Operations Management Chapter 4 - Forecasting PowerPoint presentation to accompany Heizer/Render Principles of Operations Management, 6e Operations Management, 8e © 2006 Prentice Hall, Inc.

Outline What Is Forecasting? Types Of Forecasts Forecasting Time Horizons Types Of Forecasts The Strategic Importance Of Forecasting Seven Steps In The Forecasting System

Outline – Continued Forecasting Approaches Time-series Forecasting Overview of Qualitative Methods Overview of Quantitative Methods Time-series Forecasting Forecasting In The Service Sector

?? What is Forecasting? Process of trying to predict a future event Underlying basis of all business decisions Production Inventory Personnel Facilities ??

Forecasting Time Horizons Short-range forecast Up to 1 year, generally less than 3 months Purchasing, job scheduling, workforce levels, job assignments, production levels Medium-range forecast 3 months to 3 years Sales and production planning, budgeting Long-range forecast 3+ years New product planning, facility location, research and development These ranges for time lines are just a guideline. There are no absolute rules. However, the next slide does give some basic guidelines for distinguishing the differences between them.

Distinguishing Differences 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

Types of Forecasts Economic forecasts Technological forecasts Address business cycle – inflation rate, money supply, housing starts, etc. Technological forecasts Predict rate of technological progress Impacts development of new products Demand forecasts Predict sales of existing product

Strategic Importance of Forecasting Human Resources – Hiring, training, laying off workers Capacity – Capacity shortages can result in undependable delivery, loss of customers, loss of market share Supply-Chain Management – Good supplier relations and price advance

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

The Realities! Forecasts are seldom perfect Most techniques assume an underlying stability in the system Product family and aggregated forecasts are generally more accurate than individual product forecasts Why do you think the last bullet is true?

Forecasting Approaches Qualitative Methods Used when situation is vague and little data exist New products New technology Involves intuition, experience e.g., forecasting demand for a new product

Forecasting Approaches Quantitative Methods Used when situation is ‘stable’ and historical data exist Existing products Current technology Involves mathematical techniques e.g., forecasting sales of color televisions

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

Overview of Qualitative Methods Sales force composite Estimates from individual salespersons are reviewed for reasonableness, then aggregated Consumer Market Survey Ask the customer

Overview of Quantitative Approaches Naive approach Moving averages Exponential smoothing Trend projection Linear regression Time-Series Models Associative Model

Time Series Forecasting 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 Relates the forecast to only one factor – time

Time Series Components Trend Cyclical Seasonal Random

Components of Demand Trend component Seasonal peaks Actual demand Demand for product or service | | | | 1 2 3 4 Year Seasonal peaks Actual demand Average demand over four years Random variation Figure 4.1

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

Seasonal Component Regular pattern of up and down fluctuations Due to weather, customs, etc. Occurs within a single year Number of Period Length Seasons Week Day 7 Month Week 4-4.5 Month Day 28-31 Year Quarter 4 Year Month 12 Year Week 52

Cyclical Component Repeating up and down movements Affected by business cycle, political, and economic factors Multiple years duration Often causal or associative relationships 0 5 10 15 20

Random Component Erratic, unsystematic, ‘residual’ fluctuations Due to random variation or unforeseen events Short duration and nonrepeating M T W T F

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 and efficient

∑ demand in previous n periods 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 Moving average = ∑ demand in previous n periods n

Moving Average Example January 10 February 12 March 13 April 16 May 19 June 23 July 26 Actual 3-Month Month Shed Sales Moving Average 10 12 13 (10 + 12 + 13)/3 = 11 2/3 (12 + 13 + 16)/3 = 13 2/3 (13 + 16 + 19)/3 = 16 (16 + 19 + 23)/3 = 19 1/3

Graph of Moving Average Moving Average Forecast | | | | | | | | | | | | J F M A M J J A S O N D Shed Sales 30 – 28 – 26 – 24 – 22 – 20 – 18 – 16 – 14 – 12 – 10 – Actual Sales

