Forecasting 4 PowerPoint presentation to accompany Heizer and Render Operations Management, Eleventh Edition Principles of Operations Management, Ninth Edition PowerPoint slides by Jeff Heyl 2014 2014 Pearson Pearson Education, Education, Inc.Inc. 4-1 Outline What Is Forecasting? The Strategic Importance of Forecasting Seven Steps in the Forecasting System Forecasting Approaches 2014 Pearson Education, Inc. 4-2 Outline - Continued Time-Series Forecasting Associative Forecasting Methods: Regression and Correlation Analysis Monitoring and Controlling Forecasts Forecasting in the Service Sector 2014 Pearson Education, Inc. 4-3 Learning Objectives When you complete this chapter you should be able to : 1. Understand the three time horizons and which models apply for each use 2. Explain when to use each of the four qualitative models
3. Apply the naive, moving average, exponential smoothing, and trend methods 2014 Pearson Education, Inc. 4-4 Learning Objectives When you complete this chapter you should be able to : 4. Compute three measures of forecast accuracy 5. Develop seasonal indices 6. Conduct a regression and correlation analysis 7. Use a tracking signal 2014 Pearson Education, Inc. 4-5 What is Forecasting? Process of predicting a future event Underlying basis of all business decisions ?? Production Inventory Personnel Facilities 2014 Pearson Education, Inc. 4-6 Forecasting Time Horizons 1. Short-range forecast
Up to 1 year, generally less than 3 months Purchasing, job scheduling, workforce levels, job assignments, production levels 2. Medium-range forecast 3 months to 3 years Sales and production planning, budgeting 3. Long-range forecast 3+ years New product planning, facility location, research and development 2014 Pearson Education, Inc. 4-7 Distinguishing Differences 1. Medium/long range forecasts deal with more comprehensive issues and support management decisions regarding planning and products, plants and processes 2. Short-term forecasting usually employs different methodologies than longer-term forecasting 3. Short-term forecasts tend to be more accurate than longer-term forecasts 2014 Pearson Education, Inc. 4-8 Influence of Product Life
Cycle Introduction Growth Maturity Decline Introduction and growth require longer forecasts than maturity and decline As product passes through life cycle, forecasts are useful in projecting Staffing levels Inventory levels Factory capacity 2014 Pearson Education, Inc. 4-9 Types of Forecasts 1. Economic forecasts Address business cycle inflation rate, money supply, housing starts, etc. 2. Technological forecasts Predict rate of technological progress Impacts development of new products 3. Demand forecasts Predict sales of existing products and services
2014 Pearson Education, Inc. 4 - 10 Seven Steps in Forecasting 1. Determine the use of the forecast 2. Select the items to be forecasted 3. Determine the time horizon of the forecast 4. Select the forecasting model(s) 5. Gather the data needed to make the forecast 6. Make the forecast 7. Validate and implement results 2014 Pearson Education, Inc. 4 - 11 The Realities! Forecasts are seldom perfect, unpredictable outside factors may impact the forecast Most techniques assume an underlying stability in the system Product family and aggregated forecasts are more accurate than individual product forecasts 2014 Pearson Education, Inc. 4 - 12 Forecasting Approaches Qualitative Methods Used when situation is vague and little data exist
New products New technology Involves intuition, experience e.g., forecasting sales on Internet 2014 Pearson Education, Inc. 4 - 13 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 2014 Pearson Education, Inc. 4 - 14 Overview of Qualitative Methods 1. Jury of executive opinion Pool opinions of high-level experts, sometimes augment by statistical models
2. Delphi method Panel of experts, queried iteratively 2014 Pearson Education, Inc. 4 - 15 Overview of Qualitative Methods 3. Sales force composite Estimates from individual salespersons are reviewed for reasonableness, then aggregated 4. Market Survey Ask the customer 2014 Pearson Education, Inc. 4 - 16 Jury of Executive Opinion Involves small group of high-level experts and managers Group estimates demand by working together Combines managerial experience with statistical models Relatively quick
Group-think disadvantage 2014 Pearson Education, Inc. 4 - 17 Delphi Method Iterative group process, continues until consensus is reached Staff 3 types of (Administering participants survey) Decision makers Staff Respondents 2014 Pearson Education, Inc. Decision Makers (Evaluate responses and make decisions) Respondents (People who can make valuable judgments) 4 - 18 Sales Force Composite
Each salesperson projects his or her sales Combined at district and national levels Sales reps know customers wants May be overly optimistic 2014 Pearson Education, Inc. 4 - 19 Market Survey Ask customers about purchasing plans Useful for demand and product design and planning What consumers say, and what they actually do may be different May be overly optimistic 2014 Pearson Education, Inc. 4 - 20 Overview of Quantitative Approaches 1. Naive approach 2. Moving averages 3. Exponential smoothing 4. Trend projection 5. Linear regression 2014 Pearson Education, Inc. Time-series
models Associative model 4 - 21 Time-Series Forecasting 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 influence in future 2014 Pearson Education, Inc. 4 - 22 Time-Series Components Trend Cyclical Seasonal Random 2014 Pearson Education, Inc. 4 - 23 Components of Demand Demand for product or service Trend component Seasonal peaks
Actual demand line Average demand over 4 years Random variation | 1 | 2 | 3 Time (years) 2014 Pearson Education, Inc. | 4 Figure 4.1 4 - 24 Trend Component Persistent, overall upward or downward pattern Changes due to population, technology, age, culture, etc. Typically several years duration 2014 Pearson Education, Inc. 4 - 25 Seasonal Component Regular pattern of up and down fluctuations Due to weather, customs, etc.
