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10 th ed. I see that you will get an A this semester. Forecasting 10 th ed. I see that you will get an A this semester. Forecasting 3 -1

FORECAST: § A statement about the future value of a variable of interest such FORECAST: § A statement about the future value of a variable of interest such as demand. § Forecasting is used to make informed decisions. § Long-range § Short-range 3 -2

Features of Forecasts § Assumes causal system past ==> future § Forecasts rarely perfect Features of Forecasts § 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 3 -3

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Uses of Forecasts § Forecasts affect decisions and activities throughout an organization § Accounting, Uses of Forecasts § Forecasts affect decisions and activities throughout an organization § Accounting, finance § Human resources § Marketing § MIS § Operations § Product / service design 3 -5

Examples of Forecasting Uses Accounting Cost/profit estimates Finance Cash flow and funding Human Resources Examples of Forecasting Uses Accounting Cost/profit estimates Finance Cash flow and funding Human Resources Hiring/recruiting/training Marketing Pricing, promotion, strategy MIS IT/IS systems, services Operations Schedules, MRP, workloads Product/service design Timing of new products and services 3 -6

Elements of a Good Forecast Timely Reliable ul M e gf in an Accurate Elements of a Good Forecast Timely Reliable ul M e gf in an Accurate Written sy Ea to se u 3 -7

Steps in the Forecasting Process “The forecast” Step 6 Monitor the forecast Step 5 Steps in the Forecasting Process “The forecast” Step 6 Monitor the forecast Step 5 Make the forecast Step 4 Obtain, clean and analyze data Step 3 Select a forecasting technique Step 2 Establish a time horizon Step 1 Determine purpose of forecast 3 -8

Types of Forecasts § Judgmental - uses subjective inputs (e. g. , sales force Types of Forecasts § Judgmental - uses subjective inputs (e. g. , sales force estimates). § Time series - uses historical data assuming the future will be like the past. Time could be in weeks, months, years, etc. , and is based on t=1, 2, 3, … § Associative models - uses explanatory variables to predict the future. It suggests a causal relationship, such as personal consumption being based on per capita income of households. 3 -9

Judgmental Forecasts § Executive opinions § Sales force opinions § Consumer surveys § Outside Judgmental Forecasts § Executive opinions § Sales force opinions § Consumer surveys § Outside opinion § Delphi method § Opinions of managers and staff § Achieves a consensus forecast 3 -10

Time Series Forecasts § Trend - long-term movement in data § Seasonality - short-term Time Series Forecasts § Trend - long-term movement in data § Seasonality - short-term regular variations in data § Cycle – wavelike variations of more than one year’s duration § Irregular variations - caused by unusual circumstances that are not random § Random variations - caused by chance 3 -11

Forecast Variations Irregular variation Trend Cycles 90 89 88 Seasonal variations 3 -12 Forecast Variations Irregular variation Trend Cycles 90 89 88 Seasonal variations 3 -12

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Some Common Time Series Techniques or Time Series Forecasting Models § Naïve forecasts § Some Common Time Series Techniques or Time Series Forecasting Models § Naïve forecasts § Moving average § Weighted moving average § Exponential smoothing 3 -15

Naive Forecasts The forecast for any period equals the previous period’s actual value. 3 Naive Forecasts The forecast for any period equals the previous period’s actual value. 3 -16

Naïve Forecasts § § § § Simple to use Virtually no cost Quick and Naïve Forecasts § § § § Simple to use Virtually no cost Quick and easy to prepare Data analysis is nonexistent Easily understandable Cannot provide high accuracy Can be a standard for accuracy 3 -17

Formula for Naïve Forecasts § Ft = At-1 This is the forecasting that is Formula for Naïve Forecasts § Ft = At-1 This is the forecasting that is the most responsive to changes in the past actual demand. 3 -18

Moving Average Formula § Moving average – A technique that averages a number of Moving Average Formula § Moving average – A technique that averages a number of recent actual values, updated as new values become available. Ft = MAn= At-n + … At-2 + At-1 n § Weighted moving average – More recent values in a series are given more weight in computing the forecast. Ft = WMAn= wn. At-n + … wn-1 At-2 + w 1 At-1 3 -19

