This document provides an overview of operations management forecasting models and their applications. It defines forecasting and lists its common uses. The key components of a forecast and the forecasting process are described. Both qualitative and quantitative forecasting approaches are discussed, along with their advantages and disadvantages. Specific forecasting techniques covered include time series methods, regression methods, moving averages, exponential smoothing, and naive forecasts. Examples are provided to illustrate weighted moving averages and exponential smoothing.
This powerpoint presentation was done as part of the course STAT 591 titled Mater's Seminar during Third semester of MSc. Agricultural Statistics at Agricultural College, Bapatla under ANGRAU, Andhra Pradesh.
Interventions required to meet business objectives from Forecasting Methods,
Quantitative & Qualitative Methods,
Forecast Accuracy , Error Reduction to
CPFR
1) To understand the underlying structure of Time Series represented by sequence of observations by breaking it down to its components.
2) To fit a mathematical model and proceed to forecast the future.
This powerpoint presentation was done as part of the course STAT 591 titled Mater's Seminar during Third semester of MSc. Agricultural Statistics at Agricultural College, Bapatla under ANGRAU, Andhra Pradesh.
Interventions required to meet business objectives from Forecasting Methods,
Quantitative & Qualitative Methods,
Forecast Accuracy , Error Reduction to
CPFR
1) To understand the underlying structure of Time Series represented by sequence of observations by breaking it down to its components.
2) To fit a mathematical model and proceed to forecast the future.
What is Forecasting?
Forecasting is a technique of predicting the future based on the results of previous data. It involves a
detailed analysis of past and present trends or events to predict future events. It uses statistical tools and
techniques. Therefore, it is also called Statistical analysis. In other words, we can say that forecasting acts
as a planning tool that helps enterprises to get ready for the uncertainty that can occur in the future.
Forecasting begins with management's experience and knowledge sharing. To obtain the most numerous
advantages from forecasts, organizations must know the different forecasting methods' more subtle
details. Also, understand what an appropriate forecasting method type can and cannot do, and realize
what forecast type is best suited to a specific need. Let's list down some significant benefits of forecasting:
• Better utilization of resources
• Formulating business plans
• Enhance the quality of management
• Helps in establishing a new business model
• Helps in making the best managerial decisions
A set of observations taken at a particular period of time. For example, having a set of login details at
regular interval of time of each user can be categorized as a time series. Click to explore about, Anomaly
Detection with Time Series Forecasting
What is Prediction?
Prediction is using the data to compute the Outcome of the unseen data.
How does Prediction work?
Firstly, the daily data is fetched from the market once at a time in a day and update it into the database.
Now, the prediction cycle along with learning developed with the use of newly combined data. Historical
data collected and the learning and prediction cycle developed to generate the results. The prediction
results obtained in the form of the various set of periods such as two days, four days, 14 days and so on.
Difference between Prediction and Forecasting
Prediction is the process of estimating the outcomes of unseen data. Forecasting is a sub-discipline of
prediction in which we use time-series data to make forecasts about the future. As a result, the only
distinction between prediction and forecasting is that we consider the temporal dimension. Confusing?
So do we forecast the weather or predict the weather? Consider this, What are the chances that it will
continue to rain in five minutes if it is already raining? Since it is raining right now, regardless of any other
factors that affect the weather (such as air pressure and temperature), the chances of it raining again in
five minutes are high. Right?vThe temporal dimension is whether it is raining right now or not? Without
that forecasting the next 5 mins wouldn't make much sense.
Time-Series refers to data recording at regular intervals of time. Click to explore about, Time Series
Forecasting Analysis
Why Forecasting is important?
Prediction of labor, material and other resources are highly crucial for operating. If the services are
Predicting better, then balanced
What is Forecasting?
Forecasting is a technique of predicting the future based on the results of previous data. It involves a
detailed analysis of past and present trends or events to predict future events. It uses statistical tools and
techniques. Therefore, it is also called Statistical analysis. In other words, we can say that forecasting acts
as a planning tool that helps enterprises to get ready for the uncertainty that can occur in the future.
Forecasting begins with management's experience and knowledge sharing. To obtain the most numerous
advantages from forecasts, organizations must know the different forecasting methods' more subtle
details. Also, understand what an appropriate forecasting method type can and cannot do, and realize
what forecast type is best suited to a specific need. Let's list down some significant benefits of forecasting:
• Better utilization of resources
• Formulating business plans
• Enhance the quality of management
• Helps in establishing a new business model
• Helps in making the best managerial decisions
A set of observations taken at a particular period of time. For example, having a set of login details at
regular interval of time of each user can be categorized as a time series. Click to explore about, Anomaly
Detection with Time Series Forecasting
What is Prediction?