Occurs within a single year PERIOD LENGTH SEASON LENGTH NUMBER OF SEASONS IN PATTERN Week Day Month Week 4 4.5 Month Day 28 31 Year Quarter 4 Year Month 12 Year Week 52 2014 Pearson Education, Inc. 7 4 - 26
Cyclical Component Repeating up and down movements Affected by business cycle, political, and economic factors Multiple years duration Often causal or associative relationships 0 2014 Pearson Education, Inc. 5 10 15 20 4 - 27 Random Component Erratic, unsystematic, residual fluctuations Due to random variation or unforeseen events Short duration and nonrepeating M 2014 Pearson Education, Inc. T F W
T 4 - 28 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 2014 Pearson Education, Inc. 4 - 29 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 demand in previous n periods Moving average = n 2014 Pearson Education, Inc. 4 - 30
Moving Average Example MONTH ACTUAL SHED SALES January 10 12 12 February March 3-MONTH MOVING AVERAGE April 13 13 16 May 19 (12 + 13 + 16)/3 = 13 2/3 June 23 (13 + 16 + 19)/3 = 16 July 26 August 30 (16 + 19 + 23)/3 = 19 1/3 September 28
October 18 November 16 (29 + 30 + 28)/3 = 28 December 14 (30 + 28 + 18)/3 = 25 1/3 (10 + 12 + 13)/3 = 11 2/3 (19 + 23 + 26)/3 = 22 2/3 (23 + 26 + 30)/3 = 26 1/3 (28 + 18 + 16)/3 = 20 2/3 2014 Pearson Education, Inc. 4 - 31 Weighted Moving Average Used when some trend might be present Older data usually less important Weights based on experience and intuition (( )) Weighted Weight for period n Demand in period n moving =
Weights average 2014 Pearson Education, Inc. )( 4 - 32 Weighted Moving Average MONTH ACTUAL SHED SALES January 10 12 12 February March April 13 13 16 May 19 [(3 x 13) + (2 x 12) + (10)]/6 = 12 1/6 WEIGHTS APPLIED 23 June 3-MONTH WEIGHTED MOVING AVERAGE PERIOD July 26
3 Last month August 30 2 Two months ago September 28 1 Three months ago October 18 6 Sum of the weights November Forecast for 16this month = December 3 x 14 Sales last mo. + 2 x Sales 2 mos. ago + 1 x Sales 3 mos. ago Sum of the weights 2014 Pearson Education, Inc. 4 - 33 Weighted Moving Average MONTH ACTUAL SHED SALES
January 10 12 12 February March 3-MONTH WEIGHTED MOVING AVERAGE April 13 13 16 [(3 x 13) + (2 x 12) + (10)]/6 = 12 1/6 May 19 [(3 x 16) + (2 x 13) + (12)]/6 = 14 1/3 June 23 July 26 August 30 September 28 October 18 [(3 x 30) + (2 x 26) + (23)]/6 = 27 1/2 November
16 [(3 x 28) + (2 x 30) + (26)]/6 = 28 1/3 December 14 [(3 x 18) + (2 x 28) + (30)]/6 = 23 1/3 [(3 x 19) + (2 x 16) + (13)]/6 = 17 [(3 x 23) + (2 x 19) + (16)]/6 = 20 1/2 [(3 x 26) + (2 x 23) + (19)]/6 = 23 5/6 [(3 x 16) + (2 x 18) + (28)]/6 = 18 2/3 2014 Pearson Education, Inc. 4 - 34 Potential Problems With Moving Average Increasing n smooths the forecast but makes it less sensitive to changes Does not forecast trends well Requires extensive historical data 2014 Pearson Education, Inc. 4 - 35 Graph of Moving Averages Weighted moving average 30 Sales demand 25 20 15 Actual sales
Moving average 10 5 | | | | | J F M A M Figure 4.2 2014 Pearson Education, Inc. | | J J Month | | | | | A
S O N D 4 - 36 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 2014 Pearson Education, Inc. 4 - 37 Exponential Smoothing New forecast = Last periods forecast + (Last periods actual demand Last periods forecast) Ft = Ft 1 + (At 1 - Ft 1) where
Ft = new forecast Ft 1 = previous periods forecast = At 1 = smoothing (or weighting) constant (0 1) previous periods actual demand 2014 Pearson Education, Inc. 4 - 38 Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant = .20 2014 Pearson Education, Inc. 4 - 39 Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant = .20 New forecast 2014 Pearson Education, Inc. = 142 + .2(153 142) 4 - 40 Exponential Smoothing Example Predicted demand = 142 Ford Mustangs Actual demand = 153 Smoothing constant = .20 New forecast 2014 Pearson Education, Inc.
