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Operations Management Forecasting Chapter 4 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-1 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Outline GLOBAL COMPANY PROFILE: TUPPERWARE CORPORATION WHAT IS FORECASTING? Forecasting Time Horizons The Influence of Product Life Cycle TYPES OF FORECASTS THE STRATEGIC IMPORTANCE OF FORECASTING Human Resources Capacity Supply-Chain Management SEVEN STEPS IN THE FORECASTING SYSTEM PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-2 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Outline - Continued FORECASTING APPROACHES Overview of Qualitative Methods Overview of Quantitative Methods Decomposition of Time Series Naïve Approach Moving Averages Exponential Smoothing Exponential Smoothing with Trend Adjustment Trend Projections Seasonal Variations in Data Cyclic Variations in Data TIME-SERIES FORECASTING PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-3 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Outline - Continued ASSOCIATIVE FORECASTING METHODS: REGRESSION AND CORRELATION ANALYSIS Using Regression Analysis to Forecast Standard Error of the Estimate Correlation Coefficients for Regression Lines Multiple-Regression Analysis MONITORING AND CONTROLLING FORECASTS Adaptive Smoothing Focus Forecasting FORECASTING IN THE SERVICE SECTOR PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-4 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Learning Objectives When you complete this chapter, you should be able to : Identify or Define: Forecasting Types of forecasts Time horizons Approaches to forecasts PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-5 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Learning Objectives - continued When you complete this chapter, you should be able to : Describe or Explain: Moving averages Exponential smoothing Trend projections Regression and correlation analysis Measures of forecast accuracy PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-6 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Forecasting at Tupperware Each of 50 profit centers around the world is responsible for computerized monthly, quarterly, and 12-month sales projections These projections are aggregated by region, then globally, at Tupperware’s World Headquarters Tupperware uses all techniques discussed in text PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-7 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Three Key Factors for Tupperware The number of registered “consultants” or sales representatives The percentage of currently “active” dealers (this number changes each week and month) Sales per active dealer, on a weekly basis PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-8 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Tupperware - Forecast by Consensus Although inputs come from sales, marketing, finance, and production, final forecasts are the consensus of all participating managers. The final step is Tupperware’s version of the “jury of executive opinion” PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-9 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 What is Forecasting? Process of predicting a future event Sales will be $200 Million! Underlying basis of all business decisions Production Inventory Personnel Facilities PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-10 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Types of Forecasts by Time Horizon Short-range forecast Up to 1 year; usually less than 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 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-11 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 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. PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-12 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Influence of Product Life Cycle Introduction, Growth, Maturity, Decline Stages of introduction and growth require longer forecasts than maturity and decline Forecasts useful in projecting staffing levels, inventory levels, and factory capacity as product passes through life cycle stages PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-13 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Strategy and Issues During a Product’s Life Growth Maturity Practical to change price or quality image Poor time to change image, price, or quality Competitive costs become critical Introduction Company Strategy/Issues Best period to increase market share R&D product engineering critical Strengthen niche Decline Cost control critical Defend market position Fax machines Drive-thru restaurants CD-ROM Sales 3 1/2” Floppy disks Station wagons Internet Color copiers HDTV OM Strategy/Issues Product design and development critical Frequent product and process design changes Short production runs High production costs Forecasting critical Standardization Product and process reliability Less rapid product changes - more minor changes Competitive product improvements and options Increase capacity Limited models Shift toward product focused Attention to quality Enhance distribution PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e Optimum capacity Increasing stability of process Long production runs Product improvement and cost cutting 4-14 Little product differentiation Cost