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**3 Demand Forecasting Slides prepared by Laurel Donaldson**

Douglas College

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LO 1 Identify uses of demand forecasts, distinguish between forecasting time frames, describe common features of forecasts, list the elements of a good forecast and steps of forecasting process, and contrast different forecasting approaches. Describe at least three judgmental forecasting methods. Describe the components of a time series model, and explain averaging techniques and solve typical problems. Describe trend forecasting and solve typical problems. Describe seasonality forecasting and solve typical problems. Describe associative models and solve typical problems. Describe three measures of forecast accuracy, and two ways of controlling forecasts, and solve typical problems. Identify the major factors to consider when choosing a forecasting technique. LO 2 LO 3 LO 4 LO 5 LO 6 LO 7 LO 8

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What is forecasting? Features common to all forecasts Elements of a good forecast Steps in the forecasting process Approaches to forecasting Judgmental methods Time series models Associative models Accuracy and control of forecasts Choosing a forecasting technique Excel Templates

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What is Forecasting? A demand forecast is an estimate of demand expected over a future time period I see that you will get a 100 in OM this semester. p56

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**Need to FORECAST demand!**

How big a facility do I need to manufacture a new videophone? How much money do I need to run operations of my accounting office? How many pairs of white shoes should I order for the summer season in my store? How many operators should I schedule next month for my call centre? How much lettuce should I buy for next week in my restaurant?

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**3 Uses for Forecasts: Design the System long term (annual)**

(types of products & services to offer, capacities, equipment, location) Use of the System medium term (monthly) (inventory, workforce levels, planning production) Schedule the System short term (daily, weekly) (production, purchasing, staff scheduling) p56 and 59-60

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**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 p57-58. A manager cannot simply delegate forecasting to models or computers and then forget about it, because unplanned or special occurrences can wreak havoc with forecasts. For instance, weather-related events, sales promotions, and changes in features or prices of own and competing goods or services can have a major impact on demand. Consequently, a manager must be alert to such occurrences and be ready to override forecasts. flexible businesses that can respond quickly to changes in demand require a shorter forecasting horizon, which may be more accurate, giving an advantage over less flexible ones that need to rely on longer term forecasts

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**Elements of a Good Forecast**

Accurate Reliable Meaningful Compatible Useful time horizon Easy to understand & use p58-59 1. The forecasting horizon must be long enough so that its results can be used. 2. The degree of accuracy of the forecast should be stated. 3. The forecasting method/software chosen should be reliable; it should work consistently. 4. The forecast should be expressed in meaningful units. Financial planners need to know demand in dollars, whereas demand and production planners need to know demand in units. 5. All functions of an organization should be using the same forecast. 6. The forecasting technique should be simple to understand and use.

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**Steps in the Forecasting Process**

1 Determine purpose of forecast 2 Establish a time horizon 3 Select a forecasting technique 4 Obtain, clean and analyze data 5 Make the forecast 6 Monitor the forecast P59

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**Approaches to Forecasting**

Judgmental non-quantitative analysis of subjective inputs considers “soft” information such as human factors, experience, gut instinct Quantitative Time series models extends historical patterns of numerical data Associative models create equations with explanatory variables to predict the future p59

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**Judgmental Methods Executive opinions Expert opinions**

pool opinions of high-level executives long term strategic or new product development Expert opinions Delphi method: iterative questionnaires circulated until consensus is reached. technological forecasting p60-61

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**Judgmental Methods Sales force opinions Consumer surveys**

based on direct customer contact Consumer surveys questionnaires or focus groups Historical analogies use demand for a similar product p60-61

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**The following 6 patterns could be identified in a time series:**

What is a Time Series? Time series: a time ordered sequence of observations taken at regular intervals of time The following 6 patterns could be identified in a time series: Level: (average) horizontal pattern Trend: steady upward or downward movement Seasonality: regular variations related to time of year or day Cycles: wavelike variations lasting more than one year Irregular variations: caused by unusual circumstances, not reflective of typical behaviour Random variations: residual variations after all other behaviours are accounted for (called noise) p61-62