= 142 + .2(153 142) = 142 + 2.2 = 144.2 144 cars 4 - 41 Effect of Smoothing Constants Smoothing constant generally .05 .50 As increases, older values become less significant WEIGHT ASSIGNED TO SMOOTHING CONSTANT MOST RECENT PERIOD () 2ND MOST RECENT PERIOD (1 ) 3RD MOST RECENT PERIOD (1 )2 4th MOST RECENT PERIOD (1 )3 5th MOST RECENT PERIOD (1 )4 = .1 .1 .09 .081
.073 .066 = .5 .5 .25 .125 .063 .031 2014 Pearson Education, Inc. 4 - 42 Impact of Different 225 Demand Actual demand = .5 200 175 = .1 | 150 1 | 2 | 3 | 4
| 5 | 6 | 7 | 8 | 9 Quarter 2014 Pearson Education, Inc. 4 - 43 Impact of Different 225 Actual demand values Choose high of 200 when underlying average is likely to change Choose low values of 175 when underlying average is stable | | | | | | Demand
= .5 150 1 2 3 4 5 6 = .1 | 7 | 8 | 9 Quarter 2014 Pearson Education, Inc. 4 - 44 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 2014 Pearson Education, Inc. 4 - 45 Common Measures of Error Mean Absolute Deviation (MAD) Actual - Forecast
MAD = n 2014 Pearson Education, Inc. 4 - 46 Determining the MAD QUARTER ACTUAL TONNAGE UNLOADED 1 180 175 175 2 168 175.50 = 175.00 + .10(180 175) 177.50 3 159 174.75 = 175.50 + .10(168 175.50) 172.75 4 175 173.18 = 174.75 + .10(159 174.75) 165.88 5
190 173.36 = 173.18 + .10(175 173.18) 170.44 6 205 175.02 = 173.36 + .10(190 173.36) 180.22 7 180 178.02 = 175.02 + .10(205 175.02) 192.61 8 182 178.22 = 178.02 + .10(180 178.02) 186.30 9 ? 178.59 = 178.22 + .10(182 178.22) 184.15 2014 Pearson Education, Inc. FORECAST WITH = .10 FORECAST WITH = .50 4 - 47
Determining the MAD QUARTER ACTUAL TONNAGE UNLOADED FORECAST WITH = .10 1 180 175 5.00 175 5.00 2 168 175.50 7.50 177.50 9.50 3 159 174.75 15.75 172.75 13.75 4
175 173.18 1.82 165.88 9.12 5 190 173.36 16.64 170.44 19.56 6 205 175.02 29.98 180.22 24.78 7 180 178.02 1.98 192.61 12.61 8
182 178.22 3.78 186.30 4.30 Sum of absolute deviations: MAD = 2014 Pearson Education, Inc. |Deviations| n ABSOLUTE DEVIATION FOR a = .10 FORECAST WITH = .50 ABSOLUTE DEVIATION FOR a = .50 82.45 98.62 10.31 12.33 4 - 48 Common Measures of Error Mean Squared Error (MSE) Forecast errors) ( MSE =
2 n 2014 Pearson Education, Inc. 4 - 49 Determining the MSE QUARTER ACTUAL TONNAGE UNLOADED 1 180 175 2 168 175.50 (7.5)2 = 56.25 3 159 174.75 (15.75)2 = 248.06 4 175 173.18 (1.82)2 = 3.31 5 190
173.36 (16.64)2 = 276.89 6 205 175.02 (29.98)2 = 898.80 7 180 178.02 (1.98)2 = 3.92 8 182 178.22 (3.78)2 = 14.29 FORECAST FOR = .10 (ERROR)2 52 = 25 Sum of errors squared = 1,526.52 Forecast errors) ( MSE = n 2014 Pearson Education, Inc. 2 =1,526.52 / 8 =190.8
4 - 50 Common Measures of Error Mean Absolute Percent Error (MAPE) n 100 Actual - Forecast i MAPE = i=1 2014 Pearson Education, Inc. i / Actuali n 4 - 51 Determining the MAPE QUARTER ACTUAL TONNAGE UNLOADED FORECAST FOR = .10 1 180 175.00 100(5/180) = 2.78% 2 168 175.50 100(7.5/168) = 4.46% 3
159 174.75 100(15.75/159) = 9.90% 4 175 173.18 100(1.82/175) = 1.05% 5 190 173.36 100(16.64/190) = 8.76% 6 205 175.02 100(29.98/205) = 14.62% 7 180 178.02 100(1.98/180) = 1.10% 8 182 178.22 100(3.78/182) = 2.08% ABSOLUTE PERCENT ERROR
100(ERROR/ACTUAL) Sum of % errors = 44.75% absolute percent error 44.75% MAPE = = =5.59% n 2014 Pearson Education, Inc. 8 4 - 52 Comparison of Forecast Error Quarter 1 2 3 4 5 6 7 8 Actual Tonnage Unloaded 180 168 159 175 190 205 180 182 2014 Pearson Education, Inc. Rounded Forecast with = .10
