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Chapter 3: Forecasting Definition: Forecasting is a statement about the future. It is estimating future event (variable), by casting forward past data. Past data are systematically combined in predetermined way to obtain the estimate. Forecasting is not guessing or prediction. Forecasting help managers to: • Plan the system • Plan the use of system Forecasts affect decisions and activities throughout an organization • Accounting, finance • Human resources • Marketing • MIS • Operations • Product / service design Accounting
Cost/profit estimates
Finance
Cash flow and funding
Human Resources
Hiring/recruiting/training
Marketing
Pricing, promotion, strategy
MIS
IT/IS systems, services
Operations
Schedules, MRP, workloads
Product/service design
New products and services
Common features of forecasting: 1. Forecasting is rarely perfect (deviation is expected). 2. All forecasting techniques assume that there is some degree of stability in the system, and “what happened in the past will continue to happen in the future”. 3. Forecasting for a group of items is more accurate than the forecast for individuals. 4. Forecasting accuracy increases as time horizon increases. Elements of good forecast: 1. Timely: Forecasting horizon must cover the time necessary to implement possible changes. 2. Reliable: It should work consistently. 3. Accurate: Degree of accuracy should be stated. 4. Meaningful: Should be expressed in meaningful units. Financial planners should know how many dollars needed, production should know how many units to be produced, and schedulers need to know what machines and skills will be required. 5. Written: to guarantee use of the same information and to make easier comparison to actual results. 6. Easy to use: users should be comfortable working with forecast. Types of forecast by time: • Short-range (days – weeks – months): Job scheduling, work assignments o Time spans ranging from a few days to a few weeks. o Cycles, seasonality, and trend may have little effect. o Random fluctuation is main data component.
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•
Medium term (1-2 years): Sales, production
•
Long range forecast (> 2years): change location o Time spans usually greater than one year. o Necessary to support strategic decisions about planning products, processes, and facilities.
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Example of sales forecast: Months Forecast of Sales 1 10 2 8 3 11 4 14 5 10 Total
Actual Sales
Error
8 12 7 16 8
2 4 4 2 2 14
Squared Error = E2 4 16 16 4 4 44
Forecast accuracy: • Total absolute deviation (TAD)= 14 • Mean absolute deviation (MAD)= ∑ (Actual-forecast)/n = 14/5 = 2.8 • Total Squared Error (TSE) = 44 • Mean Square Error (MSE)= 44/5 = 8.8 Steps 1. 2. 3. 4. 5. 6.
in forecast development: Determine purpose of forecast. Establish a time horizon: time limit, accuracy decreases with shorter durations. Select forecasting technique. Gather and analyze data. Prepare the forecast Monitor forecast.
Methods of forecast: 1. Quantitative (based on time series data): Time series data: a time ordered sequence of observation taken at regular intervals over time. Patterns resulting from plotting of these data are: a. Trend: A long-term upward or downward movement in data. b. Seasonality: Short-term regular variations related to calendar or time of day. c. Cycle: Wavelike variation lasting more than one year. d. Random variations: residual variations after all other behaviors are accounted for. e. Irregular variations: caused by irregular circumstances, not reflective of typical behavior. Naïve forecast: The forecast for any period equals the previous period’s actual value. • Simple to use. • Virtually no cost. • Quick and easy to prepare (no data analysis required). • Easily understandable. • Cannot provide high accuracy. • Can be a standard for accuracy and cost. Q: is the increased accuracy of another method worth the additional cost? • Can be applied in stable demand (moving around average), seasonal, and trend Examples: 1. Sales of air conditioning units next July, will be the same as the sales in last July. (Seasonal) 2. Highway traffic next Tuesday will be the same as last Tuesday (stable, moving around average). 3. If the last 2 actual values were 50 and 53, the next will be 56 (trend).
