection- Simple Linear Regression Regression Equation This model is of the form: Y = a + bX Y = dependent variable (the value of time series to be forecasted for period t) X = independent variable ( time period in which the time series is to be forecasted) a = y-axis intercept (estimated value of the time series, the constant of the regression) b = slope of regression line (absolute amount of growth per period)

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 42 Trend Projection- Calculating a and b a b Constants a and b ab The constants a and b are computed using the equations given: a b Once the a and b values are computed, a future value of X can be entered into the regression equation and a corresponding value of Y (the forecast) can be calculated.

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 43 Trend Projection- Calculating a and b Or If formula b is used first, it may be used formula a in the following format:

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 44 Example 1 for Trend Projection- Electricity sales next four quarters. Suppose we have the data show electricity sales in a city between 1997.1 and 2000.4. The data are shown in the following table. Use time series regression to forecast the electricity consumption (mn kilowatt) for the next four quarters. Do not forget to use the formulae a and b

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 45 Example1 for Trend Projection

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 46 Example1 for Trend Projection Y = 11.90 + 0.394X Y17 = 11.90 + 0.394(17) = 18.60 in the first quarter of 2001 Y18 = 11.90 + 0.394(18) = 18.99 in the second quarter of 2001 Y19 = 11.90 + 0.394(19) = 19.39 in the third quarter of 2001 Y20 = 11.90 + 0.394(20) = 19.78 in the fourth quarter of 2001 Note: Electricity sales are expected to increase by 0.394 mn kilowatt-hours per quarter.

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 47 Example 2 for Trend Projection Estimate a trend line using regression analysis Year Time Period (t) Sales (y) 2003 2004 2005 2006 2007 2008 123456123456 20 40 30 50 70 65 Use time (t) as the independent variable:

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 48 Example 2 for Trend Projection The linear trend model is: Year Time Period (t) Sales (y) 2003 2004 2005 2006 2007 2008 123456123456 20 40 30 50 70 65 (continued)

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 49 Example 2 for Trend Projection Forecast for time period 7: Year Time Period (t) Sales (y) 2003 2004 2005 2006 2007 2008 2009 12345671234567 20 40 30 50 70 65 ?? (continued)

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 50 Example for Trend Projection using-Non linear form S t = S 0 (1 + g) t Running the regression above in the form of logarithms: ln St = ln S0 + t ln (1 + g) to construct the equation which has coefficients a and b. Antilog of 2.49 is 12.06 and Antilog of 0.026 is 1.026. S t = 12.06(1.026) t

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 51 Example for Trend Projection using St = S 0 (1 + g) t S17= 12.06(1.026)17 = 18.66 in the first quarter of 2001 S18= 12.06(1.026)18 = 19.14 in the second quarter of 2001 S19= 12.06(1.026)19 = 19.64 in the third quarter of 2001 S20= 12.06(1.026)20= 20.15 in the fourth quarter of 2001 These forecasts are similar to those obtained by fitting a linear trend

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 52 Evaluating Forecast-Model Performance Accuracy Accuracy is the typical criterion for judging the performance of a forecasting approach Accuracy is how well the forecasted values match the actual values Accuracy of a forecasting approach needs to be monitored to assess the confidence you can have in its forecasts and changes in the market may require reevaluation of the approach Accuracy can be measured in several ways Standard error of the forecast (SEF) Mean absolute deviation (MAD) Mean squared error (MSE) Mean absolute percent error (MAPE) Root mean squared error (RMSE)

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 53 Forecast Accuracy Error - difference between actual value and predicted value Mean Absolute Deviation (MAD) Average absolute error Mean Squared Error (MSE) Average of squared error Mean Absolute Percent Error (MAPE) Average absolute percent error Root Mean Squared Error (RMSE) Root Average of squared error

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 54 MAD, MSE, and MAPE MAD = Actualforecast n MSE = Actualforecast ) - 1 2 n ( MAPE = Actualforecas t n / Actual*100)

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 55 MAD, MSE and MAPE MAD Easy to compute Weights errors linearly MSE Squares error More weight to large errors MAPE Puts errors in perspective RMSE Root of Squares error More weight to large errors

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 56 Example-MAD, MSE, and MAPE Compute MAD, MSE and MAP for the following data showing actual and the predicted numbers of account serviced. 22/8=2.75 76/8-1=10.86 10.26/8=1.28 %

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 57 Example: Central Call Center-Forecast Accuracy - MAD Which forecasting method (the AP = 3 moving average or the a =.25 exponential smoothing) is preferred, based on the MAD over the most recent 9 days? (Assume that the exponential smoothing forecast for Day 3 is the same as the actual call volume.)