175 175.5 174.75 173.18 173.36 175.02 178.02 178.22 Absolute Deviation for = .10 5.00 7.50 15.75 1.82 16.64 29.98 1.98 3.78 82.45 Rounded Forecast with = .50 175 177.50 172.75 165.88 170.44 180.22 192.61 186.30 Absolute Deviation for = .50 5.00 9.50 13.75 9.12
19.56 24.78 12.61 4.30 98.62 4 - 53 Comparison of Forecast Error Rounded Absolute |deviations| Actual Forecast Deviation MADTonnage = with for n Quarter Unloaded a = .10 a = .10 1 For 180 5.00 = .10 175 2 168 175.5 7.50 3 159 = 82.45/8 174.75 = 10.31 15.75 4 5 6 7 8 For 175 173.18 190
= .50 173.36 205 = 98.62/8 175.02 180 178.02 182 178.22 2014 Pearson Education, Inc. = 1.82 16.64 29.98 12.33 1.98 3.78 82.45 Rounded Forecast with = .50 175 177.50 172.75 165.88 170.44 180.22 192.61 186.30 Absolute Deviation for = .50 5.00 9.50 13.75 9.12 19.56 24.78 12.61 4.30 98.62
4 - 54 Comparison of Forecast Error 2 Rounded Absolute (forecast errors) Actual Forecast Deviation MSE = Tonnage with for n Quarter Unloaded a = .10 a = .10 1 2 3 4 5 6 7 8 5.00 For 180 = .10 175 168 175.5 7.50 = 1,526.54/8 159 174.75 = 190.82 15.75 For 175 173.18 190 = .50 173.36 205
175.02 = 1,561.91/8 180 178.02 182 178.22 MAD 2014 Pearson Education, Inc. = 1.82 16.64 29.98 195.24 1.98 3.78 82.45 10.31 Rounded Forecast with = .50 175 177.50 172.75 165.88 170.44 180.22 192.61 186.30 Absolute Deviation for = .50 5.00 9.50 13.75 9.12 19.56 24.78 12.61 4.30
98.62 12.33 4 - 55 Comparison of Forecast Error n Rounded Absolute Rounded 100|deviation |/actual i i Actual Forecast Deviation Forecast MAPE = i=1 Tonnage Quarter 1 2 3 4 5 6 7 8 Unloaded with a = .10 n for a = .10 5.00 For 180
= .10 175 168 175.5 7.50 = 44.75/8 =15.75 5.59% 159 174.75 For 175 = 190 205 180 182 173.18 1.82 .50 173.36 16.64 175.02 = 54.05/8 =29.98 6.76% 178.02 1.98 178.22 3.78 82.45 MAD 10.31 MSE 190.82 2014 Pearson Education, Inc. with a = .50 175 177.50 172.75 165.88 170.44 180.22
192.61 186.30 Absolute Deviation for = .50 5.00 9.50 13.75 9.12 19.56 24.78 12.61 4.30 98.62 12.33 195.24 4 - 56 Comparison of Forecast Error Quarter 1 2 3 4 5 6 7 8 Actual Tonnage Unloaded 180 168 159 175 190 205 180 182 Rounded Forecast
with = .10 175 175.5 174.75 173.18 173.36 175.02 178.02 178.22 MAD MSE MAPE 2014 Pearson Education, Inc. Absolute Deviation for = .10 5.00 7.50 15.75 1.82 16.64 29.98 1.98 3.78 82.45 10.31 190.82 5.59% Rounded Forecast with = .50 175 177.50 172.75 165.88 170.44 180.22 192.61 186.30
Absolute Deviation for = .50 5.00 9.50 13.75 9.12 19.56 24.78 12.61 4.30 98.62 12.33 195.24 6.76% 4 - 57 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 ^ 2014 Pearson Education, Inc. 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 4 - 58 Values of Dependent Variable (y-values) Least Squares Method Actual observation (y-value) Deviation7
Deviation5 Deviation3 Deviation1 (error) Least squares method minimizes the sum of Deviation the squared errors (deviations) 4 Deviation2 Trend line, ^y = a + bx | | | | | | | 1 2 3 4 5 6 7 Time period 2014 Pearson Education, Inc. Deviation6
Figure 4.4 4 - 59 Least Squares Method Equations to calculate the regression variables y=a+ bx xy- nxy b= x - nx 2 2 a=y- bx 2014 Pearson Education, Inc. 4 - 60 Least Squares Example YEAR ELECTRICAL POWER DEMAND YEAR ELECTRICAL POWER DEMAND 1 74 5 105 2 79 6 142