minimization Over capacity in the industry Prune line to eliminate items not returning good margin Reduce capacity © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Types of Forecasts Economic forecasts Address business cycle, e.g., inflation rate, money supply etc. Technological forecasts Predict rate of technological progress Predict acceptance of new product Demand forecasts Predict sales of existing product PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-15 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Seven Steps in Forecasting Determine the use of the forecast Select the items to be forecasted Determine the time horizon of the forecast Select the forecasting model(s) Gather the data Make the forecast Validate and implement results PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-16 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Product Demand Charted over 4 Years with Trend and Seasonality Demand for product or service Seasonal peaks Trend component Actual demand line Random variation Year 1 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e Year 2 4-17 Average demand over four years Year 3 Year 4 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Actual Demand, Moving Average, Weighted Moving Average 35 Sales Demand 30 25 Weighted moving average Actual sales 20 15 10 Moving average 5 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-18 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 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 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-19 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Forecasting Approaches Qualitative Methods Quantitative Methods Used when situation is vague & little data exist Used when situation is ‘stable’ & historical data exist New products New technology Existing products Current technology Involves intuition, experience Involves mathematical techniques e.g., forecasting sales on Internet PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e e.g., forecasting sales of color televisions 4-20 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Overview of Qualitative Methods Jury of executive opinion Pool opinions of high-level executives, sometimes augment by statistical models Delphi method Panel of experts, queried iteratively Sales force composite Estimates from individual salespersons are reviewed for reasonableness, then aggregated Consumer Market Survey Ask the customer PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-21 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 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 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-22 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 © 1995 Corel Corp. Sales Force Composite Each salesperson projects his or her sales Combined at district & national levels Sales reps know customers’ wants Tends to be overly optimistic Sales © 1995 Corel Corp. PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-23 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Delphi Method Iterative group process 3 types of people Decision makers Staff Respondents Decision Makers Staff (What will (Sales?) (Sales will be 50!) sales be? survey) Reduces ‘group-think’ Respondents (Sales will be 45, 50, 55) PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-24 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Consumer Market Survey Ask customers about purchasing plans What consumers say, and what they actually do are often different Sometimes difficult to answer How many hours will you use the Internet next week? © 1995 Corel Corp. PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-25 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Overview of Quantitative Approaches Naïve approach Moving averages Exponential smoothing Trend projection Time-series Models Linear regression Associative models PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-26 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Quantitative Forecasting Methods (Non-Naive) Quantitative Forecasting Associative Models Time Series Models Moving Average Exponential Smoothing PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e Trend Projection 4-27 Linear Regression © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 What is a Time Series? Set of evenly spaced numerical data Forecast based only on past values Obtained by observing response variable at regular time periods Assumes that factors influencing past and present will continue influence in future Example Year: Sales: 1998 78.7 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 1999 63.5 4-28 2000 89.7 2001 93.2 2002 92.1 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Time Series Components Trend Cyclical Seasonal Random PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-29 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Trend Component Persistent, overall upward or downward pattern Due to population, technology etc. Several years duration Response Mo., Qtr., Yr. PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-30 © 1984-1994 T/Maker Co. © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Seasonal Component Regular pattern of up & down fluctuations Due to weather, customs etc. Occurs within 1 year Summer Response © 1984-1994 T/Maker Co. Mo., Qtr. PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-31 