13 – 1 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Forecasting 13 For Operations Management, 9e by Krajewski/Ritzman/Malhotra © 2010 Pearson Education Homework: 2, 12, 14.

13 – 2 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Forecasting Forecasts are critical inputs to business plans, annual plans, and budgets Finance, human resources, marketing, operations, and supply chain managers need forecasts to plan: output levels, purchases of services and materials, workforce and output schedules, inventories, and long-term capacities Forecasts are made on many different variables Forecasts are important to managing both processes and managing supply chains

13 – 3 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Forecasting Rarely perfect because of randomness Forecasts more accurate for groups vs. individuals Accuracy decreases as time horizon increases I see that you will get an A this semester.

13 – 4 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Demand Patterns A time series is the repeated observations of demand for a service or product in their order of occurrence There are five basic time series patterns  Horizontal  Trend  Seasonal  Cyclical  Random

13 – 5 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Demand Patterns Quantity Time (a) Horizontal: Data cluster about a horizontal line Figure 13.1 – Patterns of Demand

13 – 6 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Demand Patterns Quantity Time (b) Trend: Data consistently increase or decrease Figure 13.1 – Patterns of Demand

13 – 7 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Demand Patterns Quantity | ||||||||||| Months (c) Seasonal: Data consistently show peaks and valleys Year 1 Year 2 Figure 13.1 – Patterns of Demand

13 – 8 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Demand Patterns Quantity |||||| Years (d) Cyclical: Data reveal gradual increases and decreases over extended periods Figure 13.1 – Patterns of Demand

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13 – 10 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Types of Forecasts Judgmental  Uses subjective inputs Time series  Uses historical data assuming the future will be like the past Associative models  Uses explanatory variable(s) to make a forecast regarding a dependent variable

13 – 11 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Judgment Methods Other methods (casual and time-series) require an adequate history file, which might not be available Salesforce estimates Executive opinion is a method in which opinions, experience, and technical knowledge of one or more managers are summarized to arrive at a single forecast Consumer surveys Outside opinion Delphi method

13 – 12 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Judgment Methods Market research is a systematic approach to determine external customer interest through data-gathering surveys Delphi method is a process of gaining consensus from a group of experts while maintaining their anonymity Useful when no historical data are available

13 – 13 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Linear Regression A dependent variable is related to one or more independent variables by a linear equation The independent variables are assumed to “cause” the results observed in the past Simple linear regression model is a straight line Y = a + bX where Y = dependent variable X = independent variable a = Y -intercept of the line b = slope of the line

13 – 14 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Linear Regression Dependent variable Independent variable X Y Estimate of Y from regression equation Regression equation: Y = a + bX Actual value of Y Value of X used to estimate Y Deviation, or error Figure 13.2 – Linear Regression Line Relative to Actual Data

13 – 15 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Linear Regression The sample correlation coefficient, r  Measures the direction and strength of the relationship between the independent variable and the dependent variable.  The value of r can range from –1.00 ≤ r ≤ 1.00 The sample coefficient of determination, r 2  Measures the amount of variation in the dependent variable about its mean that is explained by the regression line  The values of r 2 range from 0.00 ≤ r 2 ≤ 1.00 The standard error of the estimate, s yx  Measures how closely the data on the dependent variable cluster around the regression line

13 – 16 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Using Linear Regression EXAMPLE 13.1 The supply chain manager seeks a better way to forecast the demand for door hinges and believes that the demand is related to advertising expenditures. The following are sales and advertising data for the past 5 months: MonthSales (thousands of units)Advertising (thousands of $) The company will spend $1,750 next month on advertising for the product. Use linear regression to develop an equation and a forecast for this product.

13 – 17 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Using Linear Regression SOLUTION We used POM for Windows to determine the best values of a, b, the correlation coefficient, the coefficient of determination, and the standard error of the estimate a = b = r = r 2 = s yx = The regression equation is Y = – X – X

13 – 18 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Using Linear Regression The regression line is shown in Figure The r of 0.98 suggests an unusually strong positive relationship between sales and advertising expenditures. The coefficient of determination, r 2, implies that 96 percent of the variation in sales is explained by advertising expenditures. | Advertising ($000) 250 – 200 – 150 – 100 – 50 – 0 – Sales (000 units) Brass Door Hinge X X X X X X Data Forecasts Figure 13.3 – Linear Regression Line for the Sales and Advertising Data

13 – 19 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Linear Regression Output

13 – 20 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Linear Regression Assumptions  Variations around the line are random  Deviations around the line normally distributed  Predictions are being made only within the range of observed values  For best results:  Always plot the data to verify linearity  Check for data being time-dependent  Small correlation may imply that other variables are important

13 – 21 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Time Series Methods In a naive forecast the forecast for the next period equals the demand for the current period (F t = D t-1 ) Uh, give me a minute.... We sold 250 wheels last week.... Now, next week we should sell....

13 – 22 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Simple Moving Averages D t = actual demand in period t F t = forecast for period t E t = forecast error in period t n = total number of periods in the average

13 – 23 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Weighted Moving Averages Weights are given; example (.5,.3,.2)

13 – 24 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. 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.

13 – 25 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Exponential Smoothing The emphasis given to the most recent demand levels can be adjusted by changing the smoothing parameter Larger α values emphasize recent levels of demand and result in forecasts more responsive to changes in the underlying average Smaller α values treat past demand more uniformly and result in more stable forecasts Exponential smoothing is simple and requires minimal data When the underlying average is changing, results will lag actual changes

13 – 26 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Seasonal Patterns Seasonal patterns are regularly repeated upward or downward movements in demand measured in periods of less than one year Account for seasonal effects by using one of the techniques already described but to limit the data in the time series to those periods in the same season This approach accounts for seasonal effects but discards considerable information on past demand

13 – 27 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. 1.For each year, calculate the average demand for each season by dividing annual demand by the number of seasons per year 2.For each year, divide the actual demand for each season by the average demand per season, resulting in a seasonal index for each season 3.Calculate the average seasonal index for each season using the results from Step 2 4.Calculate each season’s forecast for next year Multiplicative Seasonal Method Multiplicative seasonal method, whereby seasonal factors are multiplied by an estimate of the average demand to arrive at a seasonal forecast

13 – 28 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. The manager wants to forecast customer demand for each quarter of year 5, based on an estimate of total year 5 demand of 2,600 customers Using the Multiplicative Seasonal Method EXAMPLE 13.5 The manager of the Stanley Steemer carpet cleaning company needs a quarterly forecast of the number of customers expected next year. The carpet cleaning business is seasonal, with a peak in the third quarter and a trough in the first quarter. Following are the quarterly demand data from the past 4 years: QuarterYear 1Year 2Year 3 Year Total

13 – 29 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Using the Multiplicative Seasonal Method

13 – 30 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Using the Multiplicative Seasonal Method Year1Year2Year3Year4Yr5Forecast Q Q Q Q Totals Average SFYr1SFYr2SFYr3SFYr4AvgSF Q Q Q Q

13 – 31 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Measures of Forecast Error Et2nEt2n MSE = |Et |n|Et |n MAD = (  | E t |/ D t ) (100) n MAPE =

13 – 32 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Measures of Forecast Error Simple Moving Average Weighted Moving Average Exponential Smoothing MAD Results

13 – 33 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Measures of Forecast Error Simple Moving Average Weighted Moving Average MSE Results

13 – 34 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Measures of Forecast Error MAPE Results Simple Moving Average Weighted Moving Average

13 – 35 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

13 – 36 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

13 – 37 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.