3 80 7 122 4 90 2014 Pearson Education, Inc. 4 - 61 Least Squares Example YEAR (x) ELECTRICAL POWER DEMAND (y) x2 xy 74 1 74 79 4 158 80 9 240 90 16
360 105 25 525 142 36 852 1 2 3 4 5 6 x 28 x= = 122 =4 n 7 x = 28 2014 Pearson Education, Inc. 7 y = 692 y 692 49 y= = =98.86 n 7 x2 = 140
854 xy = 3,063 4 - 62 Least Squares Example YEAR (x) xy- nxy 3,063 - ( 7) ( 4) ( 98.86) 295 b= ELECTRICAL = POWER = =10.54 DEMAND (y) x xy 28 140 - ( 7) ( 4 ) x - nx 1 2 2 2 2 74 74 1 a =y- bx =98.8679 - 10.54 4 =56.70 4 158 80 9 240
16 360 105 25 525 142 36 852 ( ) 2 Thus, 3 90 y=56.70 +10.54x 4 5 6 x 28 y+ 10.54(8) Demand in year 8 = 56.70 692 49 x= = 122 =4 y= = =98.86 = 141.02,
or 141 megawatts n 7 n 7 7 x = 28 2014 Pearson Education, Inc. y = 692 x2 = 140 854 xy = 3,063 4 - 63 Power demand (megawatts) Least Squares Example 160 150 140 130 120 110 100 90 80 70 60 50
Trend line, ^y = 56.70 + 10.54x | 1 | 2 2014 Pearson Education, Inc. | 3 | 4 | 5 Year | 6 | 7 | 8 | 9 Figure 4.5 4 - 64 Least Squares Requirements 1. We always plot the data to insure a linear relationship 2. We do not predict time periods far beyond the database 3. Deviations around the least squares line are assumed to be random 2014 Pearson Education, Inc.
4 - 65 Seasonal Variations In Data The multiplicative seasonal model can adjust trend data for seasonal variations in demand 2014 Pearson Education, Inc. 4 - 66 Seasonal Variations In Data Steps in the process for monthly seasons: 1. Find average historical demand for each month 2. Compute the average demand over all months 3. Compute a seasonal index for each month 4. Estimate next years total demand 5. Divide this estimate of total demand by the number of months, then multiply it by the seasonal index for that month 2014 Pearson Education, Inc. 4 - 67 Seasonal Index Example DEMAND MONTH YEAR 1 YEAR 2 YEAR 3 AVERAGE YEARLY DEMAND Jan 80
85 105 90 Feb 70 85 85 80 Mar 80 93 82 85 Apr 90 95 115 100 May 113 125 131 123 June
110 115 120 July 100 102 113 Aug 88 102 110 Sept 85 90 95 Oct 77 78 85 Nov 75 82 83 Dec
82 78 80 Total average annual demand = 2014 Pearson Education, Inc. AVERAGE MONTHLY DEMAND SEASONAL INDEX 115 105 100 90 80 80 80 1,128 4 - 68 Seasonal Index Example DEMAND MONTH YEAR 1 YEAR 2 YEAR 3 AVERAGE YEARLY DEMAND AVERAGE MONTHLY DEMAND Jan 80
85 105 90 94 Feb 70 85 85 80 94 Mar 80 93 82 85 94 100 94 123 94 115 94 Apr May June
Average 90 95 1,128 115 =125 = 94 monthly 113 131 12 months demand 110 115 120 July 100 102 113 105 94 Aug 88 102 110 100 94 Sept 85 90 95
90 94 Oct 77 78 85 80 94 Nov 75 82 83 80 94 Dec 82 78 80 80 94 Total average annual demand = 2014 Pearson Education, Inc. SEASONAL INDEX 1,128 4 - 69
Seasonal Index Example DEMAND MONTH YEAR 1 YEAR 2 YEAR 3 AVERAGE YEARLY DEMAND AVERAGE MONTHLY DEMAND Jan 80 85 105 90 94 Feb 70 85 85 80 94 Mar 80
93 82 85 94 Apr 90 95 115 100 94 May 113 125 131 123 94 June Seasonal110 July index = 100 SEASONAL INDEX .957( = 90/94) Average monthly
demand years 115 120 115 for past 394 102 Average 113 105 demand 94 monthly Aug 88 102 110 100 94 Sept 85 90 95 90 94 Oct 77 78 85 80 94 Nov
75 82 83 80 94 Dec 82 78 80 80 94 Total average annual demand = 2014 Pearson Education, Inc. 1,128 4 - 70 Seasonal Index Example DEMAND MONTH YEAR 1 YEAR 2 YEAR 3 AVERAGE YEARLY DEMAND AVERAGE MONTHLY DEMAND SEASONAL
