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Forecasts
To make forecasts people uses two kinds of information:(i) Current factors or conditions (ii) Past experience in a similar situation
* Forecasts are the basis for budgeting, planning capacity, sales, production and inventory, personnel, purchasing and more. * Forecasts play an important role in the planning process because they enable a manager to anticipate the future so he can plan accordingly.
Example: (i) Accounting: New product cost estimates, profit projections, cash management
etc.(ii) Human resources: Hiring activities, recruitment, training etc.(iii) Operations: Scheduling, work assignment, inventory planning etc.
There are two uses of forecasts. (i) To help managers plan the system(ii) To help them plan the use of the system.
Planning systems involves long-term plans about the types of products to offer, what facilities and equipments to have, where to locate etc.
Planning the use of systems refers to short-term and intermediate-term planning which involves planning inventory and work force, planning purchasing and production, budgeting and scheduling.
Common features to all forecasts
A wide variety of forecasting techniques are in use. In many respects, they are quite different from each other. But some features are common to all.
(i) Forecasting techniques generally assume that the same underlying casual system that existed in the past will continue to exist in the future.
(ii) Forecasts are rarely perfect; actual results usually differ from predicted values.(iii) Forecasts for groups of items tend to be more accurate than forecasts for
individual items. Because forecasting errors among items in a group usually has a cancelling effect.
(iv) Forecast accuracy decreases as the time horizon increases. Short term forecasts have lower uncertainties than the long-term forecasts.
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Elements of a good forecast
A properly prepared forecast should fulfill certain requirements. The forecasts should be
(i) timely: The forecasting must cover the time necessary to implement possible changes.
(ii) accurate: This enables users to plan for possible errors and provides a basis for comparing alternatives
(iii) reliable: A technique that sometimes provide good forecasts and sometimes poor one leaves users with the uneasy feelings.
(iv) in meaningful units: Financial planner needs to know how many dollars will be needed? Schedulers should know what machines and skills will be required?
(v) in writing: A written forecast permits an objective basis for evaluating the forecast once actual results are in.
(vi) simple to understand: Simple forecasting techniques enjoy wide spread popularity because users are more comfortable working with them.
Steps in the forecasting process:
There are six basic steps in the forecasting process:(i) Determining the purpose of the forecast: How will it be used and when will
it be needed? It will provide an indication of the level of detail required in the forecast and the level of the accuracy necessary.
(ii) Establish a time horizon: The forecasts must indicate a time interval, keeping in mind that accuracy decreases as the time horizon increases.
(iii) Select a forecast technique (iv) Gather and analyze relevant data: It helps in identifying any assumptions
that are made in conjunction with preparing and using forecast.(v) Make the forecast.(vi) Monitor the forecast: It determines whether it is performed in a satisfactory
manner. If it is not, reexamine the method. There are two general approaches fore forecasting. Either or both approaches might be used to develop forecasts.
(i) Qualitative method: It involves subjective inputs, numerical description. It includes soft information (human factor, personal opinion etc) in the forecasting process.
(ii) Quantitative method: It involves either the projection of historical data or the development of associative methods which utilize explanatory variables to make forecasts. This method mainly analyzes data.
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We classify the forecasting techniques as (i) Judgmental (ii) Time series(iii) Associative.
(i) Judgmental forecast: Judgmental forecasts rely on analysis of subjective inputs obtained from various sources such as opinion from consumer surveys, sales staff, managers and executives and experts.
(ii) Time series forecasts: Forecasts that project patterns identified in recent time series observations. It project past experience into the future.
(iii) Associative model: Forecasting technique that uses explanatory variables to predict future demand. For example, demand for paint might be related to variables such as the price per gallon and the amount spent on advertising and drying time, ease of cleanup etc.
Forecasts based on Judgment and OpinionIn some situations, forecasts rely solely on judgment and opinion. For instances,
(i) If the management must have a forecast quickly, there may not be enough time to gather and analyze quantitative data.