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Common Seasonal Patterns Period of Pattern “Season” Length Week Day Number of “Seasons” in Pattern 7 Month Week 4–4½ Month Day 28 – 31 Year Quarter 4 Year Month 12 Year Week 52 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-32 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Cyclical Component Repeating up & down movements Due to interactions of factors influencing economy Usually 2-10 years duration Cycle Response Mo., Qtr., Yr. PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-33 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Random Component Erratic, unsystematic, ‘residual’ fluctuations Due to random variation or unforeseen events © 1984-1994 T/Maker Co. Union strike Tornado Short duration & nonrepeating PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-34 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 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 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e (if quarterly or mo. data) 4-35 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 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. PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-36 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 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 Demand in Previous n Periods MA n PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-37 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Moving Average Example You’re manager of a museum store that sells historical replicas. You want to forecast sales (000) for 2003 using a 3-period moving average. 1998 4 1999 6 2000 5 2001 3 2002 7 © 1995 Corel Corp. PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-38 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Moving Average Solution Time 1998 1999 2000 2001 2002 2003 Response Yi 4 6 5 3 7 Moving Total (n=3) NA NA NA 4+6+5=15 Moving Average (n=3) NA NA NA 15/3 = 5 NA PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-39 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Moving Average Solution Time 1998 1999 2000 2001 2002 2003 Response Yi 4 6 5 3 7 Moving Total (n=3) NA NA NA 4+6+5=15 6+5+3=14 Moving Average (n=3) NA NA NA 15/3 = 5 14/3=4 2/3 NA PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-40 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Moving Average Solution Time 1998 1999 2000 2001 2002 2003 Response Yi 4 6 5 3 7 NA PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e Moving Total (n=3) NA NA NA 4+6+5=15 6+5+3=14 5+3+7=15 4-41 Moving Average (n=3) NA NA NA 15/3=5.0 14/3=4.7 15/3=5.0 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Moving Average Graph Sales 8 Actual 6 Forecast 4 2 95 96 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 97 98 Year 4-42 99 00 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Weighted Moving Average Method Used when trend is present Older data usually less important Weights based on intuition Often lay between 0 & 1, & sum to 1.0 Equation WMA = Σ(Weight for period n) (Demand in period n) PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e ΣWeights 4-43 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Actual Demand, Moving Average, Weighted Moving Average 35 Sales Demand 30 25 Weighted moving average Actual sales 20 15 10 Moving average 5 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-44 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Disadvantages of Moving Average Methods Increasing n makes forecast less sensitive to changes Do not forecast trend well Require much historical data © 1984-1994 T/Maker Co. PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-45 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Exponential Smoothing Method Form of weighted moving average Weights decline exponentially Most recent data weighted most Requires smoothing constant () Ranges from 0 to 1 Subjectively chosen Involves little record keeping of past data PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-46 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Exponential Smoothing Equations Ft = At - 1 + (1-)At - 2 + (1- )2·At - 3 + (1- )3At - 4 + ... + (1- )t-1·A0 Ft = Forecast value At = Actual value = Smoothing constant Ft = Ft-1 + (At-1 - Ft-1) Use for computing forecast PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-47 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Exponential Smoothing Example During the past 8 quarters, the Port of Baltimore has unloaded large quantities of grain. ( = .10). The first quarter forecast was 175.. Quarter Actual 1 2 3 4 5 6 7 8 9 180 168 159 175 190 205 180 182 ? PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e Find the forecast for the 9th quarter. 