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**Patterns of a Time Series**

Seasonal peaks (winters) Trend component Actual demand line Demand for snowboards Random variation p62-63 Year 1 Year 2 Year 3 Year 4

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**Time series models Naive methods Averaging methods Trend models**

Moving average Weighted moving average Exponential smoothing Trend models Linear and non-linear trend Trend adjusted exponential smoothing Techniques for seasonality Techniques for cycles p61+

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**Naive Methods Next period = last period Simple to use and understand**

Very low cost Low accuracy p 62 Formula or stable is not given. Other formulas stated in words only F = forecast A = actual

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**Naive Method - Example Uh, give me a minute....**

We sold 250 wheels last week.... Now, next week we should sell.... p62 Answer is 250

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**Naive Method with Trend: Example**

2 years ago we sold 50 memberships. Last year we sold 75 memberships. This year we expect to sell … p62 100

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Averaging Methods p63+ F = forecast A = actual = smoothing constant

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Moving Average average of last few actual data values, updated each period easy to calculate and understand smoothes bumps, lags behind changes choose number of periods to include fewer data points = more sensitive to changes more data points = smoother, less responsive p64-65

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**Moving Average - Example**

Compute a three-period moving average forecast for period 6, given the demand below p64

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**Weighted Moving Average - Example**

Compute a 4-period weighted moving average forecast for period 6 using a weight of 0.4 for the most recent period, 0.3 for the next, 0.2 for the next, and 0.1 for the next. p65 The choice of weights may involve the use of trial and error to find a suitable weighting scheme Weights must add up to 100%

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**Moving Average Example**

1 9 2 12 3 14 4 16 5 19 6 23 7 26 Period Demand Forecast 9 12 14 ( )/3 = 11 2/3 ( )/3 = 14 new example ( )/3 = 16 1/3 ( )/3 = 19 1/3

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**Graph of Moving Average**

Moving Average Forecast | | | | | | | | | | | | Quantity 30 – 28 – 26 – 24 – 22 – 20 – 18 – 16 – 14 – 12 – 10 – Actual Sales ask: What is the problem? new example

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**Moving Average Example**

Apply weights of .5 for most recent period, then .3, then .2 1 9 2 12 3 14 4 16 5 19 6 23 7 26 Period Demand Forecast 9 12 14 [(.5 x 14) + (.3 x 12) + (.2 x 9)] = 12.4 new example [(.5 x 16) + (.3 x 14) + (.2 x 12)] = 14.6 [(.5 x 19) + (.3 x 16) + (.2 x 14)] = 17.1 [(.5 x 23) + (.3 x 19) + (.2 x16)] = 20.4

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**Moving Average And Weighted Moving Average**

30 – 25 – 20 – 15 – 10 – 5 – Quantity | | | | | | | | | | | | Actual sales Moving average new example

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**Exponential Smoothing**

sophisticated weighted moving average weights decline exponentially most recent data weighted most subjectively choose smoothing constant ranges from 0 to 1 (commonly .05 to .5) widely used easy to use easy to alter weighting p66-67

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**Exponential Smoothing Formula**

Forecast = previous forecast plus a percentage of the forecast error Actual - Forecast is the error term is the % feedback Ft = Ft-1 + (At-1 - Ft-1) p66 F = forecast A = actual

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**Exponential Smoothing: Alternate Formula**

Forecast = previous forecast plus a percentage of the forecast error is the weight on actual demand (1 -) is the weight on previous forecast Ft = (1 - )Ft-1 + (At-1) p66 F = forecast A = actual

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**Exponential Smoothing: Example**

Forecasted demand = 142 video games Actual demand = 153 Smoothing constant = .20 New forecast = .2 (153) + (1 - .2)(142) = = ≈ 144 games new example using p66 alternate formula

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**Exponential Smoothing: Example**