Prediction is using the data to compute the Outcome of the unseen data.
How does Prediction work?
Firstly, the daily data is fetched from the market once at a time in a day and update it into the database.
Now, the prediction cycle along with learning developed with the use of newly combined data. Historical
data collected and the learning and prediction cycle developed to generate the results. The prediction
results obtained in the form of the various set of periods such as two days, four days, 14 days and so on.
Difference between Prediction and Forecasting
Prediction is the process of estimating the outcomes of unseen data. Forecasting is a sub-discipline of
prediction in which we use time-series data to make forecasts about the future. As a result, the only
distinction between prediction and forecasting is that we consider the temporal dimension. Confusing?
So do we forecast the weather or predict the weather? Consider this, What are the chances that it will
continue to rain in five minutes if it is already raining? Since it is raining right now, regardless of any other
factors that affect the weather (such as air pressure and temperature), the chances of it raining again in
five minutes are high. Right?vThe temporal dimension is whether it is raining right now or not? Without
that forecasting the next 5 mins wouldn't make much sense.
Time-Series refers to data recording at regular intervals of time. Click to explore about, Time Series
Forecasting Analysis
Why Forecasting is important?
Prediction of labor, material and other resources are highly crucial for operating. If the services are
Predicting better, then balanced
Operations Management course develops, among the students, a knowledge and a set of skills to manage operations of a unit, section or an organization in an efficient way. The students will learn how to optimize the resource utilization for the maximum output.
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2. OperationsManagement
Lecture Outline
Definitions of forecasting
Roles of Forecasting and applications
Components of Forecasting Demand
List the elements of a good forecast
The steps in the forecasting process
Compare and contrast qualitative and
quantitative approaches to forecasting
Advantages and disadvantages of each
Time Series Methods
Forecast Accuracy
Time Series Forecasting Using Excel (if possible)
Regression Methods
Forecasting: Models and Applications
3. OperationsManagement
Forecasting ?
• Predicting the future based on the historical data.
• A statement about the future value of a variable of interest
such as demand.
• Forecasting is used to make informed decisions.
- Long-range
- Short-range
It is the basis for budgeting, planning capacity, sales,
production and inventory, personnel, purchasing, and more.
Forecasts play an important role in the planning process to
anticipate the future plan accordingly.
Forecasting: Models and Applications
Forecasting
4. OperationsManagement
Data based - expecting that history repeats itself in a certain
way; usually given in the form of a time series, a
chronological sequence of observed data with respect to a
certain variable.
Theory based - where the external factors determine events.
Qualitative forecast methods
- subjective
Quantitative forecast methods
- based on mathematical formulas
Types of Forecasting
Two main methods:
Another distinction consists of:
Forecasting: Models and Applications
5. OperationsManagement
Decisions and activities throughout an organization
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
Uses of Forecasting
Forecasting: Models and Applications
6. OperationsManagement
• Assumes causal system
Past => Present => Future
• Forecasts rarely perfect because of randomness
• Forecasts more accurate for groups vs. individuals
• Forecast accuracy decreases as time horizon increases
Features of Forecasting
Forecasting: Models and Applications
I see that you will
get an A this semester.Timely
AccurateReliable
Written
Elements of a
Good Forecast
7. OperationsManagement
Depend on
• time frame
• demand behavior
• causes of behavior
Indicates how far into the future is forecast
• Short- to mid-range forecast
• typically encompasses the immediate future
• daily up to two years
• Long-range forecast
• usually encompasses a period of time longer
than two years
Types of Forecasting Methods
Time Frame
Forecasting: Models and Applications
8. OperationsManagement
Trend
• a gradual, long-term up or down movement of
demand
Random variations
• movements in demand that do not follow a pattern
Cycle
• an up-and-down repetitive movement in demand
Seasonal pattern
• an up-and-down repetitive movement in demand
occurring periodically
Demand Behavior
Types of Forecasting Methods
Forecasting: Models and Applications
9. OperationsManagement
Time
(a) Trend
Time
(d) Trend with seasonal pattern
Time
(c) Seasonal pattern
Time
(b) Cycle
DemandDemand
DemandDemand
Random
movement
Demand Behavior
Types of Forecasting Methods
Forecasting: Models and Applications
10. OperationsManagement
Types of Forecasting Methods
Time series
• statistical techniques that use historical demand
data to predict future demand
Regression methods
• attempt to develop a mathematical relationship
between demand and factors that cause its behavior
Qualitative
• use management judgment, expertise, and opinion
to predict future demand
Regular Behavior
Forecasting: Models and Applications
11. OperationsManagement
Steps of Forecasting Technique
Forecasting: Models and Applications
Step 1 Determine purpose of forecast
Step 2 Establish a time horizon
Step 3 Select a forecasting technique
Step 4 Obtain, clean and analyze data
Step 5 Make the forecast
Step 6 Monitor the forecast
“The forecast”
12. OperationsManagement Forecasting: Models and Applications
6. Check forecast
accuracy with one
or more measures
4. Select a forecast
model that seems
appropriate for data
5. Develop/compute
forecast for period
of historical data
8a. Forecast over
planning horizon
9. Adjust forecast
based on additional
qualitative information
and insight
10. Monitor results
and measure
forecast accuracy
8b. Select new
forecast model or
adjust parameters
of existing model
7.
