PRODUCTION AND OPERATIONS MANAGEMENT Ch. 5: Forecasting POM - J. Galván

Learning Objectives Understand techniques to foresee the future 5 POM - J. Galván 5

What is Forecasting? Process of predicting a future event Underlying basis of all business decisions Production Inventory Personnel Facilities Sales will be $200 Million! POM - J. Galván 9

Types of Forecasts by Time Horizon Short-range forecast Up to 1 year; usually < 3 months Job scheduling, worker assignments Medium-range forecast 3 months to 3 years Sales & production planning, budgeting Long-range forecast 3+ years New product planning, facility location POM - J. Galván 10

Short-term vs. Longer-term Forecasting Medium/long range forecasts deal with more comprehensive issues and support management decisions regarding planning and products, plants and processes. Short-term forecasting usually employs different methodologies than longer-term forecasting Short-term forecasts tend to be more accurate than longer-term forecasts. POM - J. Galván 11

Influence of Product Life Cycle Stages of introduction & growth require longer forecasts than maturity and decline Forecasts useful in projecting staffing levels, inventory levels, and factory capacity as product passes through stages POM - J. Galván 12

Types of Forecasts Economic forecasts Technological forecasts Address business cycle e.g., inflation rate, money supply etc. Technological forecasts Predict technological change Predict new product sales Demand forecasts Predict existing product sales POM - J. Galván 13

Seven Steps in Forecasting Determine the use of the forecast Select the items to be forecast Determine the time horizon of the forecast Select the forecasting model(s) Gather the data Make the forecast Validate and implement results POM - J. Galván 14

Realities of Forecasting Forecasts are seldom perfect Most forecasting methods assume that there is some underlying stability in the system Both product family and aggregated product forecasts are more accurate than individual product forecasts POM - J. Galván 15

Forecasting Approaches Qualitative Methods Quantitative Methods Used when situation is vague & little data exist New products New technology Involves intuition, experience e.g., forecasting sales on Internet Used when situation is ‘stable’ & historical data exist Existing products Current technology Involves mathematical techniques e.g., forecasting sales of color televisions POM - J. Galván 16

Overview of Qualitative Methods Jury of executive opinion Pool opinions of high-level executives, sometimes augment by statistical models Sales force composite estimates from individual salespersons are reviewed for reasonableness, then aggregated Delphi method Panel of experts, queried iteratively Consumer Market Survey Ask the customer POM - J. Galván 17

Jury of Executive Opinion Involves small group of high-level managers Group estimates demand by working together Combines managerial experience with statistical models Relatively quick ‘Group-think’ disadvantage POM - J. Galván © 1995 Corel Corp. 18

Sales Force Composite Each salesperson projects their sales Combined at district & national levels Sales rep’s know customers’ wants Tends to be overly optimistic Sales © 1995 Corel Corp. POM - J. Galván 19

Delphi Method Iterative group process 3 types of people Decision makers Staff Respondents Reduces ‘group-think’ Respondents Staff Decision Makers (Sales?) (Sales will be 50!) (What will sales be? survey) (Sales will be 45, 50, 55) POM - J. Galván 20

Consumer Market Survey How many hours will you use the Internet next week? © 1995 Corel Corp. Ask customers about purchasing plans What consumers say, and what they actually do are often different Sometimes difficult to answer POM - J. Galván 21

Overview of Quantitative Approaches Naïve approach Moving averages Exponential smoothing Trend projection Linear regression Time-series Models Causal models POM - J. Galván 5-22 22

Quantitative Forecasting Methods (Non-Naive) Linear Regression Causal Models Exponential Smoothing Moving Average Time Series Trend Projection POM - J. Galván 23

What is a Time Series? Set of evenly spaced numerical data Obtained by observing response variable at regular time periods Forecast based only on past values Assumes that factors influencing past, present, & future will continue Example Year: 1993 1994 1995 1996 1997 Sales: 78.7 63.5 89.7 93.2 92.1 POM - J. Galván 24

Time Series Components Trend Cyclical Seasonal Random POM - J. Galván 25

Trend Component Persistent, overall upward or downward pattern Due to population, technology etc. Several years duration Mo., Qtr., Yr. Response © 1984-1994 T/Maker Co. POM - J. Galván 26

B Cyclical Component Repeating up & down movements Due to interactions of factors influencing economy Usually 2-10 years duration Mo., Qtr., Yr. Response Cycle B POM - J. Galván 27

Seasonal Component Regular pattern of up & down fluctuations Due to weather, customs etc. Occurs within 1 year Mo., Qtr. Response Summer © 1984-1994 T/Maker Co. POM - J. Galván 28

Random Component Erratic, unsystematic, ‘residual’ fluctuations Due to random variation or unforeseen events Union strike Tornado Short duration & nonrepeating POM - J. Galván 29

General Time Series Models Any observed value in a time series is the product (or sum) of time series components Multiplicative model Yi = Ti · Si · Ci · Ri (if quarterly or mo. data) Additive model Yi = Ti + Si + Ci + Ri (if quarterly or mo. data) POM - J. Galván 30