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2. Qualitative methods: (based on judgment and opinion) 1. Jury of executives: opinions of high level executives 2. Sales force composite: estimates from sales individuals are reviewed for reasonableness (may tend to make under estimates), then aggregated. 3. Consumer market survey: Asking the customers may give best forecasts but it is higher in cost, difficult to apply. 4. Delphi method: (a) Panel of experts queried. (b) Chosen experts to participate should be of a variety of knowledgeable people in different areas (finance, marketing, production etc). They are unknown to any one, except for the coordinator. (c) Through questionnaire the coordinator obtains estimates from all participants. (d) Coordinator summarizes results and redistributes them to participants along with appropriate new questions. (e) Summarize again and refine forecasts and develop new question. Differences between qualitative and quantitative Qualitative Methods
Quantitative Methods
Uses when situation is vague and little data available New products New technology
Used in stable situations Historical data available Existing products Current technology Involves mathematical techniques Example: sales of color TVs
Example: forecasting online sales
newly
introduced
Linear regression analysis: • Establishes a relationship between a dependent variable and one or more independent variables. • In simple linear regression analysis there is only one independent variable. • If the data is a time series, the independent variable is the time period. • The dependent variable is whatever we wish to forecast. (e.g. sales)
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Regression Equation
Y
b = Delta Y / Delta X = Slope Example: b= ..0 means that for every one unit increase in X , ..0 unit will increase in Y
Delta Y
Delta X a
X
Y=a+bX
•
Y = dependent variable (example: Company Sales) X = independent variable (example: time periods, sales of other related company) a = Y-axis intercept b = Slope of regression line = delta Y/ delta X Constants a and b: o The constants a and b are computed using the following equations: b=
n∑ xy- ∑ x∑ y
∑ x ∑ y-∑ x∑ xy n ∑ x -( ∑ x) 2
a=
n ∑ x 2 -( ∑ x)2
2
2
Or, Σy=na+bΣx a= (Σy – bΣx)/n Σxy=aΣx+bΣx2
Once the a and b values are computed, a future value of X (time, or sales of other elated product) can be entered into the regression equation and a corresponding value of Y (the forecast) can be calculated. Example: College Enrollment At a small regional college enrollments have grown steadily over the past six years, as evidenced below. Use time series regression to forecast the student enrollments for the next three years. Students Students Year Enrolled (-...s) Year Enrolled (-...s) /.0 1 2./ / /.3 0 2.2 2 /.4 5 2.1 / x y x xy /.0 /.0 / /.3 1 0.5 2 /.4 4 3.6 1 2./ -5 -/.3 0 2.2 /0 -5.0 5 2.1 25 /..1 Total () * ++), o
•
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a=
91(18.1) − 21(66.5) = 2.387 6(91) − (21)2
b=
6(66.5) − 21(18.1) = 0.180 105
Y = /.236 7 ..-3.X Y6 = /.236 7 ..-3.(6) = 2.50 or 2,50. students Y3 = /.236 7 ..-3.(3) = 2.32 or 2,32. students Y4 = /.236 7 ..-3.(4) = 1..- or 1,.-. students 8ote: Enrollment is expected to increase by -3. students per year. Coefficient of Correlation (r) • The coefficient of correlation, r, explains the relative importance of the relationship between x and y. • The sign of r shows the direction of the relationship. • The absolute value of r shows the strength of the relationship. • The sign of r is always the same as the sign of b. • r can take on any value between – and +. • Meanings of several values of r: -- a perfect negative relationship (as x goes up, y goes down by one unit, and vice versa) 7- a perfect positive relationship (as x goes up, y goes up by one unit, and vice versa) . no relationship exists between x and y 7..2 a weak positive relationship -..3 a strong negative relationship Equation:
Example: Railroad Products Co) X (sales) Y (profit) x/ -/. 4.0 -1,1.. -20 --.. -3,//0 -2. -/.. -5,4.. -0. -/.0 //,0.. -6. -1.. /3,4.. -4. -5.. 25,-.. //. -3.. 13,1.. ,, *)6 (,,, r=
Xy -,-1. -,130 -,05. -,360 /,23. 2,.1. 2,45. ,,6
7(15, 440) − 1,115(93)
7(185, 425) − (1,115)2 7(1, 287.5) − (93)2 r = ..43/4
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y/ 4../0 -/-... -11... -05./0 -45... /05... 2/1... ,(7),6
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Seasonalized Time Series Regression Analysis • Select a representative historical data set. • Develop a seasonal index for each season. • Use the seasonal indexes to deseasonalize the data. • Perform linear regression analysis on the deseasonalized data. • Use the regression equation to compute the forecasts. • Use the seasonal indexes to reapply the seasonal patterns to the forecasts. • Seasonalized Times Series Regression Analysis An analyst at CPC wants to develop next year’s quarterly forecasts of sales revenue for CPC’s line of Epsilon Computers. She believes that the most recent 3 quarters of sales (shown on the next slide) are representative of next year’s sales. • Year -
Representative Historical Data Set Qtr) ($mil)) Year 6.1 / / 5.0 / 2 1.4 / 1 -5./
) Compute the Seasonal Indexes Year Q Q 6.1 5.0 / 3.2 6.1 Totals ,)7 )* Qtr. Avg. 6.30 5.40 Seas) Ind) = Q.average/*), )(* )7,
Qtr) / 2 1
($mil)) 3.2 6.1 0.1 -3..
Q 1.4 0.1 6) 0.-0 ),,7
) Deseasonalize the Data Quarterly Sales ( = actual quarter sales / seasonality index) Q Q Q Year 3.6/ 3.55 3.3. / 4.63 4.30 4.54 8otice that results have no seasonal variations.