Forecasted demand = 142 video games Actual demand = 153 Smoothing constant = .20 New forecast = ( ) = = ≈ 144 games new example using p66 formula

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**Exponential Smoothing: Example**

Prepare a forecast using smoothing constant = 0.40. What is the starting point? average of several periods of actual data subjective estimate (for this example, use 60) first actual value (naïve approach) p67 new example

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**Exponential Smoothing: Your Turn!**

What are the exponential smoothing forecasts for periods 2-5 using =0.5? Use naïve approach for 1st week new example 28

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**Exponential Smoothing: Your Turn!**

F2=(.5)(820)+(1 - .5)(820) =820 F3=(.5)(775)+( )(820)=797.5 new example 29

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**Selecting a Smoothing Constant **

225 – 200 – 175 – 150 – | | | | | | | | | Period Demand Actual demand a = .5 a = .1 p67

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**Choosing When demand is fairly stable, use a lower value for **

smoothes out random fluctuations When demand increasing or decreasing, use a higher value for more responsive to real changes Try to find balance trial and error can change over time. p67

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True or False? A moving average forecast tends to be more responsive to changes in the data series when more data points are included in the average. False As compared to a simple moving average, the weighted moving average is more reflective of the recent changes. True A smoothing constant of .1 will cause an exponential smoothing forecast to react more quickly to a sudden change than a value of .3 will.

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**Excel: Exponential Smoothing**

Solved Problem 1: Excel Template p95

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**Techniques for Trend Develop an equation that describes the trend**

Look at historical data p68

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Nonlinear Trends p68

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**Linear Trend Equation Fit a trend line to a series of historical data**

Use regression to find the equation of the line (called the Least Squares Line) p68-69

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**Linear Trend Actual observation Demand Points on the line Time**

Deviation Time Demand Actual observation Points on the line p68

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Linear Trend: Example new example, like p69

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**Excel - Linear Trend Or Insert Functions:**

Insert Chart Scatter Highlight data range Right Click on a data point Add Trendline Type: Linear Options: Show equation on chart p83 Or Insert Functions: =SLOPE(Range of y's,Range of x's) =INTERCEPT(Range of y's,Range of x's)

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Excel - Linear Trend p82

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**Trend-Adjusted Exponential Smoothing**

select values (usually through trial and error) for a = smoothing constant for average b = smoothing constant for trend estimate starting smoothed average and smoothed trend use most recent data p72-73 aka “double exponential smoothing” simple smoothing lags behind a trend, so adjust by adding a smoothed trend to the smoothed average

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**Trend-Adjusted Exponential Smoothing**

TAFt+1 = St + Tt (3–6) St = TAFt +α(At TAFt) (3–7) Tt = Tt-1 + ( St St-1 Tt-1) p72-73 aka “double exponential smoothing” simple smoothing lags behind a trend, so adjust by adding a smoothed trend to the smoothed average where St = smoothed average at the end of period t Tt = smoothed trend at the end of period t

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**Trend-Adjusted Forecast: Example**

Table 3-1 p72

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**Techniques for Seasonality**

Additive or Multiplicative Model quantity added to average or trend or proportion x average or trend Additive Model Demand = Trend + Seasonality Demand p73-74 examples of seasonality are retail trade, ice cream production, and residential natural gas sales Most seasonal variations repeat annually. also applied to shorter lengths of repeating patterns. e.g. rush hour traffic occurs twice a day Theatres and restaurants demand higher on Fridays or weekend Banks may experience daily and weekly repeating “seasonal” variations (heavier traffic at lunch, just before closing, on Friday) Multiplicative Model Demand = Trend x Seasonality time

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**Using Seasonal Relatives**

Seasonal Relative (or index) = proportion of average or trend for a season in the multiplicative model seasonal relative of 1.2 = 20% above average Deseasonalize remove seasonal component to more clearly see other components divide by seasonal relative Reseasonalize adjust the forecast for seasonal component multiply by seasonal relative p74