(ii) at another time, especially when political and economic conditions are changing, available data may be out of date and more up-to-date information might not yet be available.
In such instances forecasts are based on executive opinions, sales force opinions, consumer surveys, etc.
Executive opinions: Marketing manager, financial manager and operations manager may meet and collectively develop a forecast. This approach is used for long-term planning and new product development.
Sales force opinions: The sales staff or the customer service staff is often a good source of information because of their direct contact with customers. They are often aware of any plans the customers may be considering for the future. One of the drawbacks of this approach is that they may be unable to distinguish between what customers would like to do and what they actually will do.
Consumer surveys: Since consumers determine demand, it is better to collect information from them. If possible every customer or potential customer can be contacted. However, it is not all time possible to identify all the customer or potential customers. So, managers often rely on sample consumer opinions.
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Forecasts based on Time series:A time series is a time-oriented sequence of observations taken at regular intervals (hourly, weekly, daily, etc). The data may be measurements of demand, earnings, profits etc. These techniques are based on the assumption that future values of the series can be estimated from the past values. Analysis of time series data can be accomplished by plotting the data in any of the following patterns:
(i) Trend: It refers to a long-term upward or downward movement in the data. Example: Population shifts, changing incomes etc.
(ii) Seasonality: It refers to short-term regular variations related to calendar or time of a day. Example: Restaurants, supermarkets experiences weekly or daily seasonality.
(iii) Cycles: Cycles are wavelike variations lasting more than one year. Example: Economic, political and agricultural conditions.
Trends
Seasonality
Cycles
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(iv) Irregular variations: It caused by unusual circumstances, not relative of typical behavior. These need to be identified and remove from the data.
(v) Random variations: Random variations are residual variations that remains after all other behaviors have been accounted for. The small bumps in the figures are random variation.
Approaches involving time series dataNaive Methods: It is simple but widely used method. This is the forecast for any period equals the previous period’s actual value. For example, if the demand for a product last week was 50 KGs, the forecast for this week is 50 KGs. This method has several advantages: it has no cost, it is quick and easy, and it is easily understandable.
Techniques for Averaging:Averaging techniques smooth fluctuations in a time series because the individual highs and lows in the data offset each other when they are combined into an average. A forecast based on an average thus tends to exhibit less variability than the original data. The minor variations are treated as random variation and larger variations are viewed as real changes.
The following three techniques widely used for averaging.(i) Moving average(ii) Weighted moving average(iii) Exponential smoothing
Moving average: Technique that averages a number of recent actual data values, updated as new values become available is known as moving average forecast. The moving average forecast can be computed using the following formula
where
Irregular Trends
i = An index that corresponds to time periodn = No. of period in the moving average
= Actual value in period t-iMA = Moving average
= Forecast for time period t
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For example, implies a three-period moving average forecast, and implies a five-period moving average forecast.
Example: Compute a 3-period moving average forecast given demand for shopping carts for the last five periods.
Period Demand1 422 403 434 405 41
Solution:
The moving average for period 6 is,
If the actual demand in period 6 turns out to be 38, the moving average forecast for
period 7 would be .
20
30
40
50
0 2 4 6 8 10
Period
Dem
and
A 3 and 5-period moving average forecast against actual demand for 10 periods.
Note: The more periods in a moving average, the greater the forecast will lag changes in the data.* This technique is easy to compute and easy to understand.
i = An index that corresponds to time periodn =3= No. of period in the moving average
= Actual value in period t-iMA = Moving average
= Forecast for time period t
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* A possible disadvantage is that all values in the average are weighted equally. For example, in a 10-period moving average, each value has weight of 1/10. Hence, the oldest value has the same weight as the most recent value. Decreasing the number of values in the average increases in weight of more recent values.
Example 2: Given the following data:Period No. of complaints1 602 653 554 585 64
(a) Use naive approach to make the forecast for the next period.(b) Compute a 3-period moving average forecast.