Naive Approach Assumes demand in next period is the same as demand in most recent period e.g., If May sales were 48, then June sales will be 48 Sometimes cost effective & efficient © 1995 Corel Corp. POM - J. Galván 31

å Moving Average Method MA is a series of arithmetic means Used if little or no trend Used often for smoothing Provides overall impression of data over time Equation MA n = å Demand in Previous Periods POM - J. Galván 32

Moving Average Graph Sales 8 6 4 2 93 94 95 96 97 98 Year Actual Forecast 4 2 93 94 95 96 97 98 Year POM - J. Galván 37

Disadvantages of Moving Average Method Increasing n makes forecast less sensitive to changes Do not forecast trend well Require much historical data © 1984-1994 T/Maker Co. POM - J. Galván 39

Linear Trend Projection Used for forecasting linear trend line Assumes relationship between response variable, Y, and time, X, is a linear function Estimated by least squares method Minimizes sum of squared errors $ i Y a bX = + POM - J. Galván 66

Linear Trend Projection Model Y b > 0 a b < 0 a Time, X POM - J. Galván 67

Scatter Diagram Sales Time 1 2 3 4 92 93 94 95 96 Sales vs. Time 68 1 2 3 4 92 93 94 95 96 Sales vs. Time Time POM - J. Galván 68

Least Squares Equations Slope: Y-Intercept: POM - J. Galván 69

Multiplicative Seasonal Model Find average historical demand for each “season” by summing the demand for that season in each year, and dividing by the number of years for which you have data. Compute the average demand over all seasons by dividing the total average annual demand by the number of seasons. Compute a seasonal index by dividing that season’s historical demand (from step 1) by the average demand over all seasons. Estimate next year’s total demand Divide this estimate of total demand by the number of seasons then multiply it by the seasonal index for that season. This provides the seasonal forecast. POM - J. Galván 73

Linear Regression Model Shows linear relationship between dependent & explanatory variables Example: Sales & advertising (not time) Y-intercept Slope ^ Y = a + b X i i Dependent (response) variable Independent (explanatory) variable POM - J. Galván 74

Linear Regression Model Y Y b X i = + Error a + i Observed value Y a b X = + Regression line Error ^ i i X POM - J. Galván 75

Linear Regression Equations Slope: Y-Intercept: POM - J. Galván 76

Interpretation of Coefficients Slope (b) Estimated Y changes by b for each 1 unit increase in X If b = 2, then sales (Y) is expected to increase by 2 for each 1 unit increase in advertising (X) Y-intercept (a) Average value of Y when X = 0 If a = 4, then average sales (Y) is expected to be 4 when advertising (X) is 0 POM - J. Galván 78

Correlation Answers: ‘how strong is the linear relationship between the variables?’ Coefficient of correlation Sample correlation coefficient denoted r Values range from -1 to +1 Measures degree of association Used mainly for understanding POM - J. Galván 82

Coefficient of Correlation Values Perfect Negative Correlation Perfect Positive Correlation No Correlation -1.0 -.5 +.5 +1.0 Increasing degree of negative correlation Increasing degree of positive correlation POM - J. Galván 84

Coefficient of Correlation and Regression Model Y X i = a + b ^ POM - J. Galván 85

Guidelines for Selecting Forecasting Model You want to achieve: No pattern or direction in forecast error Error = (Yi - Yi) = (Actual - Forecast) Seen in plots of errors over time Smallest forecast error Mean square error (MSE) Mean absolute deviation (MAD) ^ POM - J. Galván 86

Pattern of Forecast Error Trend Not Fully Accounted for Desired Pattern Time (Years) Error Time (Years) Error POM - J. Galván 87

Tracking Signal Measures how well forecast is predicting actual values Ratio of running sum of forecast errors (RSFE) to mean absolute deviation (MAD) Good tracking signal has low values Should be within upper and lower control limits POM - J. Galván 93

Tracking Signal Plot POM - J. Galván 108

Forecasting in the Service Sector Presents unusual challenges special need for short term records needs differ greatly as function of industry and product issues of holidays and calendar unusual events POM - J. Galván 109

Forecasting example SALES DURING LAST YEAR LAST YEAR Real sales Spring 200 Summer 350 Fall 300 Winter 150 TOTAL ANNUAL SALES 1000 ESTIMATION: Annual increase of sales 10,00% What are the estimated seasonal sales amount for next year? POM - J. Galván

Forecasting example (II) LAST YEAR Past sales Average sales for each season Seasonal factor Total past annual sales/ nº of seasons Past sales/ Avg. Sales Spring 200 250 0,8 Summer 350 1,4 Fall 300 1,2 Winter 150 0,6 TOTAL ANNUAL SALES 1000 POM - J. Galván

Forecasting example (III) NEXT YEAR SALES 1100 (10% increase) Average sales for each season Seasonal factor Next year's seasonal forecast Total estimated annual sales/nº of seasons As calculated Avg.sales* Factor Spring ? 275 0,8 220 Summer 1,4 385 Fall 1,2 330 Winter 0,6 165 TOTAL ANNUAL POM - J. Galván