INDEX Jan 80 85 105 90 94 .957( = 90/94) Feb 70 85 85 80 94 .851( = 80/94) Mar 80 93 82 85 94 .904( = 85/94) Apr 90
95 115 100 94 1.064( = 100/94) May 113 125 131 123 94 1.309( = 123/94) June 110 115 120 115 94 1.223( = 115/94) July 100 102 113 105
94 1.117( = 105/94) Aug 88 102 110 100 94 1.064( = 100/94) Sept 85 90 95 90 94 .957( = 90/94) Oct 77 78 85 80 94 .851( = 80/94) Nov
75 82 83 80 94 .851( = 80/94) Dec 82 78 80 80 94 .851( = 80/94) Total average annual demand = 2014 Pearson Education, Inc. 1,128 4 - 71 Seasonal Index Example Seasonal forecast for Year 4 MONTH Jan DEMAND 1,200 12 Feb 1,200 12 Mar
1,200 12 Apr 1,200 12 May 1,200 12 June 1,200 12 2014 Pearson Education, Inc. x .957 = 96 x .851 = 85 x .904 = 90 x 1.064 = 106 x 1.309 = 131 x 1.223 = 122 MONTH July DEMAND 1,200 12 Aug 1,200 12 Sept 1,200 12 Oct 1,200 12
Nov 1,200 12 Dec 1,200 12 x 1.117 = 112 x 1.064 = 106 x .957 = 96 x .851 = 85 x .851 = 85 x .851 = 85 4 - 72 Seasonal Index Example Year 4 Forecast Year 3 Demand Year 2 Demand Year 1 Demand 140 Demand 130 120 110 100 90 80 70 | J | F 2014 Pearson Education, Inc. | M
| A | M | | J J Time | A | S | O | N | D 4 - 73 San Diego Hospital Trend Data Figure 4.6 10,200 Inpatient Days 10,000 9,800 9573 9,600 9530 9,400 9551 9659
9616 9594 9637 9745 9702 9680 9724 9766 9,200 9,000 | | | | | | | | | | | | Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 67 68 69 70 71 72 73 74 75 76 77 78 Month 2014 Pearson Education, Inc. 4 - 74 San Diego Hospital Seasonality Indices for Adult Inpatient Days at San Diego Hospital MONTH SEASONALITY INDEX January 1.04 July
1.03 February 0.97 August 1.04 March 1.02 September 0.97 April 1.01 October 1.00 May 0.99 November 0.96 June 0.99 December 0.98 2014 Pearson Education, Inc. MONTH SEASONALITY INDEX
4 - 75 San Diego Hospital Figure 4.7 Seasonal Indices Index for Inpatient Days 1.06 1.04 1.04 1.02 1.02 1.01 1.00 0.99 1.00 0.97 0.97 0.94 0.92 0.98 0.99 0.98 0.96 1.03 1.04 0.96 | |
| | | | | | | | | | Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 67 68 69 70 71 72 73 74 75 76 77 78 Month 2014 Pearson Education, Inc. 4 - 76 San Diego Hospital Period 67 68 69 70 71 72 Month Jan Feb Mar Apr May June 9,911
9,265 9,164 9,691 9,520 9,542 Period 73 74 75 76 77 78 Month July Aug Sept Oct Nov Dec 9,949 10,068 9,411 9,724 9,355
9,572 Forecast with Trend & Seasonality Forecast with Trend & Seasonality 2014 Pearson Education, Inc. 4 - 77 San Diego Hospital Figure 4.8 Combined Trend and Seasonal Forecast 10,200 10068 9949 Inpatient Days 10,000 9911 9764 9,800 9724 9691 9572 9,600 9520 9542 9,400 9,200 9,000 9411 9265
9355 | | | | | | | | | | | | Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec 67 68 69 70 71 72 73 74 75 76 77 78 Month 2014 Pearson Education, Inc. 4 - 78 Adjusting Trend Data yseasonal =Index ytrend forecast Quarter I: yI =(1.30)($100,000) =$130,000 Quarter II: yII =(.90)($120,000) =$108,000 Quarter III: yIII =(.70)($140,000) =$98,000 Quarter IV: yIV =(1.10)($160,000) =$176,000 2014 Pearson Education, Inc. 4 - 79 Associative Forecasting Used when changes in one or more independent variables can be used to predict the changes in the dependent variable Most common technique is linear regression analysis We apply this technique just as we did in the time-series example 2014 Pearson Education, Inc.