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 58 MAD MA = 20.5/9 = 2.27 MAD MA = 20.5/9 = 2.27 Example: Central Call Center-Forecast Accuracy - MAD MAD EXP = 18.0/9= 2.0 MAD EXP = 18.0/9= 2.0 E AP4 = 161-187.3=26.3 E AP4 = 161-187.3=26.3 E EXP4 = 161-186=25.0 E EXP4 = 161-186=25.0 F4 MA = (186 + 217 + 159)/3 = 187.33 calls F4 MA = (186 + 217 + 159)/3 = 187.33 calls F4 EXP = 186 +.25(186 – 186) = 186.00 calls F4 EXP = 186 +.25(186 – 186) = 186.00 calls

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 59 Example-For MA Techniques Electricity sales data from 2000.1 to 2002.4 (t=12)-Forecast Accuracy - RMSE AP = 3 moving average AP = 5 moving average

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 60 Example-For MA Techniques Electricity sales data from 2000.1 to 2002.4 (t=12)-Forecast Accuracy - RMSE RMSE for 3-qma=2.95 RMSE for 5-qma=2.99 Thus three-quarter moving average forecast is marginally better than the corresponding five- moving average forecast. Sqroot of 78.33/9=2.95 Sqroot of 62.48/7=2.98

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 61 Example-Exponential Smoothing Forecast Accuracy - RMSE F 2 = 0.3 (20)+(1-0.3) 21=20.7 with w=0.3 F 2 = 0.5 (20)+(1-0.5) 21=20.5 with w=0.5 (20+22+...23)/12=21=F 1

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 62 Example-Exponential Smoothing Forecast Accuracy - RMSE F 2 = 0.3 (20)+(1-0.3) 21=20.7 with w=0.3 F 2 = 0.5 (20)+(1-0.5) 21=20.5 with w=0.5 RMSE with w=0.3 is 2.70 RMSE with w=0.5 is 2.91 Both exponential forecasts are better than the previous techniques in terms of average values.

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 63 Seasonal Variation

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 64 Seasonal Variation Ratio to Trend Method Actual Trend Forecast Ratio = Seasonal Adjustment = Average of Ratios for Each Seasonal Period Adjusted Forecast = Trend Forecast Seasonal Adjustment

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 65 Seasonal Variation Ratio to Trend Method: Example Calculation for Quarter 1 Trend Forecast for 2001.1 = 11.90 + (0.394)(17) = 18.60 Seasonally Adjusted Forecast for 2001.1 = (18.60)(0.887) = 16.50 Deseasonalize data=actual sales/seasonal relative (index)

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 66 Seasonal Variation Select a representative historical data set. Develop a seasonal index for each season. Use the seasonal indexes to deseasonalize the data. Perform linear regression analysis on the deseasonalized data. Use the regression equation to compute the forecasts. Use the seasonal indexes to reapply the seasonal patterns to the forecasts.

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 67 Example: Computer Products Corp. Seasonalized Times Series Regression Analysis An analyst at CPC wants to develop next year’s quarterly forecasts of sales revenue for CPC’s line of Epsilon Computers. The analyst believes that the most recent 8 quarters of sales (shown on the next slide) are representative of next year’s sales. Calculate the seasonal indexes

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 68 Example: Computer Products Corp.

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 69 Example: Computer Products Corp.

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 70 Unseasonalized vs. Seasonalized Quarter Seasonalized Sales Seasonal Index Deseasonalized Sales 1 2 3 4 5 6 7 8 9 10 11 … 23 40 25 27 32 48 33 37 50 40 0.825 1.310 0.920 0.945 0.825 1.310 0.920 0.945 0.825 1.310 0.920 … 27.88 30.53 27.17 28.57 38.79 36.64 35.87 39.15 44.85 38.17 43.48 …

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 71 Deflating a Time Series Observed values can be adjusted to base year equivalent Allows uniform comparison over time Deflation formula: where = adjusted time series value at time t y t = value of the time series at time t I t = index value at time t

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 72 Deflating a Time Series: Example Which movie made more money (in real terms)? Year Movie Title Total Gross $ 1939 Gone With the Wind 199 1977Star Wars461 1997Titanic601 (Total Gross $ = Total domestic gross ticket receipts in $millions)

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 73 Deflating a Time Series: Example Year Movie Title Total Gross CPI (base year = 1984) Gross adjusted to 1984 dollars 1939 Gone With the Wind 19913.91431.7 1977Star Wars46160.6760.7 1997Titanic601160.5374.5 GWTW made about twice as much as Star Wars, and about 4 times as much as Titanic when measured in equivalent dollars

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MGMT 405, POM, 2010/11. Lec Notes © Stevenson, McGraw Hill, 2007- Assoc. Prof. Sami Fethi, EMU, All Right Reserved. Forecasting; Chapter 3 74 Thanks

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