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4-1 Operations Management Forecasting Chapter 4

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4-2 Examples Predict the next number in the pattern: a) 3.7, 3.7, 3.7, 3.7, 3.7, ? b) 2.5, 4.5, 6.5, 8.5, 10.5, ? c) 5.0, 7.5, 6.0, 4.5, 7.0, 9.5, 8.0, 6.5, ?

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4-3 Examples Predict the next number in the pattern: a) 3.7, 3.7, 3.7, 3.7, 3.7, y = 3.7 b) 2.5, 4.5, 6.5, 8.5, 10.5, y = x c) 5.0, 7.5, 6.0, 4.5, 7.0, 9.5, 8.0, 6.5, y = x + c i c 1 = 0; c 2 = 2; c 3 = 0; c 4 = -2; etc

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4-4 Outline What is Forecasting ? Time horizons. Life cycle. Types of Forecasts. Eight Steps in the Forecasting System. Forecasting Approaches: Overview of Qualitative Methods. Overview of Quantitative Methods.

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4-5 Outline - Continued Time-Series Forecasting: Moving Averages. Exponential Smoothing. Trend Projection. Associative Forecasting Methods: Regression and Correlation Analysis. Monitoring and Controlling Forecasts. Forecasting in the Service Sector.

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4-6 What is Forecasting? Art and science of predicting future events. Underlying basis of all business decisions. Production & Inventory. Personnel & Facilities. Focus on forecasting demand. Sales will be $200 Million!

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4-7 Short-range forecast: 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. Types of Forecasts by Time Horizon

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4-8 Short- vs. Long-term Forecasting Medium & Long range forecasts: Long range for design of system. Deal with comprehensive issues. Support management decisions regarding planning. Short-term forecasts: To plan detailed use of system. Usually use quantitative techniques. More accurate than longer-term forecasts.

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4-9 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 (expansion and contraction), as product passes through life cycle stages.

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4-10 Forecasting During the Life Cycle Hard to forecast. Need long-range forecasts. Often use qualitative models. IntroductionGrowthMaturityDecline Sales Forecasting critical, both for future magnitude and growth rate. Long-range forecasts still important. Easier to forecast. Use quantitative models. Hard to forecast, but forecasting is less important. Time

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4-11 Eight 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. Monitor forecasts and adjust when needed.

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4-12 Realities of Forecasting Assumes future will be like the past (causal factors will be the same). Forecasts are imperfect. Forecasts for groups of product are more accurate than forecasts for individual products. Accuracy decreases with length of forecast.

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4-13 Forecasting Approaches Used when situation is ‘stable’ & historical data exist. Existing products & current technology. No significant changes expected. Involves mathematical techniques. Example: forecasting sales of color televisions. Quantitative Methods Used when little data or time exist. New products & technology. Long time horizon. Major changes expected. Involves intuition, experience. Example: forecasting for e-commerce sales. Qualitative Methods

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4-14 Overview of Qualitative Methods Jury of executive opinion. Combine opinions from executives. Sales force composite. Aggregate estimates from salespersons. Delphi method. Query experts interatively. Consumer market survey. Survey current and potential customers.

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4-15 Seek opinions/estimates from small group of high-level managers working together. Combines managerial experience with statistical models. + Relatively quick. - ‘Group-think’. - Leader may dominate. Jury of Executive Opinion

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4-16 Sales Force Composite Each salesperson projects their sales. Aggregate projections at district & national levels. + Sales rep’s know customers. - Must not reward inaccurate forecasts. May over- or under-forecast to acquire more resources.

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4-17 Delphi Method Iterative group process. 3 types of people: Decision makers. Staff. Respondents. + Reduces ‘group-think’. - Takes time. Respondents Staff (Make forecast) (Provide input to decision makers) Decision Makers (Administer)

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4-18 Consumer Market Survey Ask customers about purchasing plans. + Relatively simple. - What consumers say, and what they actually do are often different. How many hours will you use the Internet next week?