Is accuracy
of forecast
acceptable?
1. Identify the
purpose of forecast
3. Plot data and
identify patterns
2. Collect
historical data
No
Yes
Copyright 2011 John Wiley & Sons, Inc.
Steps of Forecasting Technique
13. OperationsManagement Forecasting: Models and Applications
Judgmental
- uses subjective inputs for qualitative methods
Time series
- uses historical data assuming the future will be like
the past or present data
Associative models
- uses explanatory variables to predict the future
Forecasting Techniques
14. OperationsManagement Forecasting: Models and Applications
Forecasts are largely intuitive, whereas others integrate data
and perhaps even mathematical or statistical techniques.
Judgmental forecasts consist of:
forecasts by experts in the same field,
forecasts by individual sales people,
forecasts by division or product-line managers,
consumer surveys,
outside/ external experts or technical reports
Historical analogy relies on comparisons; Delphi method
o Opinions of managers and staff
o Achieves a consensus forecast
Opinion and Judgmental Methods
Forecasting Techniques
15. OperationsManagement Forecasting: Models and Applications
Forecasting Techniques
Time series Analysis
A time series is a set of observations of a variable at
regular intervals over time.
Assume that what has occurred in the past will continue
to occur in the future.
Components of a time series are generally classified as
trend T, cyclical C, seasonal S, and random or irregular R.
Time series analysis includes:
• moving average
• exponential smoothing
• linear trend line
Data are tabulated or graphed to show the nature of the
time dependence.
16. OperationsManagement Forecasting: Models and Applications
Following are the steps in time series forecasting:
1. Plot historical data to confirm relationship (e.g.,
linear, exponential, logarithmic etc).
2. Develop a trend equation (T ) to describe the data.
3. Develop a seasonal index (e.g., monthly index values).
4. Project trend into the future (e.g., monthly trend values).
5. Multiply trend values by corresponding seasonal
index values.
6. Modify projected values by any knowledge of:
• Cyclical business conditions (C) ,
• Anticipated irregular effects (R) .
Time series forecasting procedure
Forecasting Techniques
17. OperationsManagement
Simple to use
Virtually no cost
Quick and easy to prepare
Data analysis is nonexistent
Easily understandable
Cannot provide high accuracy
Can be a standard for accuracy
Naïve Forecasts
Forecasting Techniques
The forecast for any period equals the previous period’s
actual value.
Demand in current period is used as next period’s
forecast
Why Naïve Forecasts ?
Uh, give me a minute....
We sold 250 wheels last week....
Now, next week we should
sell.... 250???
Forecasting: Models and Applications
18. OperationsManagement
Forecasting Techniques
Forecasting: Models and Applications
Jan 120
Feb 90
Mar 100
Apr 75
May 110
June 50
July 75
Aug 130
Sept 110
Oct 90
ORDERS
Month Per Month
-
120
90
100
75
110
50
75
130
110
90Nov - ??
Forecast
Naïve Forecasts
Mathematical formula
used in Naïve:
• Stable time series
data
F (t ) = A (t -1)
• Seasonal variations
F (t ) = A (t – n )
• Data with trends
F (t ) = A ( t - 1) +
(A (t -1) – A(t – 2 ))
19. OperationsManagement
Three methods for describing trend are:
1. Moving average,
2. Hand fitting, and
3. Least squares.
A centered moving average is obtained by summing and
averaging the values from a given number of periods
repetitively, each time deleting the oldest value and adding
a new value.
Moving averages can smooth out fluctuations in any data,
while preserving the general pattern of the.
