Introduction to Operations Management Forecasting (Ch.3) Hansoo Kim ( 金翰秀 ) Dept. of Management Information Systems, YUST

OM Overview Class Overview (Ch. 0) Project Management (Ch. 17) Strategic Capacity Planning (Ch. 5, 5S) Operations, Productivity, and Strategy (Ch. 1, 2) Mgmt of Quality/ Six Sigma Quality (Ch. 9, 10) Supply Chain Management (Ch 11) Location Planning and Analysis (Ch. 8) Demand Mgmt Forecasting (Ch 3) Inventory Management (Ch. 12) Aggregated Planning (Ch. 13) Queueing/ Simulation (Ch. 18) MRP & ERP (Ch 14) JIT & Lean Mfg System (Ch. 15) Term Project Process Selection/ Facility Layout; LP (Ch. 6, 6S) X X XXX X X X X

Today’s Outline  What is Forecasting? 수요예측이란 ?  Types of Forecasting 종류  Seven Steps of Forecasting 절차  Qualitative vs. Quantitative Forecasts 정성적 / 정량적 방법  Various Forecasting Methods 여러 가지 수요예측 방법들  Evaluation Measures 평가방법

Terms( 용어 )  Associative models （联合模型）  Bias （偏差）  Centered moving average （中心滑动 平均数）  Control chart （控制图）  Correlation （想关系数）  Cycles （循环变动）  Delphi method （德尔菲法）  Error （误差）  Exponential smoothing （指数平滑法）  Forecast ( 预册 )  Irregular variation （不规则变化）  Judgmental forecasts （通过判断作出 预测）  Least square line （最小二乘直线）  Linear trend equation （线形趋势模型）  Mean absolute deviation, MAD （绝对 平均偏差）  Mean squared error, MSE （标准偏差）  Moving average （滑动平均法）  Naive forecast （简单预测法）  Predictor variable （预测变动）  Random variations （随机变量）  Regression （回归分析）  Seasonal variations （季节性变动）  Time series （时间序列）  Tracking signal （跟踪信号）  Trend （长期趋势变动）  Trend-adjusted exponential smoothing （调整长期趋势后的指数平滑法）

Example: Forecasting Demand > Products ---  Lost Sales Demand < Products ---  Inventory cost  What is demand in 21 st week?

What is Forecasting?  The art and science of predicting future events, Using historical data  Underlying basis of all business decisions Production Inventory Personnel Facilities Sales will be $200 Million! CRM: Customer Relation Management

AccountingCost/profit estimates FinanceCash flow and funding Human ResourcesHiring/recruiting/training MarketingPricing, promotion, strategy MISIT/IS systems, services OperationsSchedules, MRP, workloads Product/service designNew products and services Uses of Forecasts

Types of Forecasts by Time Horizon  Short-range forecast ( 단기 예측 ) Up to 1 year; usually less than 3 months Job scheduling, worker assignments  Medium-range forecast ( 중기 예측 ) 3 months to 3 years Sales & production planning, budgeting  Long-range forecast ( 장기 예측 ) 3 + years New product planning, facility location, R&D

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 ( 도입기, 성장기, 성숙기, 쇠퇴기 )

Strategy and Issues During a Product ’ s Life

Steps in the Forecasting Process Step 1 Determine purpose of forecast Step 2 Establish a time horizon Step 3 Select a forecasting technique Step 4 Obtain, clean and analyze data Step 5 Make the forecast Step 6 Monitor the forecast “The forecast”

Realities of Forecasting  Forecasts are seldom perfect ( 수요예측은 잘 맞지 않는다 !!) stability  Most forecasting methods assume that there is some underlying stability in the system ( 신제품 보다는 성숙기에 도달한 제품 ) product family and aggregated product  Both product family and aggregated product forecasts are more accurate than individual product forecasts ( 단일제품 보다는 제품群으로 예측하는 것이 더 정확하다 )

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 ( 정량적방법 )  Used when situation is vague & little data exist  New products  New technology  Involves intuition, experience  e.g., forecasting sales on Internet Qualitative Methods ( 정성적방법 )

Overview of Qualitative Methods ( 정 성적인 방법들 )  Jury of executive opinion Pool opinions of high-level executives, sometimes augment by statistical models  Delphi method ( 델파이 기법 )** Panel of experts, queried iteratively  Sales force composite Estimates from individual salespersons are reviewed for reasonableness, then aggregated  Consumer Market Survey Ask the customer

Overview of Quantitative Approaches  Naïve approach  Moving averages  Exponential smoothing  Trend projection  Linear regression Time-series Models Associative models

What is a Time Series?  Set of evenly spaced numerical data Obtained by observing response variable at regular time periods  Forecast based only on past values Assumes that factors influencing past and present will continue influence in future  Example Year: Sales:

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

Time Series Components Trend Seasonal Cyclical Random

Overview of Qualitative Methods ( 정량적 인 방법들 )  Naïve Approach  Moving Average (MA) 滑动平均法  Weighted Moving Average  Exponential Smoothing Method ( 指数平滑法 )  Exponential Smoothing with Trend Adjustment ( 调整长期趋势后的指数平滑法 )

Naive Approach ( 简单预测法 )  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.