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**Times Series Decomposition**

1. Compute the seasonal relatives. 2. De-seasonalize the demand data. 3. Fit a model to de-seasonalized demand data, e.g., moving average or trend. 4. Forecast using this model and the de-seasonalized demand data. 5. Re-seasonalize the deseasonalized forecasts. p74

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**Techniques for Seasonality - Example**

Predict quarterly demand for a certain loveseat The series has both trend and seasonality. Quarterly relatives : Q1 = 1.20, Q2 = 1.10, Q3 = 0.75, Q4 = 0.95. Trend equation yt= t (t = 1 in first quarter of 2003) Predict demand for quarter 3 of 2006 p76

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**Associative Forecasting**

If I want to predict ridership originating from a new train station, what data might I look at? Find (predictor) variables that are associated with ridership at other stations. Associated = correlated = as one moves the other moves Create a model that shows the relationship between the predictor variables and the predicted variable (e.g. ridership) Technique is regression analysis Simple linear regression with one variable Multiple regression (can be non-linear) Test the model to see which variables most useful in predicting ridership (look at r2) Use the model to predict ridership, given values of the predictor variables. p79+

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Associative Models Predictor variables (x): used to predict values of the variable of interest (y) (also called independent variables) Linear regression: process of finding a straight line that best fits a set of points on a graph (use the Least Squares Equation) p79 Multiple regression: models with more than one predictor variable (computations complex, created with computer)

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**Simple Linear Regression**

Computed relationship p82 Note the equations and method is same as for linear trend would a linear model be reasonable?

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**Excel: Simple Linear Regression**

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Correlation and Excel Correlation coefficient (r): measure of the strength of relationship between two variables ranges from -1 to +1 -1 = two variables move together in same direction +1 = two variables move together in opposite direction =CORREL(Range of y values, Range of x values) r2 measures proportion of variation in the values of y that is “explained” by the predictor variables in the regression model ranges from 0 to 1 higher values = more useful predictors =RSQ(Range of y values, Range of x values) p83

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**Linear Regression Assumptions**

Predictions are being made only within the range of observed values relationship may be non-linear outside that range y-intercept often not meaningful Variations around the line are random and normally distributed For best results: Always plot the data to verify linearity Small correlation may imply that other variables are important only first point in text p 82

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**Accuracy and Control of Forecasts**

Error = Actual value - Forecast value +ve = forecast too low, -ve = too high Three measures of forecasts are used: Mean absolute deviation (MAD) Mean squared error (MSE) Mean absolute percent error (MAPE) Control charts plot errors to see if within pre-set control limits Tracking signal Ratio of cumulative error and MAD p86-87

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Error, MAD, MSE and MAPE p86

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**MAD, MSE and MAPE p86-87 MAD Easy to compute Weights errors linearly**

Squares error More weight to large errors MAPE Puts errors in perspective above 70% satisfactory p86-87

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**Error, MAD, MSE and MAPE: Example**

Compute MAD, MSE, and MAPE for the following data. new example

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**Forecast Errors bias = the sum of the forecast errors**

+ve bias = frequent underestimation -ve bias = frequent overestimation possible sources of error include: Model may be inadequate (things have changed) Incorrect use of forecasting technique Irregular variations p87

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**Controlling the Forecasting Process**

Control chart A visual tool for monitoring forecast errors Used to detect non-randomness in errors Set limits that are multiples of the √MSE Forecasting errors are “in control” when only random errors, no errors from identifiable causes “in control” if All errors are within control limits No patterns (e.g. trends or cycles) are present errors outside limit = need corrective action p87

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**Control Chart Upper limit Lower limit Time Error**

Upper limit Lower limit Range of acceptable variation Time Error Need for corrective action p87

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**Controlling Forecasts: Control Limits**

Standard deviation of error = Control Limits = 0 ± 2 (or 3) s p87-88 95% of all errors should be within 2s 97.7% of all errors should be within 3s