Forecasting Techniques
Trend Technique
Moving Average Method:
Forecasting: Models and Applications
20. OperationsManagement
The generalized formula for moving average method is:
Moving average / simple moving average
Weighted moving average
Exponential smoothing
Moving Average Method Cont…
𝑴𝑨 =
𝒙
Number of Period
Techniques for Averaging
– Averaging method
– Weights most recent data more strongly
– Reacts more to recent changes
– Widely used, accurate method
Forecasting: Models and Applications
Forecasting Techniques
21. OperationsManagement
A technique that averages a number of recent actual
values, updated as new values become available.
MAn =
n
i = 1
Di
n
Simple Moving average
where
n = number of periods
in the moving
average
Di = demand in period i
Ft = MAn=
n
At-n + … At-2 + At-1
Or,
Forecasting: Models and Applications
Forecasting Techniques
22. OperationsManagement
3-month Simple Moving Average
Jan 120
Feb 90
Mar 100
Apr 75
May 110
June 50
July 75
Aug 130
Sept 110
Oct 90
Nov -
Orders
Month Per Month
MA3 =
3
i = 1
Di
3
=
90 + 110 + 130
3
= 110 orders for Nov
–
–
–
103.3
88.3
95.0
78.3
78.3
85.0
105.0
110.0
Moving
Average
Forecasting: Models and Applications
Forecasting Techniques
23. OperationsManagement
Jan 120
Feb 90
Mar 100
Apr 75
May 110
June 50
July 75
Aug 130
Sept 110
Oct 90
Nov -
Orders
Month Per Month
–
–
–
–
–
99.0
85.0
82.0
88.0
95.0
91.0
Moving
Average
5-month Simple Moving Average
MA5 =
5
i = 1
Di
5
=
90 + 110 + 130+75+50
5
= 91 orders for Nov
Forecasting: Models and Applications
Forecasting Techniques
24. OperationsManagement
150 –
125 –
100 –
75 –
50 –
25 –
0 – | | | | | | | | | | |
Jan Feb Mar Apr May June July Aug Sept Oct Nov
Actual
Orders
Month
5-month
3-month
Effect of 3-month and 5-month moving average
Forecasting: Models and Applications
Forecasting Techniques
25. OperationsManagement
More recent values in a series are given more weight in
computing the forecast.
Adjusts moving average method to more closely reflect
data fluctuations
Weighted Moving Average
WMAn =
i = 1
Wi Di
where
Wi = the weight for period i,
between 0 and 100 %
Wi = 1.00
n
Ft = WMAn=
wnAt-n + … wn-1At-2 + w1At-1
n
Forecasting Techniques
Forecasting: Models and Applications
26. OperationsManagement
MONTH WEIGHT DATA
August 17% 130
September 33% 110
October 50% 90
WMA3 =
3
i = 1
Wi Di
= (0.50)(90) + (0.33)(110) + (0.17)(130)
= 103.4 orders
November Forecast
Forecasting Techniques
Forecasting: Models and Applications
Example: Weighted Moving Average
27. OperationsManagement Forecasting: Models and Applications
Example: Weighted Moving Average
Forecasting Techniques
Shipments (in tons) of welded tube by an aluminum producer
are shown below:
a) Graph the data, and comment on the relationship.
b) Compute a 3-year moving average, plot it as a dotted
line, and use it to forecast shipments in year 12.
c) Using a weight of 3 for the most recent data, 2 for
the next, and 1 for the oldest, forecast shipments in
year 12.
Ref. Operations management, A. Kumar and N. Suresh, New Age, pp. 108-109
28. OperationsManagement
Solution:
Year Shipments 3-y moving
average
1 2 -
2 3 3.7
3 6 6.3
4 10 8.0
5 8 8.3
6 7 9.0
7 12 11.0
8 14 13.3
9 14 15.3
10 18 17.0
11 19 -
The MA forecast for year 12 would be
that of the latest average, 17.0 tons.
