PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc.,

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-1 Operations Management Forecasting Chapter 4

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-2 Outline  WHAT IS FORECASTING?  TYPES OF FORECASTS  THE STRATEGIC IMPORTANCE OF FORECASTING  FORECASTING APPROACHES  Overview of Qualitative Methods  Overview of Quantitative Methods  TIME-SERIES FORECASTING  Naïve Approach  Moving Averages  Exponential Smoothing  Exponential Smoothing with Trend Adjustment  Trend Projections  Seasonal Variations in Data  Cyclic Variations in Data  ASSOCIATIVE FORECASTING METHODS: REGRESSION AND CORRELATION ANALYSIS  MONITORING AND CONTROLLING FORECASTS

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-3 What is Forecasting?  Process of predicting a future event  Underlying basis of all business decisions  Production  Inventory  Personnel  Facilities Sales will be $200 Million!

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-4  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 Types of Forecasts by Time Horizon

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-5 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 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-6 Influence of Product Life Cycle  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 Introduction, Growth, Maturity, Decline

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-7 Strategy and Issues During a Product’s Life IntroductionGrowth Maturity Decline Standardization Less rapid product changes - more minor changes Optimum capacity Increasing stability of process Long production runs Product improvement and cost cutting Little product differentiation Cost minimization Over capacity in the industry Prune line to eliminate items not returning good margin Reduce capacity Forecasting critical Product and process reliability Competitive product improvements and options Increase capacity Shift toward product focused Enhance distribution Product design and development critical Frequent product and process design changes Short production runs High production costs Limited models Attention to quality Best period to increase market share R&D product engineering critical Practical to change price or quality image Strengthen niche Cost control critical Poor time to change image, price, or quality Competitive costs become critical Defend market position OM Strategy/Issues Company Strategy/Issues HDTV CD-ROM Color copiers Drive-thru restaurants Fax machines Station wagons Sales 3 1/2” Floppy disks Internet

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-8 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 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-9 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 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-10 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 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-11 Forecasting Approaches  Used when situation is ‘stable’ & historical data exist  Existing products  Current technology  Involves mathematical techniques  e.g., forecasting sales of color televisions Quantitative Methods  Used when situation is vague & little data exist  New products  New technology  Involves intuition, experience  e.g., forecasting sales on Internet Qualitative Methods

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-12 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 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-13  Involves small group of high-level managers  Group estimates demand by working together  Combines managerial experience with statistical models  Relatively quick  ‘Group-think’ disadvantage © 1995 Corel Corp. Jury of Executive Opinion

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-14 Delphi Method  Iterative group process  3 types of people  Decision makers  Staff  Respondents  Reduces ‘group-think’ Respondents Staff Decision Makers (Sales?) ( What will sales be? survey) (Sales will be 45, 50, 55) (Sales will be 50!)

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-15 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

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-16 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 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-17 Overview of Quantitative Approaches  Naïve approach  Moving averages  Exponential smoothing  Trend projection  Linear regression Time-series Models Associative models

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-18  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 and present will continue influence in future  Example Year:19981999200020012002 Sales:78.763.589.793.292.1 What is a Time Series?

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-19 Trend Seasonal Cyclical Random Time Series Components

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-20 Product Demand Charted over 4 Years with Trend and Seasonality Year 1 Year 2 Year 3 Year 4 Seasonal peaksTrend component Actual demand line Average demand over four years Demand for product or service Random variation

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-21  Persistent, overall upward or downward pattern  Due to population, technology etc.  Several years duration Mo., Qtr., Yr. Response © 1984-1994 T/Maker Co. Trend Component

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-22  Regular pattern of up & down fluctuations  Due to weather, customs etc.  Occurs within 1 year Mo., Qtr. Response Summer © 1984-1994 T/Maker Co. Seasonal Component

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-23  Repeating up & down movements  Due to interactions of factors influencing economy  Usually 2-10 years duration Mo., Qtr., Yr. Response Cycle  Cyclical Component

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-24  Erratic, unsystematic, ‘residual’ fluctuations  Due to random variation or unforeseen events  Union strike  Tornado  Short duration & nonrepeating © 1984-1994 T/Maker Co. Random Component

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-25  Any observed value in a time series is the product (or sum) of time series components  Multiplicative model  Y i = T i · S i · C i · R i (if quarterly or mo. data)  Additive model  Y i = T i + S i + C i + R i (if quarterly or mo. data) General Time Series Models

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-26 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 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-27  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 n  Demand in Previous Periods Periods Moving Average Method

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-28 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. 19984 1999 6 20005 20013 20027 © 1995 Corel Corp. Moving Average Example

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-29 Moving Average Solution

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-32 959697989900 Year Sales 2 4 6 8 Actual Forecast Moving Average Graph