Simple Moving Average Actual Demand MA 5 MA 3 Ft = MAn= At-1 + Simple Moving Average Actual Demand MA 5 MA 3 Ft = MAn= At-1 + At-2 + … At-n n 3 -20

Exponential Smoothing Ft = Ft-1 + (At-1 - Ft-1) § Weighted averaging method based Exponential Smoothing Ft = Ft-1 + (At-1 - Ft-1) § Weighted averaging method based on previous forecast plus a percentage of the forecast error § A-F is the error term, is the % feedback 3 -21

Exponential Smoothing Formula Ft = Ft-1 + (At-1 - Ft-1) • Premise--The most recent Exponential Smoothing Formula Ft = Ft-1 + (At-1 - Ft-1) • 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. § The symbol “α” is the Greek letter “alpha. ” Alpha is called the smoothing constant. Note that alpha varies from zero to one. 3 -22

Exponential Smoothing 3 -23 Exponential Smoothing 3 -23

Picking a Smoothing Constant Actual . 4 . 1 3 -24 Picking a Smoothing Constant Actual . 4 . 1 3 -24

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Homework Problem Referring to page 118 in the text, do problems 2 a and Homework Problem Referring to page 118 in the text, do problems 2 a and 2 b, but skip problem 2 b(1) which asks for a linear trend equation. Complete and partial solutions of homework problems are found on the slides at the end of this session. For this problem and for all homework problems, do not go to the solutions until you have made a strong effort to solve the problems. 3 -26

Linear Trend Equation Ft Ft = Yt = a + bt 0 1 2 Linear Trend Equation Ft Ft = Yt = a + bt 0 1 2 3 4 5 § § t Ft = Forecast for period t t = The time period being forecasted a = Value of Ft at t = 0 b = Slope of the line 3 -27

Calculating a and b Yt = a + bt where b and a follow Calculating a and b Yt = a + bt where b and a follow from the following formulae: n (ty) - t y b = 2 - ( t) 2 n t y - b t a = n 3 -28

Linear Trend Equation Example Calculations of b and a are from the sums given Linear Trend Equation Example Calculations of b and a are from the sums given in the table on Ft = Yt = a + bt the left. n = 10 Ft = Yt = a + bt = 67. 78 + 5. 79 t 3 -29

Plot of Previous Slide Y t 3 -30 Plot of Previous Slide Y t 3 -30

Homework Problem Referring to page 118 in the text, do 2 b(1), which asks Homework Problem Referring to page 118 in the text, do 2 b(1), which asks for a linear trend equation. Also, do problem 2 c. However, change problem 2 c to read as follows: “Which method seems MOST appropriate? Why? ” 3 -31

Associative Forecasting § Associative models - uses explanatory variables to predict the future. It Associative Forecasting § Associative models - uses explanatory variables to predict the future. It suggests a causal relationship, such as personal consumption being based on per capita income of households 3 -32

Example of an Associative Forecast: Using x to Predict y Computed relationship A straight Example of an Associative Forecast: Using x to Predict y Computed relationship A straight line is fitted to a set of sample points. 3 -33

Example of an Associative Forecast Equation for Automobiles (with several variables, and nonlinear) 3 Example of an Associative Forecast Equation for Automobiles (with several variables, and nonlinear) 3 -34

Forecast Accuracy § Error - difference between actual value and predicted value § Mean 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 3 -35

Some Measures of Forecasting Accuracy MAD = Actual forecast n MSE = ( Actual Some Measures of Forecasting Accuracy MAD = Actual forecast n MSE = ( Actual forecast) 2 n -1 Note that the errors are taken for each of the past n periods where the actual demand is known. 3 -36

Some Characteristics of MAD and MSE § MAD § Easy to compute § Weights Some Characteristics of MAD and MSE § MAD § Easy to compute § Weights errors linearly § MSE § Squares error § More weight to large errors 3 -37

Sources of Forecast errors § Model may be inadequate § Irregular variations § Incorrect Sources of Forecast errors § Model may be inadequate § Irregular variations § Incorrect use of forecasting technique 3 -38

In-class assignment The next two slides ask some basic questions about forecasting, and give In-class assignment The next two slides ask some basic questions about forecasting, and give some examples of measuring forecasting error. These slides make up an in-class assignment. You can try to answer the questions on the slides. However, if you have difficulty with all or some of the questions, we will do them in class. At least become familiar with the questions before the next class. If you find the next two slides difficult to read, simply magnify the size of the slides. If you can, please try to print a hardcopy of the next two slides and bring them to class. If you can set the resolution of your printer, it is suggested that you set it to a high resolution for the best printed copy. 3 -39