4-48 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Exponential Smoothing Solution Ft = Ft-1 + 0.1(At-1 - Ft-1) Quarter Actual 1 180 2 168 3 159 4 175 5 190 6 205 Forecast, F t (α = .10) 175.00 (Given) 175.00 + PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-49 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Exponential Smoothing Solution Ft = Ft-1 + 0.1(At-1 - Ft-1) Forecast, F t (α = .10) Quarter Actual 1 180 2 168 3 159 4 175 5 190 6 205 175.00 (Given) 175.00 + .10( PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-50 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Exponential Smoothing Solution Ft = Ft-1 + 0.1(At-1 - Ft-1) Quarter Actual 1 180 2 168 3 159 4 175 5 190 6 205 Forecast, Ft (α = .10) 175.00 (Given) 175.00 + .10(180 - PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-51 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Exponential Smoothing Solution Ft = Ft-1 + 0.1(At-1 - Ft-1) Forecast, Ft (α = .10) Quarter Actual 1 180 2 168 3 159 4 175 5 190 6 205 175.00 (Given) 175.00 + .10(180 - 175.00) PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-52 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Exponential Smoothing Solution Ft = Ft-1 + 0.1(At-1 - Ft-1) Forecast, Ft (α = .10) Quarter Actual 1 180 2 168 3 159 4 175 5 190 6 205 175.00 (Given) 175.00 + .10(180 - 175.00) = 175.50 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-53 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Exponential Smoothing Solution Ft = Ft-1 + 0.1(At-1 - Ft-1) Forecast, F t (α = .10) Quarter Actual 1 180 2 168 175.00 + .10(180 - 175.00) = 175.50 3 159 175.50 + .10(168 - 175.50) = 174.75 4 175 5 190 6 205 175.00 (Given) PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-54 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Exponential Smoothing Solution Ft = Ft-1 + 0.1(At-1 - Ft-1) Forecast, F t (α = .10) Quarter Actual 1995 180 175.00 (Given) 1996 168 175.00 + .10(180 - 175.00) = 175.50 1997 159 175.50 + .10(168 - 175.50) = 174.75 1998 175 174.75 + .10(159 - 174.75)= 173.18 1999 190 2000 205 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-55 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Exponential Smoothing Solution Ft = Ft-1 + 0.1(At-1 - Ft-1) Forecast, F t (α = .10) Quarter Actual 1 180 175.00 (Given) 2 168 175.00 + .10(180 - 175.00) = 175.50 3 4 159 175.50 + .10(168 - 175.50) = 174.75 175 174.75 + .10(159 - 174.75) = 173.18 5 190 173.18 + .10(175 - 173.18) = 173.36 6 205 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-56 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Exponential Smoothing Solution Ft = Ft-1 + 0.1(At-1 - Ft-1) Forecast, F t (α = .10) Quarter Actual 1 180 175.00 (Given) 2 168 175.00 + .10(180 - 175.00) = 175.50 3 159 175.50 + .10(168 - 175.50) = 174.75 4 175 174.75 + .10(159 - 174.75) = 173.18 5 190 173.18 + .10(175 - 173.18) = 173.36 6 205 173.36 + .10(190 - 173.36) = 175.02 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-57 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Exponential Smoothing Solution Ft = Ft-1 + 0.1(At-1 - Ft-1) Actual Forecast, F t (α = .10) 4 175 174.75 + .10(159 - 174.75) = 173.18 5 190 173.18 + .10(175 - 173.18) = 173.36 6 7 205 180 173.36 + .10(190 - 173.36) = 175.02 175.02 + .10(205 - 175.02) = 178.02 Time 8 9 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-58 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Exponential Smoothing Solution Ft = Ft-1 + 0.1(At-1 - Ft-1) Time Forecast, F t (α = .10) Actual 4 175 174.75 + .10(159 - 174.75) = 173.18 5 190 173.18 + .10(175 - 173.18) = 173.36 6 7 205 180 8 9 182 ? 173.36 + .10(190 - 173.36) = 175.02 175.02 + .10(205 - 175.02) = 178.02 178.02 + .10(180 - 178.02) = 178.22 178.22 + .10(182 - 178.22) = 178.58 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-59 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Forecast Effects of Smoothing Constant Ft = At - 1 + (1- )At - 2 + (1- )2At - 3 + ... Weights = Prior Period 2 periods ago 3 periods ago = 0.10 (1 - ) (1 - )2 10% = 0.90 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-60 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Forecast Effects of Smoothing Constant Ft = At - 1 + (1- ) At - 2 + (1- )2At - 3 + ... Weights = Prior Period = 0.10 2 periods ago 3 periods ago (1 - ) 10% 9% (1 - )2 = 0.90 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-61 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Forecast Effects of Smoothing Constant Ft = At - 1 + (1- )At - 2 + (1- )2At - 3 + ... Weights = Prior Period = 0.10 2 periods ago 3 periods ago (1 - ) (1 - )2 10% 9% 8.1% = 0.90 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-62 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Forecast Effects of Smoothing Constant Ft = At - 1 + (1- )At - 2 + (1- )2At - 3 + ... Weights = Prior Period 2 periods ago 3 periods ago (1 - ) (1 - )2 = 0.10 10% 9% 8.1% = 0.90 90% PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-63 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Forecast Effects of Smoothing Constant Ft = At - 1 + (1- ) At - 2 + (1- )2At - 3 + ... Weights = Prior Period 2 periods ago 3 periods ago (1 - ) (1 - )2 = 0.10 10% 9% 8.1% = 0.90 90% 9% PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-64 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Forecast Effects of Smoothing Constant Ft = At - 1 + (1- ) At - 2 + (1- )2At - 3 + ... Weights = Prior Period = 0.10 = 0.90 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 2 periods ago 3 periods ago (1 - ) (1 - )2 10% 9% 8.1% 90% 9% 0.9% 4-65 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Impact of 250 Forecast (0.5) Actual Tonage 200 150 Forecast (0.1) Actual 100 50 0 1 2 3 4 5 6 7 8 9 Quarter PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-66 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Choosing Seek to minimize the Mean Absolute Deviation (MAD) If: Then: Forecast error = demand - forecast MAD PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e forecast errors n 4-67 