4 - 1 Course Title: Production and Operations Management Course Code: MGT 362 Course Book: Operations Management 10 th Edition. By Jay Heizer & Barry Render

4 - 2 Chapter 4: Forecasting

4 - 3 Summery of Previous Presentation (1/3)  Global Company Profile: Disney World  What Is Forecasting?  Forecasting Time Horizons  The Influence of Product Life Cycle  Types Of Forecasts

4 - 4 Summery of Previous Presentation (2/3)  The Strategic Importance of Forecasting  Human Resources  Capacity  Supply Chain Management  Seven Steps in the Forecasting System

4 - 5 Summery of Previous Presentation (3/3)  Forecasting Approaches  Overview of Qualitative Methods  Overview of Quantitative Methods

4 - 6 Summary of Today's Presentation  Time-Series Forecasting  Decomposition of a Time Series  Naive Approach  Moving Averages  Exponential Smoothing  Exponential Smoothing with Trend Adjustment  Trend Projections

4 - 7 Overview of Quantitative Approaches 1.Naive approach 2.Moving averages 3.Exponential smoothing 4.Trend projection 5.Linear regression time-series models associative model

4 - 8  Set of evenly spaced numerical data  Obtained by observing response variable at regular time periods  Forecast based only on past values, no other variables important  Assumes that factors influencing past and present will continue to influence in future Time Series Forecasting

4 - 9 Trend Seasonal Cyclical Random Time Series Components

Components of Demand Demand for product or service |||| 1234 Time (years) Average demand over 4 years Trend component Actual demand line Random variation Figure 4.1 Seasonal peaks

 Persistent, overall upward or downward pattern  Changes due to population, technology, age, culture, etc.  Typically several years duration Trend Component

 Regular pattern of up and down fluctuations  Due to weather, customs, etc.  Occurs within a single year Seasonal Component Number of PeriodLengthSeasons WeekDay7 MonthWeek4-4.5 MonthDay28-31 YearQuarter4 YearMonth12 YearWeek52

 Repeating up and down movements  Affected by business cycle, political, and economic factors  Multiple years duration  Often causal or associative relationships Cyclical Component

 Erratic, unsystematic, ‘residual’ fluctuations  Due to random variation or unforeseen events  Short duration and no repeating Random Component MTWTFMTWTF

Naive Approach  Assumes demand in next period is the same as demand in most recent period  e.g., If January sales were 68, then February sales will be 68  Sometimes cost effective and efficient  Can be good starting point

 MA is a series of arithmetic means  Used if little or no trend  Used often for smoothing Moving Average Method Moving average = ∑ demand in previous n periods n

January10 February12 March13 April16 May19 June23 July26 Actual3-Month MonthShed SalesMoving Average ( )/3 = 13 2 / 3 ( )/3 = 16 ( )/3 = 19 1 / 3 Moving Average Example ( )/3 = 11 2 / 3

Graph of Moving Average ||||||||||||JFMAMJJASOND||||||||||||JFMAMJJASOND Shed Sales 30 – 28 – 26 – 24 – 22 – 20 – 18 – 16 – 14 – 12 – 10 – Actual Sales Moving Average Forecast

 Used when some trend might be present  Older data usually less important  Weights based on experience and intuition Weighted Moving Average Weighted moving average = ∑ (weight for period n) x (demand in period n) ∑ weights

January10 February12 March13 April16 May19 June23 July26 Actual3-Month Weighted MonthShed SalesMoving Average [(3 x 16) + (2 x 13) + (12)]/6 = 14 1 / 3 [(3 x 19) + (2 x 16) + (13)]/6 = 17 [(3 x 23) + (2 x 19) + (16)]/6 = 20 1 / 2 Weighted Moving Average [(3 x 13) + (2 x 12) + (10)]/6 = 12 1 / 6 Weights AppliedPeriod 3 3Last month 2 2Two months ago 1 1Three months ago 6Sum of weights

 Increasing n smooth the forecast but makes it less sensitive to changes  Do not forecast trends well  Require extensive historical data Potential Problems With Moving Average

Moving Average And Weighted Moving Average 30 – 25 – 20 – 15 – 10 – 5 – Sales demand ||||||||||||JFMAMJJASOND||||||||||||JFMAMJJASOND Actual sales Moving average Weighted moving average Figure 4.2

 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

Exponential Smoothing New forecast =Last period’s forecast +  (Last period’s actual demand – Last period’s forecast) F t = F t – 1 +  (A t – 1 - F t – 1 ) whereF t =new forecast F t – 1 =previous forecast  =smoothing (or weighting) constant (0 ≤  ≤ 1)

Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant  =.20

Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant  =.20 New forecast= (153 – 142)

Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant  =.20 New forecast= (153 – 142) = = ≈ 144 cars

Impact of Different  225 – 200 – 175 – 150 – ||||||||| ||||||||| Quarter Demand  =.1 Actual demand  =.5

Impact of Different  225 – 200 – 175 – 150 – ||||||||| ||||||||| Quarter Demand  =.1 Actual demand  =.5  Chose high values of  when underlying average is likely to change  Choose low values of  when underlying average is stable

Choosing  The objective is to obtain the most accurate forecast no matter the technique We generally do this by selecting the model that gives us the lowest forecast error Forecast error= Actual demand - Forecast value = A t - F t

Common Measures of Error Mean Absolute Deviation (MAD) MAD = ∑ |Actual - Forecast| n Mean Squared Error (MSE) MSE = ∑ (Forecast Errors) 2 n

Common Measures of Error Mean Absolute Percent Error (MAPE) MAPE = ∑ 100|Actual i - Forecast i |/Actual i n i = 1

Comparison of Forecast Error RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  =

Comparison of Forecast Error RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  = MAD = ∑ |deviations| n = 82.45/8 = For  =.10 = 98.62/8 = For  =.50

Comparison of Forecast Error RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  = MAD = 1,526.54/8 = For  =.10 = 1,561.91/8 = For  =.50 MSE = ∑ (forecast errors) 2 n

Comparison of Forecast Error RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  = MAD MSE = 44.75/8 = 5.59% For  =.10 = 54.05/8 = 6.76% For  =.50 MAPE = ∑ 100|deviation i |/actual i n i = 1

Comparison of Forecast Error RoundedAbsoluteRoundedAbsolute ActualForecastDeviationForecastDeviation Tonnagewithforwithfor QuarterUnloaded  =.10  =.10  =.50  = MAD MSE MAPE5.59%6.76%

Summary of Today's Presentation  Time-Series Forecasting  Decomposition of a Time Series  Naive Approach  Moving Averages  Exponential Smoothing  Exponential Smoothing with Trend Adjustment  Trend Projections