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-33  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) ΣWeights Weighted Moving Average Method

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-34 Actual Demand, Moving Average, Weighted Moving Average Actual sales Moving average Weighted moving average

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-35  Increasing n makes forecast less sensitive to changes  Do not forecast trend well  Require much historical data © 1984-1994 T/Maker Co. Disadvantages of Moving Average Methods

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-36  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 Exponential Smoothing Method

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-37 F t : Forecast for period t, t=1,2,...,n. A t : Actual value in period t, t=1,2,...,n  = Smoothing constant  F t = F t -1 +  ( A t -1 - F t -1 ) OR  F t =  A t -1 + (1-  ) F t -1 Exponential Smoothing Equations

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-38 During the past 8 quarters, the Port of Baltimore has unloaded large quantities of grain. (  =.10). The first quarter forecast was 175.. QuarterActual 1180 2168 3159 4175 5190 6205 7180 8182 9? Exponential Smoothing Example Find the forecast for the 9 th quarter.

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-39 F t = F t -1 + 0.1( A t -1 - F t -1 ) QuarterActual Forecast, F t ( α =.10) 1 180175.00 (Given) 2168 3159 4175 5190 6 205 175.00 + Exponential Smoothing Solution

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-40 Quarter Actua Actual Forecast, F t ( α =.10) 1180 175.00 (Given) 2168 175.00 +.10( 3159 4175 5190 6205 Exponential Smoothing Solution F t = F t -1 + 0.1( A t -1 - F t -1 )

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-41 QuarterActual Forecast,F t ( α =.10) 1180 175.00 (Given) 2168 175.00 +.10(180 - 3159 4175 5190 6205 Exponential Smoothing Solution F t = F t -1 + 0.1( A t -1 - F t -1 )

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-42 QuarterActual Forecast,F t ( α =.10) 1180 175.00 (Given) 2168 175.00 +.10(180 - 175.00) 3159 4175 5190 6205 Exponential Smoothing Solution F t = F t -1 + 0.1( A t -1 - F t -1 )

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-43 QuarterActual Forecast,F t ( αααα =.10) 1180 175.00 (Given) 2168 175.00 +.10(180 - 175.00) = 175.50 3159 4175 5190 6205 Exponential Smoothing Solution F t = F t -1 + 0.1( A t -1 - F t -1 )

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-44 F t = F t -1 + 0.1( A t -1 - F t -1 ) QuarterActual Forecast, F t ( α =.10) 1180175.00 (Given) 2168 175.00 +.10(180 - 175.00) = 175.50 3159 175.50 +.10(168 - 175.50) = 174.75 4175 5190 6205 Exponential Smoothing Solution

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-45 F t = F t -1 + 0.1( A t -1 - F t -1 ) Quarter Actual Forecast, F t ( α =.10) 1995180175.00 (Given) 1996168175.00 +.10(180 - 175.00) = 175.50 1997159175.50 +.10(168 - 175.50) = 174.75 1998175 1999190 2000205 174.75 +.10(159 - 174.75)= 173.18 Exponential Smoothing Solution

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-46 F t = F t -1 + 0.1( A t -1 - F t -1 ) QuarterActual Forecast, F t ( α =.10) 1180175.00 (Given) 2168175.00 +.10(180 - 175.00) = 175.50 3159175.50 +.10(168 - 175.50) = 174.75 4 175174.75 +.10(159 - 174.75) = 173.18 5190173.18 +.10(175 - 173.18) = 173.36 6205 Exponential Smoothing Solution

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-47 F t = F t -1 + 0.1( A t -1 - F t -1 ) QuarterActual Forecast, F t ( α =.10) 1180175.00 (Given) 2168175.00 +.10(180 - 175.00) = 175.50 3159175.50 +.10(168 - 175.50) = 174.75 4175174.75 +.10(159 - 174.75) = 173.18 5190173.18 +.10(175 - 173.18) = 173.36 6205173.36 +.10(190 - 173.36) = 175.02 Exponential Smoothing Solution

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-48 F t = F t -1 + 0.1( A t -1 - F t -1 ) TimeActual Forecast, F t ( α =.10) 4175174.75 +.10(159 - 174.75) = 173.18 5190173.18 +.10(175 - 173.18) = 173.36 6205173.36 +.10(190 - 173.36) = 175.02 Exponential Smoothing Solution 7180 8 175.02 +.10(205 - 175.02) = 178.02 9

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-49 F t = F t -1 + 0.1( A t -1 - F t -1 ) TimeActual Forecast, F t ( α =.10) 4 175174.75 +.10(159 - 174.75) = 173.18 5 190173.18 +.10(175 - 173.18) = 173.36 6 205173.36 +.10(190 - 173.36) = 175.02 Exponential Smoothing Solution 7 180 8 175.02 +.10(205 - 175.02) = 178.02 9 178.22 +.10(182 - 178.22) = 178.58 182 178.02 +.10(180 - 178.02) = 178.22 ?