Weighted moving average: A weighted average is similar to the moving average, except that it assigns more weight to the most recent values in a time series. For example, the most recent value might be assigned a value of 0.4, the next most recent value a weight of 0.3, the next after that a weight of 0.2, and the next after that a weight of 0.1. Note that the sum of the weights is 1.0.The weighted moving average can be computed by the following formula
The advantage of a weighted average over a simple moving average is that the weighted average is more reflective of the most recent occurrences. However, the choice of the weight is somewhat arbitrary and generally involves the use of trial and error to find a suitable weighting scheme.
Example 1: Given the demand for shopping carts for the last five periods.Period Demand1 422 403 434 405 41
(a) Compute a weighted moving average forecast using a weight of 0.4 for the most recent period, 0.3 for the next most recent, 0.2 for the next, and the next after that a weight of 0.1.
(b) If the actual demand for period 6 is 39, forecast demand for period 7 using the same weights as in part (a).
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Solution: (a)
(b)
Example 2: Given the following data:Period No. of complaints1 602 653 554 585 64
(a) Compute a weighted moving average forecast using a weight of 0.4 for the most recent period, 0.3 for the next most recent, 0.2 for the next, and the next after that a weight of 0.1.(b) If the actual demand for period 6 is 59, forecast demand for period 7 using the same weights as in part (a).
Exponential smoothing:
Weighted averaging method based on previous forecast plus a percentage of the forecast error. It is sophisticated weighted average method that is still relatively easy to use and understand.
Next forecast = Previous forecast + (actual – previous forecast)That is,
where
Commonly used value of ranges from 0.05 to 0.5. Low values are used when the average tends to be stable. Higher values of are used when the average is not stable.
= The smoothing constant = % of the error= Actual value in the previous period
= Forecast for time period t= Forecast for the previous time period
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Example 1: Given the following data:Period No. of complaints1 602 653 554 585 64
Use exponential smoothing approach with a smoothing constant of 0.4 to make the forecast for the next period.
Solution:Period No. of complaints Forecast Calculations1 60 60 is the initial forecast 2 65 60 60 + 0.4(65-60) = 623 55 62 62 + 0.4(55-62) = 59.24 58 59.2 59.2 + 0.4(58-59.2) = 58.725 64 58.72 58.72 + 0.4(64-58.72) = 60.836 60.83
Example 2: Given the demand for shopping carts for the last five periods.Period Demand1 422 403 434 405 41
Use exponential smoothing approach with a smoothing constant of 0.3 to make the forecast for the next period.
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Techniques for Trends:
Analysis of trends involves developing an equation that will suitably describe the trend. It may be linear or may not be. Linear trends are fairly common.There are two techniques that can be used to develop forecasts when trend is present.
(i) Use of a trend equation(ii) An extension of exponential smoothing.
Trend Equation: A linear trend equation has the form where
The coefficients of the line a and b can be computed from the historical data using the formulas:
and where n is the number of periods
and y is the time series.
= Specified no. of time periods from t = 0 = Value of at t = 0= Slope of the line= Forecast for time period t
btaFt
t
yt
yb
a t
y
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Example: Cell phone for a firm over the last 10 weeks are shown as follows. Would a linear trend line be appropriate? Determine the equation of the trend line and predict sales for weeks 11 and 12.
Week 1 2 3 4 5 6 7 8 9 10Unit Sales 700 724 720 728 740 742 758 750 770 775
690
700
710
720
730
740
750
760
770
780
0 2 4 6 8 10
Weeks
Sal
es
This plot suggests that a linear trend is appropriate.
Given
The trend line is where t = 0 for period 0.The forecast for period 11 is The forecast for period 12 is
690
700
710
720
730
740
750
760
770
780
790
800
-3 2 7 12
Weeks
Sale
s
t y ty1 700 7002 724 14483 720 21604 728 29125 740 37006 742 44527 758 53068 750 60009 770 693010 775 7750
7407 41358
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Example2: Plot the following data on a graph and verify visually that a linear trend line is appropriate. Develop a line trend equation. Then use the equation to predict the next two values of the series.