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**Control Chart Example 1 90 100 -10 100 2 95 100 -5 25**

A F A - F Month (Sales) (Forecast) Error MSE 1575 new example Errors should be within ± 2(16.2). Lower limit = Upper limit = 32.4

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**Control Chart Example All the errors are within the control limits**

new example All the errors are within the control limits

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**Pharmacy Forecast Control: Your Turn!**

Below is a pharmacy’s actual sales and forecasted demand for a certain prescription drug for 5 months. How accurate is their forecast? Calculate MAD and MSE and create a control chart. new example Month Sales Forecast 1 220 n/a 2 250 255 3 210 205 4 300 320 5 325 315 31

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**Pharmacy Forecast Control: Your Turn!**

Month Sales Forecast Abs Error 1 220 n/a 2 250 255 5 3 210 205 4 300 320 20 325 315 10 40 Sq. Error 25 400 100 550 new example 32

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**Pharmacy Forecast Control: Your Turn!**

Errors should be within ± 2(11.7). Lower limit = Upper limit = 23.4 new example All the errors are within the control limits

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**Tracking Signal Tracking signal = (Actual - forecast) MAD**

ratio of cumulative error to MAD can be plotted on a control chart investigate if TS > 4 Tracking signal = (Actual - forecast) MAD p89-90

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True or False? When error values fall outside the limits of a control chart, this signals a need for corrective action Ans: True When all errors plotted on a control chart are either all positive, or all negative, this shows that the forecasting technique is performing adequately. Ans: False A random pattern of errors within the limits of a control chart signals a need for corrective action.

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**Choosing a Forecasting Technique**

No single technique works in every situation Two most important factors Cost Accuracy Other factors include availability of: Historical data Computers Time needed to gather and analyze the data Forecast horizon p90-91

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**Choosing a Forecast Technique**

Forecasting Method Amount of Historical Data Data Pattern Forecast Horizon Preparation time Complexity Simple exponential smoothing 5 to 10 observations Data should be stationary Short Little sophistication Trend- adjusted exponential smoothing 10 to 15 observations Trend Short to medium Moderate sophistication Regression Trend models 10 to 20 Short, medium, long Seasonal Enough to see 3 peaks and troughs seasonal patterns Short to moderate Causal regression models 10 observations per independent variable Can handle complex patterns Medium or long Long development time, short time implementation Considerable sophistication Source: J. Holton Wilson and D. Allison-Koerber, “Combining Subjective and Objective Forecasts Improves Results,” Journal of Business Forecasting Methods & Systems, 11(3) Fall 1992, p. 4.

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**Choosing a Forecast Technique**

Factor Short Term Medium Term Long Term 1. Frequency daily, weekly monthly, quarterly annual 2. Level of aggregation Item Product family Total output 3. Type of model Smoothing Trend Seasonal Regression Managerial Judgment Regression 4. Degree of management involvement Low Moderate High 5. Cost per forecast Source: C. L. Jain, “Benchmarking Forecasting Models,” Journal of Business Forecasting Methods & Systems, Fall 2002, pp. 18–20, 30.

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Which technique? Sales for a product have been fairly consistent over several years, although showing a steady upward trend. The company wants to understand what drives sales. The best forecasting technique would be: A) trend models B) judgmental methods C) moving averages D) regression models E) exponential smoothing techniques Ans: D

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**Describe at least three judgmental forecasting methods.**

Describe the components of a time series model, and explain averaging techniques and solve typical problems. Describe trend forecasting and solve typical problems. Describe seasonality forecasting and solve typical problems. Describe associative models and solve typical problems.

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**Identify uses of demand forecasts**

Distinguish between forecasting time frames Describe common features of forecasts List the elements of a good forecast and steps of forecasting process, Contrast different forecasting approaches. Describe three measures of forecast accuracy, and two ways of controlling forecasts, and solve typical problems. Identify the major factors to consider when choosing a forecasting technique.

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