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-50 F t =  A t - 1 +  (1-  ) A t - 2 +  (1-  ) 2 A t - 3 +... Forecast Effects of Smoothing Constant  Weights Prior Period  2 periods ago  (1 -  ) 3 periods ago  (1 -  ) 2 ==  = 0.10  = 0.90 10%

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-51 F t =  A t - 1 +  (1-  ) A t - 2 +  (1-  ) 2 A t - 3 +... Forecast Effects of Smoothing Constant  Weights Prior Period  2 periods ago  (1 -  ) 3 periods ago  (1 -  ) 2 ==  = 0.10  = 0.90 10% 9%

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-52 F t =  A t - 1 +  (1-  ) A t - 2 +  (1-  ) 2 A t - 3 +... Forecast Effects of Smoothing Constant  Weights Prior Period  2 periods ago  (1 -  ) 3 periods ago  (1 -  ) 2 ==  = 0.10  = 0.90 10% 9% 8.1%

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-53 F t =  A t - 1 +  (1-  ) A t - 2 +  (1-  ) 2 A t - 3 +... Forecast Effects of Smoothing Constant  Weights Prior Period  2 periods ago  (1 -  ) 3 periods ago  (1 -  ) 2 ==  = 0.10  = 0.90 10% 9% 8.1% 90%

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-54 F t =  A t - 1 +  (1-  ) A t - 2 +  (1-  ) 2 A t - 3 +... Forecast Effects of Smoothing Constant  Weights Prior Period  2 periods ago  (1 -  ) 3 periods ago  (1 -  ) 2 ==  = 0.10  = 0.90 10% 9% 8.1% 90%9%

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-55 F t =  A t - 1 +  (1-  ) A t - 2 +  (1-  ) 2 A t - 3 +... Forecast Effects of Smoothing Constant  Weights Prior Period  2 periods ago  (1 -  ) 3 periods ago  (1 -  ) 2 ==  = 0.10  = 0.90 10% 9% 8.1% 90%9%0.9%

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-56 Impact of 

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-57 Choosing  Seek to minimize the Mean Absolute Deviation (MAD) If:Forecast error = demand - forecast Then:

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-58  F t = exponentially smoothed forecast in period t  T t = exponentially smoothed trend in period t  A t = actual demand in period t  = smoothing constant for the average  = smoothing constant for the trend Exponential Smoothing with Trend Adjustment “ Double Exponential Smoothing”

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-59 Exponential Smoothing with Trend Adjustment FITt : Forecast including trend in period t, t=1,2,...,n FIT t = F t +T t where F t =  A t-1 +(1-  ) FIT t-1 T t =  (F t - F t-1 ) + (1-  )T t-1

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-61 Comparing Actual and Forecasts

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-62  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 YabX i  Linear Trend Projection using Regression

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-63 Least Squares Deviation Time Values of Dependent Variable Actual observation Point on regression line

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-64 Least Squares Equations Equation: Slope: Y-Intercept:

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-65 Using a Trend Line YearDemand 1997 74 1998 79 1999 80 2000 90 2001 105 2002 142 2003 122 The demand for electrical power at N.Y.Edison over the years 1997 – 2003 is given at the left. Find the overall trend.

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-66 Finding a Trend Line YearTime Period Power Demand x2x2 xy 19971741 19982794158 19993809240 200049016360 2001510525525 2002614236852 2003712249854  x=28  y=692  x 2 =140  xy=3,063

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-67 The Trend Line Equation

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-68 Actual and Trend Forecast

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-69 Seasonality Analysis Critical in capacity planning when high demand occurs in: -electric power during winter -banks during Friday afternoons -buses subways during rush hours, -restaurants during lunch and dinner, etc.

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-71 Ex. 9 Monthly Sales of IBM Laptops Sales DemandAverage Demand Month2000200120022000-2002MonthlySeasonal Index Jan808510590940.957 Feb7085 80940.851 Mar80938285940.904 Apr9095115100941.064 May113125131123941.309 Jun110115120115941.223 Jul100102113105941.117 Aug88102110100941.064 Sept85909590940.957 Oct77788580940.851 Nov75728380940.851 Dec827880 940.851

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-72 Question: 1) Let the forecasted demand in 2003 be 1200 units. Give forecasts for January 2003 IBM labtop sales? F 37 =average monthly sales in 2003*January index =1200/12 * 0.957 = 96! (so we assume no trend at all) 2) If no info is given on next year’s demand, how would you give the forecast for January 2003 IBM labtop sales?