Q -5.-3.. ) -6..0 )(
Q 3.61 4.66
) Perform Regression on Deseasonalized Data X y x/ xy 3.6/ 3.6/ / 3.55 1 -6.2/ 2 3.3 4 /5.1. 1 3.61 -5 21.45 0 4.63 /0 13.4. 5 4.30 25 04.6 4.54 14 56.32 3 4.66 51 63.-5 Total + 7)6 6 )*
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Total 21.4 (year-) 24.- (y/) 7)6 *), 1....
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a=
204(74.01) − 36(341.39) = 8.357 8(204) − (36)2
8(341.39) − 36(74.01) = 0.199 8(204) − (36)2 Y = 3.206 7 ..-44X
b=
) Compute the Deseasonalized Forecasts Y4 = 3.206 7 ..-44(4) = -..-13 Y-. = 3.206 7 ..-44(-.) = -..216 Y-- = 3.206 7 ..-44(--) = -..015 Y-/ = 3.206 7 ..-44(-/) = -..610 8ote: Average sales are expected to increase by ..-44 million (about @/..,...) per quarter. 0. Seasonalize the Forecasts: (= deseaonalized forecasts x seasonality index) Yr. Quarter Index Deseasonalized Seasonalized Forecast Forecast 2 .314 -..-13 ()+ 2 / .60-..216 7)77 2 2 .006 -..015 ,)(7 2 1 -.312 -..610 *)(6 Moving Average Technique that averages a number of recent actual values, updated as new values become available. It can be calculated using the following equation:
Ft = MAn = Σ Ai / n Where: 8umber of periods=n Actual values in periodi = Ai Moving Average = MA Index corresponds to period = i Forecast for time periodt = Ft Example: MA2 refers to a three-period moving average forecast, and MA0 would refer to a five period moving average forecast. Calculate three period moving average for: Period Demand / 6 2 1 6 0 F5 = (1271.71-) / 2 = 1-.22 If actual demand in period 5 turns out to be *, so F6 = (1.71-7*) / 2 = 1.... Note that: the forecast is updated by adding the newest actual value and dropping the oldest) Advantage of moving average: Easy to use and to compute. Disadvantage: values in the average are weighted equally. For example, in a ten- period moving average each the same weight of -/-., the oldest has an equal value to the most recent.
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Weighted moving average: More recent values in a series are given more weight in computing a forecast. Example: The weight of most recent value = ..1., next most recent weight = ..2., next = ../., and next= ..-.. Total weights always = ) In the last example: forecast of period 5 will be: F5 = ..1. (1-) 7 ..2.(1.) 7 ../.(12) 7 ..-.(1.) = 1If actual demand of period 5 is *. Forecast of period 6 will be: F6 = ..1.(24) 7 ..2.(1-) 7 ../.(1.) 7 ..-.(12) = 1../ Advantage: more reflective of the most recent occurrences. Exponential Smoothing: Weighted averaging method based on previous forecast plus a percentage (α) of the forecast error. 8ext forecast = Previous forecast 7 α ( Actual – Previous forescast) Where (Actual – Previous forecast) = forecast error, α is a percentage of the error.
Ft = Ft-- 7 α (At-- – Ft--) Where, Ft = Forecast for period t Ft-- = Forecast for previous period α = Smoothing constant At-- = Actual demand or sales for the previous period. Example: If the previous forecast was 1/ units, actual demand was 1. units, and α = ..-.. The new forecast would be: Ft = 1/ 7 ..-. (1.-1/) = 1-.3 Then if the actual demand turns out to be 12, the next forecast would be: Ft = 1-.3 7 ..-. (12-1-.3) = 1-.4/ α = 6)6 Period
α = 6)6 Forecast Error
Actual Forecast Error Demand 1/ / 1. 1/ -/ 1/... -/ 2 12 1-.3 -./ 1-./. -.3 1 1. 1-.4/ --.4/ 1-.4/ --.4/ 0 11-.62 -..62 1-.-0 -..-0 5 24 1-.55 -/.55 1-..4 -/..4 6 15 1-.24 1.51../0 0.60 3 11 1-.30 /.-0 1/.00 -.10 4 10 1/..6 /.42 12.-2 -.36 Relation between the smoothing constant and response to error: • Exponential smoothing is one of the most widely used techniques in forecasting. • The quickness of the forecast adjustment to error is determined by the smoothing constant α. • The closer the value of α to zero, the slower the forecast will respond to error more smoothing. • The closer the value of α to -..., the greater the forecast will respond to error less smoothing. • Smoothing means that values are less variable smooth curve • To choose the best forecasting method Calculate forecasts and choose method with least MAD. So, steps will be: make forecasting by various methods calculate MAD for each method method with the least MAD is the best. (in exam question) 8otice that -. MA2 means start by calculating F1. /. If F- is not given assume that F-=A- (if F- is given, don’t use it in calculation of MAD in MA) 2. In calculation of MAD to compare accuracy, use same periods.
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