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Exponential Smoothing with Trend Adjustment Forecast including trend (FITt) = exponentially smoothed forecast (Ft) + exponentially smoothed trend (Tt) PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-68 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Exponential Smoothing with Trend Adjustment - continued or Ft = Last period’s forecast + (Last period’s actual – Last period’s forecast) Ft = Ft-1 + (At-1 – Ft-1) Tt = (Forecast this period - Forecast last period) + (1-)(Trend estimate last period or Tt = (Ft - Ft-1) + (1- )Tt-1 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-69 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Exponential Smoothing with Trend Adjustment - continued Ft = exponentially smoothed forecast of the data series in period t Tt = exponentially smoothed trend in period t At = actual demand in period t = smoothing constant for the average = smoothing constant for the trend PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-70 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Comparing Actual and Forecasts 40 35 Actual Demand 30 Demand 25 20 15 Smoothed Forecast Forecast including trend 10 Smoothed Trend 5 0 1 2 3 4 5 6 7 8 9 10 Month PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-71 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Regression PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-72 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Least Squares Values of Dependent Variable Actual observation Deviation Deviation Deviation Deviation Deviation Deviation Deviation Point on regression line Yˆ a bx Time PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-73 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Actual and the Least Squares Line PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-74 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Linear Trend Projection Used for forecasting linear trend line Assumes relationship between response variable, Y, and time, X, is a linear function Yi a bX i Estimated by least squares method Minimizes sum of squared errors PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-75 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Scatter Diagram Sales (in $ hundreds of thousands) Sales versus Payroll 4 3 2 1 0 0 1 2 3 4 5 6 Area Payroll (in $ hundreds of millions) PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-77 7 8 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Least Squares Equations Equation: ˆ i a bx i Y n Slope: x i y i nx y b i n x i nx i Y-Intercept: PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e a y bx 4-78 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Computation Table Xi X1 Yi Y1 2 Xi X1 2 2 X2 Y2 X2 : : : Xn ΣX i X iY i Y1 2 X 1Y 1 Y2 2 X 2Y 2 : 2 Yn Xn ΣYi 2 ΣX i PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 2 Yi 4-79 : 2 X nY n 2 ΣY i ΣX iY i Yn © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Using a Trend Line Year 1997 1998 1999 2000 2001 2002 2003 The demand for electrical power at N.Y.Edison over the years 1997 – 2003 is given at the left. Find the overall trend. Demand 74 79 80 90 105 142 122 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-80 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Finding a Trend Line Year 1997 1998 1999 2000 2001 2002 2003 Time Power x2 xy Period Demand 1 74 1 74 2 79 4 158 3 80 9 240 4 90 16 360 5 105 25 525 6 142 36 852 7 122 49 854 x=28 y=692 x2=140 xy=3,063 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-81 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 The Trend Line Equation x Σx 28 4 n 7 b Σxy - nxy 3,063 (7)(4)(98. 86) 295 10.54 2 2 2 28 Σx nx 140 (7)(4) y Σy 692 98.86 n 7 a y - bx 98.86- 10.54(4) 56.70 Demandin 2004 56.70 10.54(8) 141.02megawat t s Demandin 2005 56.70 10.54(9) 151.56megawat t s PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-82 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Actual and Trend Forecast PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-83 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Monthly Sales of Laptop Computers Month Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec 2000 80 70 80 90 113 110 100 88 85 77 75 82 Sales Demand 2001 2002 85 105 85 85 93 82 95 115 125 131 115 120 102 113 102 110 90 95 78 85 72 83 78 80 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e Average Demand 2000-2002 Monthly 90 94 80 94 85 94 100 94 123 94 115 94 105 94 100 94 90 94 80 94 80 94 80 94 4-84 Seasonal Index 0.957 0.851 0.904 1.064 1.309 1.223 1.117 1.064 0.957 0.851 0.851 0.851 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Demand for IBM Laptops PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-85 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 San Diego Hospital – Inpatient Days 10200 1.06 Combined Forecast 10000 9800 1.04 Trend 1.02 9600 1 9400 0.98 Seasonal Index 9200 0.96 9000 0.94 8800 0.92 Jan Feb Mar Apr PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e May Jun 4-86 Jul Aug Sep Oct Nov Dec © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 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. PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-87 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Linear Regression Model Shows linear relationship between dependent & explanatory variables Example: Sales & advertising (not