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-73 Answer: Step 1: Apply trend analysis by using average monthly sales data only. (use 12 data points), Step 2: Alternative approach: Deseasonalize the time series data by where is the deseasonalized value of Apply trend analysis by using all deseasonalized data points (use 36 data points). Alternative approach: Apply exponential smoothing with trend to deseasonalized data points.

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-74 Demand for IBM Laptops

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-75 Example 10 : San Diego Hospital used 66 data points to reach to the following trend equation: = Patient days (deseasonalized value) = time in months Forecast the patient days in the next month?

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-76 San Diego Hospital – Inpatient Days

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-77 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 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-78 Regression

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-79 YX ii = a b  Shows linear relationship between dependent & explanatory variables  Example: Sales & advertising ( not time) Dependent (response) variable Independent (explanatory) variable Slope Y-intercept ^ Linear Regression Model +

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-80 Y X Y a i  ^ ii bX i = ++ + Error Observed value YabX = ++ Regression line Linear Regression Model

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-81 Linear Regression Equations Equation: Slope: Y-Intercept:

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-82  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 Interpretation of Coefficients

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-83 Least Squares Assumptions  Relationship is assumed to be linear.  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.

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-84  Variation of actual Y from predicted Y  Measured by standard error of estimate, S Y,X  Affects several factors  Parameter significance  Prediction accuracy Random Error Variation

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-85 Standard Error of the Estimate

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-86 Assumptions on Error Terms The mean of errors for each x is zero. Standard deviation of error terms, S Y,X is the same for each x. Errors are independent of each other. Errors are normally distributed with mean=0 and variance= S Y,X. for each x.

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-87  Answers: ‘ how strong is the linear relationship between the variables?’  Correlation coefficient, r  Values range from -1 to +1  Measures degree of association  Used mainly for understanding Correlation

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-88 Sample Coefficient of Correlation

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-89 Coefficient of Correlation and Regression Model

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-90 Coefficient of Determination If we do not use any regression model, total sum of square of errors, SST If we use a regression model, sum of squares of errors Then sum of squares of errors due to regression We define coef. of determination

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-91 Coefficient of determination r 2 is the variation in y that is explained and hence recovered/eliminated by the regression equation ! Correlation coeficient r can also be found by using

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-92  You want to achieve:  No pattern or direction in forecast error, remember independency of errors assumption.  Error = ( Y i - Y i ) = (Actual - Forecast)  Seen in plots of errors over time  Smallest forecast error  Mean square error (MSE)  Mean absolute deviation (MAD)  Mean absolute percent error Guidelines for Selecting Forecasting Model ^

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-93 Time (Years) Error 0 0 Desired Pattern Time (Years) Error 0 Trend Not Fully Accounted for Pattern of Forecast Error Residual Analysis: Validation

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-94  Mean Square Error (MSE)  Mean Absolute Deviation (MAD)  Mean Absolute Percent Error (MAPE) Forecast Error Equations

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-95 You’re a marketing analyst for Hasbro Toys. You’ve forecast sales with a linear model & exponential smoothing. Which model do you use? ActualLinear ModelExponential Smoothing YearSalesForecastForecast (.9) 199810.61.0 199911.31.0 200022.01.9 200122.72.0 200243.43.8 Selecting Forecasting Model Example

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-96 MSE = Σ Error 2 / 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 Linear Model Evaluation Y i 1 1 2 2 4 ^ Y i ^ 0.6 1.3 2.0 2.7 3.4 Year 1998 1999 2000 2001 2002 Total 0.4 -0.3 0.0 -0.7 0.6 0.0 Error 0.16 0.09 0.00 0.49 0.36 1.10 Error 2 0.4 0.3 0.0 0.7 0.6 2.0 |Error| Actual 0.40 0.30 0.00 0.35 0.15 1.20

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-97 MSE = Σ Error 2 / 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 Exponential Smoothing Model Evaluation

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-98 Comparison of the Models Linear Model: MSE = Σ Error 2 / 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 Error 2 / 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 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-99  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 Tracking Signal

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-100 Tracking Signal Equation

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-101 Tracking Signal Computation

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-114 Plot of a Tracking Signal Time Lower control limit Upper control limit Signal exceeded limit Tracking signal Acceptable range MAD + 0 -

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-115 Tracking Signals Tracking Signal Forecast Actual demand

PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-116 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 © 2004 by Prentice Hall, Inc., Upper Saddle River, N.J. 07458 4-117 Forecast of Sales by Hour for Fast Food Restaurant 11-12 12-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11

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PowerPoint presentation to accompany Heizer/Render – Principles of Operations Management, 5e, and Operations Management, 7e © 2004 by Prentice Hall, Inc.,

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