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

Weighted Moving Average Weights Applied Period 3 Last month 2 Two months ago 1 Three months ago 6 Sum of weights Weighted Moving Average January 10 February 12 March 13 April 16 May 19 June 23 July 26 Actual 3-Month Weighted Month Shed Sales Moving Average [(3 x 16) + (2 x 13) + (12)]/6 = 141/3 [(3 x 19) + (2 x 16) + (13)]/6 = 17 [(3 x 23) + (2 x 19) + (16)]/6 = 201/2 10 12 13 [(3 x 13) + (2 x 12) + (10)]/6 = 121/6

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

Moving Average And Weighted Moving Average 30 – 25 – 20 – 15 – 10 – 5 – Sales demand | | | | | | | | | | | | J F M A M J J A S O N D Actual sales Moving average Figure 4.2

Exponential Smoothing 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 New forecast = last period’s forecast + a (last period’s actual demand – last period’s forecast) Ft = Ft – 1 + a(At – 1 - Ft – 1) where Ft = new forecast Ft – 1 = previous forecast a = smoothing (or weighting) constant (0  a  1)

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

Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant a = .20 New forecast = 142 + .2(153 – 142)

Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant a = .20 New forecast = 142 + .2(153 – 142) = 142 + 2.2 = 144.2 ≈ 144 cars

Effect of Smoothing Constants Weight Assigned to Most 2nd Most 3rd Most 4th Most 5th Most Recent Recent Recent Recent Recent Smoothing Period Period Period Period Period Constant (a) a(1 - a) a(1 - a)2 a(1 - a)3 a(1 - a)4 a = .1 .1 .09 .081 .073 .066 a = .5 .5 .25 .125 .063 .031

Impact of Different  Actual demand a = .5 a = .1 225 – 200 – 175 – 225 – 200 – 175 – 150 – | | | | | | | | | 1 2 3 4 5 6 7 8 9 Quarter Demand Actual demand a = .5 a = .1

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 = At - Ft

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 ∑ |actuali - forecasti|/actuali n i = 1 We will not be using this one, but I left this slide in for completeness.

Comparison of Forecast Error Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonnage with for with for Quarter Unloaded a = .10 a = .10 a = .50 a = .50 1 180 175 5 175 5 2 168 176 8 178 10 3 159 175 16 173 14 4 175 173 2 166 9 5 190 173 17 170 20 6 205 175 30 180 25 7 180 178 2 193 13 8 182 178 4 186 4 84 100

Comparison of Forecast Error MAD = ∑ |deviations| n Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonage with for with for Quarter Unloaded a = .10 a = .10 a = .50 a = .50 1 180 175 5 175 5 2 168 176 8 178 10 3 159 175 16 173 14 4 175 173 2 166 9 5 190 173 17 170 20 6 205 175 30 180 25 7 180 178 2 193 13 8 182 178 4 186 4 84 100 = 84/8 = 10.50 For a = .10 = 100/8 = 12.50 For a = .50

Comparison of Forecast Error MSE = ∑ (forecast errors)2 n Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonage with for with for Quarter Unloaded a = .10 a = .10 a = .50 a = .50 1 180 175 5 175 5 2 168 176 8 178 10 3 159 175 16 173 14 4 175 173 2 166 9 5 190 173 17 170 20 6 205 175 30 180 25 7 180 178 2 193 13 8 182 178 4 186 4 84 100 MAD 10.50 12.50 = 1,558/8 = 194.75 For a = .10 = 1,612/8 = 201.50 For a = .50

Comparison of Forecast Error MAPE = 100 ∑ |deviationi|/actuali n i = 1 Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonage with for with for Quarter Unloaded a = .10 a = .10 a = .50 a = .50 1 180 175 5 175 5 2 168 176 8 178 10 3 159 175 16 173 14 4 175 173 2 166 9 5 190 173 17 170 20 6 205 175 30 180 25 7 180 178 2 193 13 8 182 178 4 186 4 84 100 MAD 10.50 12.50 MSE 194.75 201.50 = 45.62/8 = 5.70% For a = .10 = 54.8/8 = 6.85% For a = .50