time) Y-intercept Slope ^ Yi = a + bX i Dependent (response) variable PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e Independent (explanatory) variable 4-88 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Linear Regression Equations Equation: Yˆ i a bx i n Slope: b x i y i nx y i 1 n x i2 nx 2 i 1 Y-Intercept: PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e a y bx 4-90 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Computation Table Xi X1 Yi 2 Xi 2 Yi X iY i Y1 X1 2 Y1 2 X 1Y 1 2 Y2 2 X 2Y 2 X2 Y2 X2 : : : Xn ΣXi : 2 Yn Xn ΣYi 2 ΣXi PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-91 : 2 X nY n 2 ΣYi Σ X iY i Yn © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 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 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-92 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Random Error Variation Variation of actual Y from predicted Y Measured by standard error of estimate Sample standard deviation of errors Denoted SY,X Affects several factors Parameter significance Prediction accuracy PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-93 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Least Squares Assumptions Relationship is assumed to be linear. Plot the data first - if curve appears to be present, use curvilinear analysis. Relationship is assumed to hold only within or slightly outside data range. Do not attempt to predict time periods far beyond the range of the data base. Deviations around least squares line are assumed to be random. PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-94 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Standard Error of the Estimate n 2 y y i c S y,x i 1 n2 n y i 1 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 2 i n n i 1 i 1 a y i b xi y i n2 4-95 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 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 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-96 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Sample Coefficient of Correlation r n n n i i i n x i yi x i yi n n n n n x i x i n yi yi i i i i PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-97 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Coefficient of Correlation and Regression Model Y r=1 Y Y^i = a + b X i r = -1 Y^i = a + b X i X Y X r = .89 Y^i = a + b X i Y r=0 Y^i = a + b X i X X r2 = square of correlation coefficient (r), is the percent of the variation in y that is explained by the regression equation PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-99 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Guidelines for Selecting Forecasting Model You want to achieve: No pattern or direction in forecast error ^ Error = (Y - Y ) = (Actual - Forecast) i i Seen in plots of errors over time Smallest forecast error Mean square error (MSE) Mean absolute deviation (MAD) PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-100 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Pattern of Forecast Error Trend Not Fully Accounted for Desired Pattern Error Error 0 0 Time (Years) PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e Time (Years) 4-101 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Forecast Error Equations Mean Square Error (MSE) (y yˆ ) forecast n 2 MSE i 1 i i n errors 2 n Mean Absolute Deviation (MAD) | y yˆ | | forecast n MAD i i 1 n i errors | n Mean Absolute Percent Error (MAPE) n MAPE 100 i 1 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e actual i forecast i actual i n 4-102 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Selecting Forecasting Model Example You’re a marketing analyst for Hasbro Toys. You’ve forecast sales with a linear model & exponential smoothing. Which model do you use? Actual Linear Model Year Sales Forecast Exponential Smoothing Forecast (.9) 1998 1999 2000 2001 2002 1 1 2 2 4 0.6 1.3 2.0 2.7 3.4 1.0 1.0 1.9 2.0 3.8 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-103 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Linear Model Evaluation Year Yi Y^ i 1998 1999 2000 2001 2002 1 1 2 2 4 0.6 1.3 2.0 2.7 3.4 Total Error Error2 |Error| 0.4 -0.3 0.0 -0.7 0.6 0.16 0.09 0.00 0.49 0.36 0.4 0.3 0.0 0.7 0.6 0.0 1.10 2.0 |Error| Actual 0.40 0.30 0.00 0.35 0.15 1.20 MSE = Σ Error2 / n = 1.10 / 5 = 0.220 MAD = Σ |Error| / n = 2.0 / 5 = 0.400 MAPE = 100 Σ|absolute percent errors|/n= 1.20/5 = 0.240 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-104 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Exponential Smoothing Model Evaluation Year Y 1998 1999 2000 2001 2002 1 1 2 2 4 i Y^ i 1.0 1.0 1.9 2.0 3.8 Total Error Error2 |Error| 0.0 0.0 0.1 0.0 0.2 0.00 0.00 0.01 0.00 0.04 0.0 0.0 0.1 0.0 0.2 0.3 0.05 0.3 |Error| Actual 0.00 0.00 0.05 0.00 0.05 0.10 MSE = Σ Error2 / n = 0.05 / 5 = 0.01 MAD = Σ |Error| / n = 0.3 / 5 = 0.06 MAPE = 100 Σ |Absolute percent errors|/n = 0.10/5 = 0.02 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-105 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Exponential Smoothing Model Evaluation Linear Model: MSE = Σ Error2 / n = 1.10 / 5 = .220 MAD = Σ |Error| / n = 2.0 / 5 = .400 MAPE = 100 Σ|absolute percent errors|/n= 1.20/5 = 0.240 Exponential Smoothing Model: MSE = Σ Error2 / n = 0.05 / 5 = 0.01 MAD = Σ |Error| / n = 0.3 / 5 = 0.06 MAPE = 100 Σ |Absolute percent errors|/n = 0.10/5 = 0.02 