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4-19 Quantitative Forecasting Methods Quantitative Forecasting Linear Regression Associative Models Exponential Smoothing Moving Average Time Series Models Trend Projection

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4-20 Set of evenly spaced numerical data. From observing response variable at regular time periods. Forecast based only on past values. Assumes that factors influencing past will continue influence in future. Example: Year: Sales: What is a Time Series?

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4-21 Trend Seasonal Cyclical Random Time Series Components

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4-22 Product Demand over 4 Years Year 1 Year 2 Year 3 Year 4 Demand for product or service

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4-23 Product Demand over 4 Years Actual demand line Year 1 Year 2 Year 3 Year 4 Seasonal peaks Trend component Demand for product or service Random variation Cyclic component

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4-24 Persistent, overall upward or downward pattern. Due to population, technology etc. Several years duration. Time Trend Component

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4-25 Regular pattern of up & down fluctuations. Due to weather, customs etc. Occurs within 1 year. Quarterly, monthly, weekly, etc. Time Demand Summer Seasonal Component

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4-26 Repeating up & down movements. Due to interactions of factors influencing economy. Usually 2-10 years duration. Year Demand Cycle Cyclical Component

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4-27 Erratic, unsystematic, ‘residual’ fluctuations. Due to random variation or unforeseen events. Union strike Tornado Short duration & non-repeating. Random Component

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4-28 Any value in a time series is a combination of the trend, seasonal, cyclic, and random components. Multiplicative model: Y i = T i · S i · C i · R i Additive model: Y i = T i + S i + C i + R i General Time Series Models

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4-29 Naive Approach 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. Usually not good.

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4-30 MA is a series of arithmetic means. Used if little or no trend. Used often for smoothing. MA n n Demand in previous periods periods Moving Average Method

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4-31 You’re manager of a museum store that sells historical replicas. You want to forecast sales (in thousands) for months 4 and 5 using a 3-period moving average. Month 14 Month 2 6 Month 35 Month 4? Month 5? Moving Average Example

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4-32 Moving Average Forecast MonthResponse Y i Moving Total (n=3) Moving Average (n=3) 14NA ? 5? 4+6+5=15 15/3=5 6 ?

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4-33 Month Moving Average Graph Sales Actual Forecast

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4-34 Actual Demand for Month 4 = 3

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4-35 Month Moving Average Graph Sales Actual Forecast

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4-36 Moving Average Forecast MonthResponse Y i Moving Total (n=3) Moving Average (n=3) 14NA =1414/3= ?

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4-37 Month Moving Average Graph Sales Actual Forecast

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4-38 Actual Demand for Month 5 = 7 MonthResponse Y i Moving Total (n=3) Moving Average (n=3) 14NA =1414/3= ?

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4-39 Month Moving Average Graph Sales Actual Forecast

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4-40 Moving Average Forecasts MonthResponse Y i Moving Total (n=3) Moving Average (n=3) 14NA =1515/3= =1414/3= ? 5+3+7=1515/3=5.0

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4-41 Month Moving Average Graph Sales Actual Forecast

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4-42 Gives more emphasis to recent data. Weights decrease for older data. Weights sum to 1.0. May be based on intuition. Sum of digits weights: numerators are consecutive. 3/6, 2/6, 1/6 4/10, 3/10, 2/10, 1/10 WMA = Σ [(Weight for period n) (Demand in period n)] ΣWeights Weighted Moving Average Method

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4-43 Weighted Moving Average: 3/6, 2/6, 1/6 MonthResponse Y i Weighted Moving Average 14 NA /6 = ? ? ?