Comparison of Forecast Error Rounded Absolute Rounded Absolute Actual Forecast Deviation Forecast Deviation Tonnage with for with for Quarter Unloaded a = .10 a = .10 a = .50 a = .50 1 180 175 5 175 5 2 168 176 8 178 10 3 159 175 16 173 14 4 175 173 2 166 9 5 190 173 17 170 20 6 205 175 30 180 25 7 180 178 2 193 13 8 182 178 4 186 4 84 100 MAD 10.50 12.50 MSE 194.75 201.50 MAPE 5.70% 6.85%

Trend Projections Fitting a trend line to historical data points to project into the medium-to-long-range Linear trends can be found using the least squares technique y = a + bx ^ where y = computed value of the variable to be predicted (dependent variable) a = y-axis intercept b = slope of the regression line x = the independent variable ^

Actual observation (y value) Least Squares Method Time period Values of Dependent Variable Deviation1 Deviation5 Deviation7 Deviation2 Deviation6 Deviation4 Deviation3 Actual observation (y value) Trend line, y = a + bx ^ Figure 4.4

Actual observation (y value) Least Squares Method Time period Values of Dependent Variable Actual observation (y value) Deviation7 Deviation5 Deviation6 Deviation3 Least squares method minimizes the sum of the squared errors (deviations) Deviation4 Trend line, y = a + bx ^ Deviation1 Deviation2 Figure 4.4

Least Squares Method Equations to calculate the regression variables y = a + bx ^ b = Sxy - nxy Sx2 - nx2 a = y - bx

Least Squares Example Time Electrical Power Year Period (x) Demand x2 xy 1999 1 74 1 74 2000 2 79 4 158 2001 3 80 9 240 2002 4 90 16 360 2003 5 105 25 525 2004 6 142 36 852 2005 7 122 49 854 ∑x = 28 ∑y = 692 ∑x2 = 140 ∑xy = 3,063 x = 4 y = 98.86 b = = = 10.54 ∑xy - nxy ∑x2 - nx2 3,063 - (7)(4)(98.86) 140 - (7)(42) a = y - bx = 98.86 - 10.54(4) = 56.70

Least Squares Example The trend line is y = 56.70 + 10.54x ^ Time Electrical Power Year Period (x) Demand x2 xy 1999 1 74 1 74 2000 2 79 4 158 2001 3 80 9 240 2002 4 90 16 360 2003 5 105 25 525 2004 6 142 36 852 2005 7 122 49 854 Sx = 28 Sy = 692 Sx2 = 140 Sxy = 3,063 x = 4 y = 98.86 The trend line is y = 56.70 + 10.54x ^ b = = = 10.54 Sxy - nxy Sx2 - nx2 3,063 - (7)(4)(98.86) 140 - (7)(42) a = y - bx = 98.86 - 10.54(4) = 56.70

Least Squares Example Trend line, y = 56.70 + 10.54x ^ 160 – 150 – | | | | | | | | | 1999 2000 2001 2002 2003 2004 2005 2006 2007 160 – 150 – 140 – 130 – 120 – 110 – 100 – 90 – 80 – 70 – 60 – 50 – Year Power demand

Least Squares Requirements We always plot the data to insure a linear relationship We do not predict time periods far beyond the database Deviations around the least squares line are assumed to be random

Forecasting in the Service Sector Presents unusual challenges Special need for short term records Needs differ greatly as function of industry and product Holidays and other calendar events Unusual events

Fast Food Restaurant Forecast 20% – 15% – 10% – 5% – 11-12 1-2 3-4 5-6 7-8 9-10 12-1 2-3 4-5 6-7 8-9 10-11 (Lunchtime) (Dinnertime) Hour of day Percentage of sales Figure 4.12