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-106 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Tracking Signal Measures how well the 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 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-107 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Tracking Signal Equation RSFE TS MAD n y i yˆ i i MAD forecast PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e error MAD 4-108 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Tracking Signal Computation Mo Fcst Act Error RSFE Abs Cum MAD Error |Error| 1 100 90 2 100 95 3 100 115 4 100 100 5 100 125 6 100 140 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-109 TS © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Tracking Signal Computation Mo Forc Act Error RSFE Abs Cum MAD Error |Error| 1 100 90 2 100 95 3 100 115 4 100 100 5 100 125 6 100 140 TS -10 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e Error = Actual - Forecast = 90 - 100 = -10 4-110 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Tracking Signal Computation Mo Forc Act Error RSFE Abs Cum MAD Error |Error| 1 100 90 2 100 95 3 100 115 4 100 100 5 100 125 6 100 140 -10 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e TS -10 RSFE = Errors = NA + (-10) = -10 4-111 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Tracking Signal Computation Mo Forc Act Error RSFE Abs Cum MAD Error |Error| 1 100 90 2 100 95 3 100 115 4 100 100 5 100 125 6 100 140 -10 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e -10 TS 10 Abs Error = |Error| = |-10| = 10 4-112 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Tracking Signal Computation Mo Forc Act Error RSFE Abs Cum MAD Error |Error| 1 100 90 2 100 95 3 100 115 4 100 100 5 100 125 6 100 140 -10 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e -10 10 TS 10 Cum |Error| = |Errors| = NA + 10 = 10 4-113 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Tracking Signal Computation Mo Forc Act Error RSFE Abs Cum MAD Error |Error| 1 100 90 2 100 95 3 100 115 4 100 100 5 100 125 6 100 140 -10 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e -10 10 TS 10 10.0 MAD = |Errors|/n = 10/1 = 10 4-114 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Tracking Signal Computation Mo Forc Act Error RSFE Abs Cum MAD Error |Error| 1 100 90 2 100 95 3 100 115 4 100 100 5 100 125 6 100 140 -10 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e -10 10 10 10.0 TS -1 TS = RSFE/MAD = -10/10 = -1 4-115 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Tracking Signal Computation Mo Forc Act Error RSFE Abs Cum MAD Error |Error| 1 100 90 -10 2 100 95 -5 3 100 115 4 100 100 5 100 125 6 100 140 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e -10 10 10 10.0 TS -1 Error = Actual - Forecast = 95 - 100 = -5 4-116 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Tracking Signal Computation Mo Forc Act Error RSFE Abs Cum MAD Error |Error| 1 100 90 -10 -10 2 100 95 -5 -15 3 100 115 4 100 100 5 100 125 6 100 140 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 10 10 10.0 TS -1 RSFE = Errors = (-10) + (-5) = -15 4-117 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Tracking Signal Computation Mo Forc Act Error RSFE Abs Cum MAD Error |Error| 1 100 90 -10 -10 10 2 100 95 -5 -15 5 3 100 115 4 100 100 5 100 125 6 100 140 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 10 10.0 TS -1 Abs Error = |Error| = |-5| = 5 4-118 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Tracking Signal Computation Mo Forc Act Error RSFE Abs Cum MAD Error |Error| 1 100 90 -10 -10 10 2 100 95 -5 -15 5 3 100 115 4 100 100 5 100 125 6 100 140 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 10 10.0 TS -1 15 Cum Error = |Errors| = 10 + 5 = 15 4-119 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Tracking Signal Computation Mo Forc Act Error RSFE Abs Cum MAD Error |Error| 1 100 90 -10 -10 10 2 100 95 -5 -15 5 3 100 115 4 100 100 5 100 125 6 100 140 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 10 10.0 15 TS -1 7.5 MAD = |Errors|/n = 15/2 = 7.5 4-120 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Tracking Signal Computation Mo Forc Act Error RSFE Abs Cum MAD Error |Error| 1 100 90 -10 -10 10 2 100 95 -5 -15 5 3 100 115 4 100 100 5 100 125 6 100 140 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e TS 10 10.0 -1 15 -2 7.5 TS = RSFE/MAD = -15/7.5 = -2 4-121 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Plot of a Tracking Signal Signal exceeded limit + Upper control limit 0 - Tracking signal Acceptable range Lower control limit Time PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-122 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 160 140 120 100 80 60 40 20 0 3 2 Forecast 1 Actual demand 0 Tracking Signal -1 -2 Tracking Singal Actual Demand Tracking Signals -3 0 1 2 3 4 5 6 7 Time PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-123 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 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 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e 4-124 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 Forecast of Sales by Hour for Fast Food Restaurant 20 15 10 5 0 +11-12 +1-2 11-12 12-1 1-2 2-3 PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e +3-4 +5-6 3-4 4-5 5-6 4-125 +7-8 +9-10 6-7 7-8 8-9 9-10 10-11 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458