Moving Average (MA) Method 滑动平均法  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 where F t = Forecast for time period t MA n = n period moving average A t – 1 = Actual value in period t – 1 n = Number of periods (data points) in the moving average For example, MA 3 would refer to a three-period moving average forecast, and MA 5 would refer to a five-period moving average forecast.

Moving Average Example You’re manager of a museum store that sells historical replicas. You want to forecast sales for 2008 using a 3-period moving average © 1995 Corel Corp.

Moving Average Solution

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) ΣWeights

Actual Demand, Moving Average, Weighted Moving Average Actual sales Moving average Weighted moving average

Disadvantages of Moving Average Methods  Increasing n makes forecast less sensitive to changes  Do not forecast trend well  Require much historical data

Measure for Forecasting Error  Mean Square Error (MSE, 标准偏差 )  Mean Absolute Deviation (MAD, 绝对平均偏差 )  Mean Absolute Percent Error (MAPE)

Exponential Smoothing Method ( 指 数平滑法 )  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 Equations  F t =  A t -1 +  (1-  )A t -2 +  (1-  ) 2 ·A t  (1-  ) 3 A t  (1-  ) t-1 ·A 0 F t = Forecast value A t = Actual value  = Smoothing constant  F t = F t-1 +  (A t-1 - F t-1 ) =  A t-1 +(1-  ) F t-1 Use for computing forecast

Exponential Smoothing Example During the past 8 quarters, the Port of Baltimore has unloaded large quantities of grain. (  =.10). The first quarter forecast was QuarterActual ? Find the forecast for the 9 th quarter.

Exponential Smoothing Solution F t = F t ( A t -1 - F t -1 ) QuarterActual Forecast, F t ( α =.10) (Given) ( ) = ( ) = ( ) = ( ) = ( ) =

Exponential Smoothing Solution F t = F t ( A t -1 - F t -1 ) TimeActual Forecast, F t ( α =.10) ( ) = ( ) = ( ) = ( ) = ( ) = ( ) = ?

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

Impact of 

Choosing  Mean Absolute Deviation (MAD) Seek to minimize the Mean Absolute Deviation (MAD) If:Forecast error = demand - forecast Then:

Using MS-Excel  Naïve  MA  WMA  Exponential Smoothing Method

Associative Model: Regression ( 회기분석, 回归分析 ) Deviation Time Values of Dependent Variable Actual observation Point on regression line

Actual and the Least Squares Line

Linear Trend Projection  Used for forecasting linear trend line  Assumes relationship between response variable, Y, and time, X, is a linear function  Estimated by least squares method Minimizes sum of squared errors i YabX i 

Linear Trend Projection Model b > 0 b < 0 a a Y Time, X

Least Squares Equations Equation: Slope: Y-Intercept:

Computation Table ( 계산표 )

Using Regression Model  YearDemand        The demand for electrical power at N.Y.Edison over the years 2000 – 2006 is given at the left. Find the overall trend.

Calculation for finding a and b YearTime Period Power Demand x2x2 xy  x=28  y=692  x 2 =140  xy=3,063

The Trend Line Equation

Actual and Trend Forecast

 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 Correlation ( 상관관계 )

Sample Coefficient of Correlation ( 想关系数 )

Coefficient of Correlation and Regression Model r 2 = square of correlation coefficient (r), is the percent of the variation in y that is explained by the regression equation

 You want to achieve: No pattern or direction in forecast error  Error (or Bias) = (Y i - Y i ) = (Actual - Forecast)  Seen in plots of errors over time Smallest forecast error  Mean square error (MSE)  Mean absolute deviation (MAD) Guidelines for Selecting Forecasting Model ^

Time (Years) Error 0 0 Desired Pattern Time (Years) Error 0 Trend Not Fully Accounted for Pattern of Forecast Error

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) Selecting Forecasting Model Example

MSE = Σ Error 2 / n = 1.10 / 5 = MAD = Σ |Error| / n = 2.0 / 5 = MAPE = 100 Σ|absolute percent errors|/ n = 1.20/5 = Linear Model Evaluation Y i ^ Y i ^ Year Total Error Error |Error| Actual

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

Exponential Smoothing Model Evaluation ( 어떤 모델이 더 좋은가 ?) 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 = 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

 Measures how well the forecast is predicting actual values running sum of forecast errors mean absolute deviation  Ratio of running sum of forecast errors (RSFE) to mean absolute deviation (MAD) = RSFE/MAD Good tracking signal has low values  Should be within upper and lower control limits Tracking Signal ( 跟踪信号 )

Tracking Signal Equation

Tracking Signal Computation

Plot of a Tracking Signal Time Lower control limit Upper control limit Signal exceeded limit Tracking signal Acceptable range MAD + 0 -

The % of Points included within the Control Limits for a range of 1 to 4 MAD ±1 MAD ±2 MAD ±3 MAD ±4 MAD Number of MADRelated STDEV% ± % ± % ± % ± %

Formula Review

Summary  What is Forecasting?  Types of Forecasting Qualitative Methods Quantitative Methods  Quantitative Methods Naïve MA Exponential Smoothing Regression  Evaluation Measures MSE, MAD, MAPE

What to do  HW Example 1, 2, 3, 8, 9, 10 Solved Problems 1, 6, 7