4 - 80 Associative Forecasting Forecasting an outcome based on predictor variables using the least squares technique ^ y = a + bx ^ 2014 Pearson Education, Inc. where y = value of the dependent variable (in our example, sales) a = y-axis intercept b = slope of the regression line x = the independent variable 4 - 81 Associative Forecasting Example NODELS SALES (IN $ MILLIONS), y AREA PAYROLL (IN $ BILLIONS), x NODELS SALES (IN $ MILLIONS), y AREA PAYROLL (IN $ BILLIONS), x 2.0 1 2.0 2 3.0
3 2.0 1 2.5 4 3.5 7 Nodels sales (in$ millions) 4.0 3.0 2.0 1.0 0 | | | | | | | 1 2 3 4 5
6 7 Area payroll (in $ billions) 2014 Pearson Education, Inc. 4 - 82 Associative Forecasting Example SALES, y PAYROLL, x xy 2.0 1 1 2.0 3.0 3 9 9.0 2.5 4 16 10.0 2.0 2 4
4.0 2.0 1 1 2.0 3.5 7 49 24.5 y = 15.0 x = x= 18 x =18 =3 6 6 x2 = y= xy- nxy 51.5 - (6)(3)(2.5) b= = =.25 80 - (6)(3 ) x - nx 2 x2 2
2014 Pearson Education, Inc. 2 80 xy = 51.5 y =15 =2.5 6 6 a=y- bx =2.5 - (.25)(3) =1.75 4 - 83 Associative Forecasting Example SALES, y PAYROLL, x xy 1 2.0 9 9.0 2.0 1 3.0 3 2.5 4 2.0
2 2.0 1 1 2.0 3.5 7 49 24.5 y = 15.0 x = x= 18 x =18 =3 6 y=1.75 +.25x 16 10.0 Sales =1.75 4 +.25(payroll) 4.0 6 x2 = y= xy- nxy 51.5 - (6)(3)(2.5) b= = =.25 80 - (6)(3 )
x - nx 2 x2 2 2014 Pearson Education, Inc. 2 80 xy = 51.5 y =15 =2.5 6 6 a=y- bx =2.5 - (.25)(3) =1.75 4 - 84 Associative Forecasting Example SALES, y PAYROLL, x 1 3.0 4.0 3 Nodels sales (in$ millions) 2.0 2.5 2.0 1 2.0 9
9.0 2 2.0 2.0 1 1 2.0 3.5 7 49 24.5 y = 15.0 1.0 x = | 18 | 2 x1=18 =3 0 x= 6 | 2 2014 Pearson Education, Inc. x2 =
80 | | xy = | 51.5 | 3 4 y 5 15 6 7 y = = =2.5 6 Area payroll (in6$ billions) 6 xy- nxy 51.5 - (6)(3)(2.5) b= = =.25 80 - (6)(3 ) x - nx 2 xy y=1.75 +.25x 16 10.0 Sales =1.75 4 +.25(payroll) 4.0 4 3.0 x2 2
a=y- bx =2.5 - (.25)(3) =1.75 4 - 85 Associative Forecasting Example If payroll next year is estimated to be $6 billion, then: Sales (in $ millions) = 1.75 + .25(6) = 1.75 + 1.5 = 3.25 Sales = $3,250,000 2014 Pearson Education, Inc. 4 - 86 Associative Forecasting Example Nodels sales (in$ millions) If payroll4.0 next year is estimated to be $6 billion, then: 3.25 3.0 2.0 Sales (in$ millions) = 1.75 + .25(6) 1.0 = 1.75 + 1.5 = 3.25 | 0 2014 Pearson Education, Inc. 1 | |
| | | 2 3 4 5 6 Sales = $3,250,000 Area payroll (in $ billions) | 7 4 - 87 Standard Error of the Estimate A forecast is just a point estimate of a future value This point is actually the mean of a probability distribution Nodels sales (in$ millions) 4.0 3.25 3.0 2014 Pearson Education, Inc. y=1.75 +.25x 2.0
1.0 0 Figure 4.9 Regression line, | 1 | 2 | 3 | 4 | 5 | 6 | 7 Area payroll (in $ billions) 4 - 88 Standard Error of the Estimate Sy,x = where y = 2 ( yy ) c n- 2
y-value of each data point yc = computed value of the dependent variable, from the regression equation n = number of data points 2014 Pearson Education, Inc. 4 - 89 Standard Error of the Estimate Computationally, this equation is considerably easier to use Sy,x = 2 y - a y- b xy n- 2 We use the standard error to set up prediction intervals around the point estimate 2014 Pearson Education, Inc. 4 - 90 Standard Error of the Estimate Sy,x = 2 y - a y- b xy n- 2 39.5 - 1.75(15.0) - .25(51.5) = 6- 2 The standard error of the estimate is $306,000 in sales Nodels sales
(in$ millions) = .09375 =.306 (in $ millions) 4.0 3.25 3.0 2.0 1.0 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 Area payroll (in $ billions) 2014 Pearson Education, Inc. 4 - 91 Correlation How strong is the linear relationship between the variables? Correlation does not necessarily imply causality!