The data are plotted as shown:
Moving average:
= 17.8 tons
Example: WMA Cont…
Forecasting Techniques
Forecasting: Models and Applications
29. OperationsManagement
The equation used for forecast for next period is:
where:
Ft +1 = forecast for next period
Dt = actual demand for present period
Ft = previously determined forecast for present period
𝜶 = weighting factor, smoothing constant
Exponential Smoothing
𝑭 𝒕+𝟏 = 𝜶𝑫 𝒕 + 𝟏 − 𝜶 𝑭 𝒕
Effect of Smoothing Constant
0.0 1.0
If = 0.20, then Ft +1 = 0.20 Dt + 0.80 Ft If = 0, then Ft +1 = 0 Dt + 1 Ft = Ft
Forecast does not reflect recent data
If = 1, then Ft +1 = 1 Dt + 0 Ft = Dt ; Forecast based only on most recent data
Forecasting Techniques
Forecasting: Models and Applications
30. OperationsManagement
Example: Exponential Smoothing
Period Month Demand
1 Jan 37
2 Feb 40
3 Mar 41
4 Apr 37
5 May 45
6 Jun 50
7 Jul 43
8 Aug 47
9 Sep 56
10 Oct 52
11 Nov 55
12 Dec 54
F2 = D1 + (1 - )F1
= (0.30)(37) + (0.70)(37)
= 37
F3 = D2 + (1 - )F2
= (0.30)(40) + (0.70)(37)
= 37.9
F13 = D12 + (1 - )F12
= (0.30)(54) + (0.70)(50.84)
= 51.79
Letting, =0.30
and so on. Similarly …
Forecasting Techniques
Forecasting: Models and Applications
31. OperationsManagement
Forecast, Ft + 1
Period Month Demand ( = 0.3) ( = 0.5)
1 Jan 37 – –
2 Feb 40 37.00 37.00
3 Mar 41 37.90 38.50
4 Apr 37 38.83 39.75
5 May 45 38.28 38.37
6 Jun 50 40.29 41.68
7 Jul 43 43.20 45.84
8 Aug 47 43.14 44.42
9 Sep 56 44.30 45.71
10 Oct 52 47.81 50.85
11 Nov 55 49.06 51.42
12 Dec 54 50.84 53.21
13 Jan – 51.79 53.61
Example: Exponential Smoothing
Forecasting Techniques
Forecasting: Models and Applications
34. OperationsManagement
The generalized equation
y = a + bx
Where,
a = intercept
b = slope of the line
x = time period
y = forecast for
demand for period x
where
n = number of periods
= mean of the x values
= mean of the y values
𝒃 =
𝒙𝒚 − 𝒏. 𝒙. 𝒚
𝒙 𝟐 − 𝒏 𝒙 𝟐
𝒂 = 𝒚 − 𝒃 𝒙
𝒙 =
𝒙
𝒏
𝒚 =
𝒚
𝒏
Linear Trend Line
Forecasting Techniques
Forecasting: Models and Applications
36. OperationsManagement
Linear regression
• mathematical technique that relates a dependent
variable to an independent variable in the form of a
linear equation
Correlation
• a measure of the strength of the relationship between
independent and dependent variables
Regression Method
The generalized equation, y = a + bx
Where, a = intercept, b = slope of the line, x = time
period, and y = forecast for demand for period x
Linear Regression
n = number of periods𝒃 =
𝒙𝒚 − 𝒏. 𝒙. 𝒚
𝒙 𝟐 − 𝒏 𝒙 𝟐
𝒂 = 𝒚 − 𝒃 𝒙
Forecasting Techniques
Forecasting: Models and Applications
38. OperationsManagement
Correlation, r
• Measure of strength of relationship
• Varies between -1.00 and +1.00
Coefficient of determination, r2
• Percentage of variation in dependent variable resulting
from changes in the independent variable
Computing coefficient of correlation:
Forecasting Techniques
Forecasting: Models and Applications
Correlation
n xy - x y
[n x2 - ( x)2] [n y2 - ( y)2]
r =
(8)(2,167.7) - (49)(346.9)
[(8)(311) - (49)2] [(8)(15,224.7) - (346.9)2]
r = =0.947
39. OperationsManagement
Multiple Regression
Study the relationship of demand to two or more independent
variables
The relationship is expressed as:
y = 0 + 1x1 + 2x2 … + kxk
where
0 = the intercept
1, … , k = parameters for the independent variables
x1, … , xk = independent variables
Forecasting Techniques
Forecasting: Models and Applications
40. OperationsManagement
r2, the coefficient
of determination
Regression equation
coefficients for x1 and x2
Multiple Regression
Forecasting Techniques
Forecasting: Models and Applications
y = 19,094.42 + 3560.99 x1 + .0368 x2
y = 19,094.42 + 3560.99 (7) + .0368 (60,000)
= 46,229.35
46. OperationsManagement
No single technique works in every situation
Two most important factors
o Cost and Accuracy
Other factors include the availability of:
Historical data
Computers
Time needed to gather and analyze the data
Forecast horizon
Forecasts are the basis for many decisions
Work to improve short-term forecasts
Accurate short-term forecasts improve
• Profits
• Lower inventory levels
• Reduce inventory shortages
• Improve customer service levels
• Enhance forecasting credibility
Forecasting: Models and Applications
Choosing Forecasting Tech