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Choosing a Forecasting Technique § No single technique works in every situation § Two Choosing a Forecasting Technique § No single technique works in every situation § Two most important factors § Cost § Accuracy § Other factors include the availability of: § § Historical data Computers Time needed to gather and analyze the data Forecast horizon 3 -42

Good Operations Strategy § Understand that forecasts are the basis for many decisions § Good Operations Strategy § Understand that forecasts are the basis for many decisions § Work to improve short-term forecasts § Understand that accurate short-term forecasts have benefits for the following: § § § Profits Lower inventory levels Reduce inventory shortages Improve customer service levels Enhance forecasting credibility 3 -43

Supply Chain Forecasts § Sharing forecasts with suppliers can § Improve forecast quality in Supply Chain Forecasts § Sharing forecasts with suppliers can § Improve forecast quality in the supply chain § Lower costs § Lead to shorter lead times 3 -44

Common Nonlinear Trends Parabolic Exponential Growth 3 -45 Common Nonlinear Trends Parabolic Exponential Growth 3 -45

Exponential Smoothing 3 -46 Exponential Smoothing 3 -46

Linear Trend Equation 3 -47 Linear Trend Equation 3 -47

Simple Linear Regression 3 -48 Simple Linear Regression 3 -48

Homework Problem Solutions 2 a Sales 20 0 F M A M Month J Homework Problem Solutions 2 a Sales 20 0 F M A M Month J J A S 3 -49

2 b(1) t Y t 2 1 19 19 1 2 18 36 4 2 b(1) t Y t 2 1 19 19 1 2 18 36 4 3 15 45 9 4 20 80 16 5 18 90 25 6 22 132 36 7 20 140 49 28 132 542 140 To solve this problem, we need to plug the appropriate values into the equation Ft = Yt = a + bt Hence, n = 7, t = 28, t 2 = 140 Therefore, Yt = 16. 86 +. 50 t For the September forecast, t = 8, and Yt = 16. 86 +. 50(8) = 20. 86 3 -50

2 b(2) 3 -51 2 b(2) 3 -51

2 b(3) Ft = Ft-1 + (At-1 - Ft-1) Month Forecast = F(old) + 2 b(3) Ft = Ft-1 + (At-1 - Ft-1) Month Forecast = F(old) + . 20[Actual – F(old)] April 18. 8 = 19 + . 20[ 18 – 19 ] May 18. 04= 18. 8 + . 20[ 15 – 18. 8 ] June 18. 43= 18. 04 + . 20[ 20 – 18. 04 ] July 18. 34= 18. 43 + . 20[ 18 – 18. 43 ] August 19. 07= 18. 34 + . 20[ 22 – 18. 34 ] September 19. 26= 19. 07 + . 20[ 20 – 19. 07 ] Answer is 19. 26 (or actually, 19, 260 units). 3 -52

2 b(4) Ft = At-1 This formula is telling us that the forecast in 2 b(4) Ft = At-1 This formula is telling us that the forecast in period t is simply the actual demand for period t-1, or simply, the actual demand of the previous period. For the September forecast, the answer would be the actual demand in August. Hence, the answer is 20 (or 20, 000 units) 3 -53

2 b(5) Ft = WMAn= wn. At-n + … wn-1 At-2 + w 1 2 b(5) Ft = WMAn= wn. At-n + … wn-1 At-2 + w 1 At-1 =. 6 (20) +. 3(22) +. 1(18) = 20. 4, (or 20, 400 units) Note that the more recent actual demand values are usually given more weight in computing the forecast. 3 -54

2 c Change this problem to read “which method seems the most appropriate? ” 2 c Change this problem to read “which method seems the most appropriate? ” To logically find the answer, go back to the plot in 2 a, and make your best guess as to where the September actual demand might be on the plot or graph. Hence, you need to see a pattern on the plot. Once you have September on the plot, find the method from part b of the problem which comes the closest to your guess on the plot. The answer should be the linear trend equation. 3 -55

See you next class 3 -56 See you next class 3 -56