Coefficient of correlation, r, measures degree of association Values range from -1 to +1 2014 Pearson Education, Inc. 4 - 92 Correlation Coefficient r= n xy 2 n x - 2014 Pearson Education, Inc. ( x y 2 x n y - ) 2 ( y ) 2 4 - 93 Correlation Coefficient Figure 4.10 y y
x x (a) Perfect negative correlation y (e) Perfect positive correlation y y x x (b) Negative correlation (d) Positive correlation x (c) No correlation | High 1.0 Moderate | | 0.8 0.6 2014 Pearson Education, Inc. |
| Low Low | Moderate | 0.4 0.2 0 0.2 0.4 Correlation coefficient values | | 0.6 0.8 High 1.0 4 - 94 Correlation Coefficient y y = x x2 xy y2 2.0
1 1 2.0 4.0 3.0 3 9 9.0 9.0 2.5 4 16 10.0 6.25 2.0 2 4 4.0 4.0 2.0 1 1 2.0 4.0
3.5 7 49 24.5 12.25 15.0 x = r= = 2014 Pearson Education, Inc. 18 x2 = 80 xy = 51.5 y2 = 39.5 (6)(51.5) (18)(15.0) (6)(80) (18) 2 (16)(39.5) (15.0) 2 309 - 270 (156)(12) = 39 1,872 =
39 =.901 43.3 4 - 95 Correlation Coefficient of Determination, r2, measures the percent of change in y predicted by the change in x Values range from 0 to 1 Easy to interpret For the Nodel Construction example: r = .901 r2 = .81 2014 Pearson Education, Inc. 4 - 96 Multiple-Regression Analysis If more than one independent variable is to be used in the model, linear regression can be extended to multiple regression to accommodate several independent variables y=a+ b1x1 + b2 x2 Computationally, this is quite complex and generally done on the computer 2014 Pearson Education, Inc. 4 - 97 Multiple-Regression Analysis In the Nodel example, including interest rates in the model gives the new equation: y=1.80 +.30x1 - 5.0x2 An improved correlation coefficient of r = .96 suggests this model does a better job of predicting the change in construction sales
Sales = 1.80 + .30(6) - 5.0(.12) = 3.00 Sales = $3,000,000 2014 Pearson Education, Inc. 4 - 98 Monitoring and Controlling Forecasts Tracking Signal Measures how well the forecast is predicting actual values Ratio of cumulative forecast errors to mean absolute deviation (MAD) Good tracking signal has low values If forecasts are continually high or low, the forecast has a bias error 2014 Pearson Education, Inc. 4 - 99 Monitoring and Controlling Forecasts Tracking = signal Cumulative error MAD (Actual demand in period i - Forecast demand in period i) = Actual - Forecast n 2014 Pearson Education, Inc. 4 - 100
Tracking Signal Figure 4.11 Signal exceeding limit Tracking signal Upper control limit + Acceptable range 0 MADs Lower control limit Time 2014 Pearson Education, Inc. 4 - 101 Tracking Signal Example QTR ACTUAL DEMAND FORECAST DEMAND ERROR CUM ERROR ABSOLUTE FORECAST ERROR CUM ABS FORECAST ERROR MAD TRACKING SIGNAL (CUM ERROR/MAD)
1 90 100 10 10 10 10 10.0 10/10 = 1 2 95 100 5 15 5 15 7.5 15/7.5 = 2 3 115 100 +15 0 15
30 10. 0/10 = 0 4 100 110 10 10 10 40 10. 10/10 = 1 5 125 110 +15 +5 15 55 11.0 +5/11 = +0.5 6 140 110
+30 +35 30 85 14.2 +35/14.2 = +2.5 Forecast errors 85 = =14.2 At the end of quarter 6, MAD = n 6 Cumulative error 35 Tracking signal = = =2.5 MADs MAD 14.2 2014 Pearson Education, Inc. 4 - 102 Adaptive Smoothing Its possible to use the computer to continually monitor forecast error and adjust the values of the and b coefficients used in exponential smoothing to continually minimize forecast error This technique is called adaptive smoothing 2014 Pearson Education, Inc. 4 - 103
Focus Forecasting Developed at American Hardware Supply, based on two principles: 1. Sophisticated forecasting models are not always better than simple ones 2. There is no single technique that should be used for all products or services Uses historical data to test multiple forecasting models for individual items Forecasting model with the lowest error used to forecast the next demand 2014 Pearson Education, Inc. 4 - 104 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 2014 Pearson Education, Inc.
4 - 105 Percentage of sales by hour of day Fast Food Restaurant Forecast 20% Figure 4.12 15% 10% 5% 11-12 1-2 12-1 (Lunchtime) 2014 Pearson Education, Inc. 2-3 3-4 4-5 5-6 7-8 6-7 (Dinnertime) Hour of day 8-9 9-10 10-11 4 - 106 FedEx Call Center Forecast Figure 4.12
12% 10% 8% 6% 4% 2% 0% 2 4 2014 Pearson Education, Inc. 6 8 A.M. 10 12 2 Hour of day 4 6 8 P.M. 10 12 4 - 107 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the publisher. Printed in the United States of America. 2014 Pearson Education, Inc. 4 - 108
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