Period 1 2 3 4 5 6 7 8 9Demand 44 52 50 54 55 55 60 56 62 Associative forecasting techniques:
The essence of associative techniques is the development of an equation that summarizes the effects of predictor variables (which is used to predict values of the variable of interest). Linear regression method is used for this analysis.
Linear regression method: Technique for fitting a line to a set of points. The objective in linear regression is to obtain an equation of a straight line that minimizes the sum of squared vertical deviations of data points from the line. The least squares line has the equation
The line intersect the y axis where y = a. The slope of the line is b.The coefficients of the line a and b can be computed from the formulas:
and where n is the number of periods
and y is the time series.
= predictor or independent variable = Value of at x = 0= Slope of the line= Predicted or dependent variable
bxayc
x
yx
yb
a x
y
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Example: Healthy hamburger has a chain of 12 stores in California. Sales figures and profits for the stores given below. Obtain a regression line for the data and predict for a store assuming sales of $10 million.
Unit sales x $ million
7 2 6 4 14 15 16 12 14 20 15 7
Profit y $ million
0.15 0.10 0.13 .15 .25 0.27 0.24 0.2 0.27 0.44 0.34 0.17
Solution: Step1: Plot the data and decide if a linear model is reasonable.Step2:
Obtain the regression . For example, for sale of x = 7, estimated profit is or $162,1124.
y
0
5
1015
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25
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3540
45
50
0 5 10 15 20 25
Example: The owner of a hardware store has noted a sales pattern for window locks that seems to be parallel the number of break-ins reported each week in the newspaper. The data are:
x y Forecasts7 .15 0.16211242 0.10 0.08246126 0.13 0.14618224 0.15 0.114321714 0.25 0.27362415 0.27 0.289554316 0.24 0.305484512 0.20 0.241763614 0.27 0.27362420 0.44 0.369205415 0.34 0.28955437 0.17 0.1621124
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sales 46 18 20 22 27 34 14 37 30Break-ins 3 3 3 5 4 7 2 6 4
(a) Plot the data to see the type of the graph(b) Obtain a regression equation for the data.(c) Estimate sales when the number of break-ins is 5.
Comments on the use of linear regression:
1. Variations around the line are random.2. Deviations around the line should be narrowly distributed.3. Predictions are made within the range of the observed values.
Forecast accuracy:Forecasting accuracy is a significant factor when deciding among forecasting alternatives. Accuracy is based on the historical error performance of a forecast.Three common methods for measuring historical errors are:
(i) Mean absolute deviation (MAD): Average absolute error. MAD =
(ii) Mean squared error (MSE): Average of squared errors. MSE =
(iii) Mean absolute percent error (MAPE): Average absolute percent error.
MAPE =
Example: Compute MAD, MSE, and MAPE for the following data.
Period Actual Forecast Error (A-F)1 217 215 2 2 4 0.92%2 213 216 -3 3 9 1.413 216 215 1 1 1 0.464 210 214 -4 4 16 1.95 213 211 2 2 4 0.946 219 214 5 5 25 2.287 216 217 -1 1 1 0.468 212 216 -4 4 16 1.89
-2 22 76 10.26%
(i) Mean absolute deviation (MAD) =
(ii) Mean squared error (MSE) =
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(iii) Mean absolute percent error (MAPE) =
Example 2: Calculate MAD, MSE and MAPE for the following data and compare them.
Month Demand ForecastTechnique 1 Technique 2
1 492 488 4952 470 484 4823 485 480 4784 493 490 4885 498 497 4926 492 493 493
Control forecast/ Monitor forecast:
Tracking signal method:
Tracking signal method is used to monitor a forecast. This method is an older method which is the ratio of the cumulative forecast error to the corresponding value of MAD.
Tracking signalt =
Example: For above example,
Tracking signalt =
15