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4-44 Weighted Moving Average: 3/6, 2/6, 1/6 MonthResponse Y i Weighted Moving Average 14 NA /6 = ? 25/6 = /6 = 5.333

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4-45 Increasing n makes forecast: Less sensitive to changes. Less sensitive to recent data. Weights control emphasis on recent data. Do not forecast trend well. Require historical data. Moving Average Methods Moving Average Methods

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4-46 Moving Average Graph Time Demand Actual

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4-47 Moving Average Graph Time Demand Actual Small n Large n

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4-48 Weighted Moving Average Graph Time Demand Actual Large weight on recent data Small weight on recent data

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4-49 Form of weighted moving average. Weights decline exponentially. Most recent data weighted most. Requires smoothing constant ( ). Usually ranges from 0.05 to 0.5 Should be chosen to give good forecast. Involves little record keeping of past data. Exponential Smoothing Method

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4-50 F t = F t -1 + ( A t -1 - F t -1 ) F t = Forecast value for time t A t-1 = Actual value at time t-1 = Smoothing constant Need initial forecast F t-1 to start. Could be given or use moving average. Exponential Smoothing Equation

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4-51 You want to forecast product demand using exponential smoothing with =.10. Suppose in the most recent month (month 6) the forecast was 175 and the actual demand was 180. Month 6180 Month 7 ? Month 8? Month 9? Month 10? Exponential Smoothing Example

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4-52 α F t = F t -1 + α ( A t -1 - F t -1 ) Month Actual Forecast,F t ( αααα =.10) (Given) 7? ( ) = ? 9? 10? 11 ? Exponential Smoothing - Month 7

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4-53 Exponential Smoothing - Month 8 α F t = F t -1 + α ( A t -1 - F t -1 ) Actual Forecast, F t ( α =.10) (Given) ( ) = ? ( ) = ? ? ? Month

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4-54 Exponential Smoothing Solution α F t = F t -1 + α ( A t -1 - F t -1 ) Actual Forecast, F t ( α =.10) (Given) ( ) = ( ) = ? ( ) = ? ? Month

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( ) = Exponential Smoothing Solution α F t = F t -1 + α ( A t -1 - F t -1 ) Actual Forecast, F t ( α =.10) (Given) ( ) = ( ) = ( ) = ? ( ) = Month

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4-56 Month Sales Actual Forecast Exponential Smoothing Graph

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4-57 α Increasing α makes forecast: More sensitive to changes. More sensitive to recent data. α α controls emphasis on recent data. Do not forecast trend well. Trend adjusted exponential smoothing - p Exponential Smoothing Methods Exponential Smoothing Methods

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4-58 Exponential Smoothing Graph Time Demand Actual

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4-59 Exponential Smoothing Graph Time Demand Actual Large α Small α

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4-60 F t = A t (1- ) A t (1- ) 2 A t Forecast Effects of Smoothing Constant Weights Prior Period 2 periods ago (1 - ) 3 periods ago (1 - ) 2 == = 0.10 = % 9% 8.1% 90%9%0.9%

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4-61 Choosing - Comparing Forecasts A good method has a small error. Choose to produce a small error. Error = Demand - Forecast Error > 0 if forecast is too low Error < 0 if forecast is too high MAD = Mean Absolute Deviation : Average of absolute values of errors. MSE = Mean Squared Error : Average of squared errors. MAPE = Mean Absolute Percentage Error : Average of absolute value of percentage errors.

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4-62 Mean Absolute Deviation (MAD) Mean Squared Error (MSE) Forecast Error Equations

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4-63 Mean Absolute Percentage Error (MAPE) Forecast Error Equations

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4-64 MAD F1 = 9/4 = 2.25 F2 = 10/4 = 2.5 MSE F1 = 31/4 = 7.75 F2 = 26/4 = 6.5 MAPE F1 = = 17.1% F2 = = 15.6% Forecast Error Example Actual F1 F1 error F2 F2 error

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4-65 MAD F1 = 9/4 = 2.25 F2 = 10/4 = 2.5 MSE F1 = 31/4 = 7.75 F2 = 26/4 = 6.5 MAPE F1 = = 17.1% F2 = = 15.6% Which Forecast is Best?

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