introductory operations management: lecture 3 - forecasting
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CHAPTER 3: FORECASTING I
Lecture 3
OUTLINE
Introduction Features common to all forecasts Elements of a good forecast Steps in forecasting process Forecasting techniques and common models Forecasts based on Time series data
Naïve methods Techniques for averaging Techniques for trend
INTRODUCTION What is a forecast?
A statement about future values of a variable, in other words forecasts are prediction of future
Something that can be predicted in advance Better predictions lead to informed decisions Example of forecast
Weather forecast Forecasting the demand of a product before it occurs
Manufacture according to the predicted demand Companies that does demand forecasting: Wal-Mart,
JCPenney, Gap, P & G etc. Forecasting helps managers by reducing some of
the uncertainty, thereby allowing them to develop meaningful plans, how? Anticipating what buyers want Reasonable approximation
INTRODUCTION Forecasts are the basis for budgeting, planning
capacity, sales, production and inventory, personnel, purchasing etc.
Forecasts affects decisions in all the departments in an organization Accounting – new product estimated cost, profit
projections Finance – replacement of equipment, amount of
funding/borrowing needs Human Resources – hiring activities, layoff planning Marketing – pricing and promotions etc. MIS – new/revised information systems Operations – schedules, capacity planning, work
assignments, inventory planning, make-or-buy decisions, outsourcing etc.
Product/service design – timeline to design a new product etc.
INTRODUCTION Forecasting is an important concept for yield
management - percentage of capacity being used Match capacity with demand results in high yield
Two uses of forecast Plan the system – long term planning
Products and service to offer, equipment, locations etc. Plan the use of system – short term and intermediate
range planning Inventory, work force levels, purchasing, budgeting,
scheduling etc. Forecasting is not an exact science, it is a blend
of art and science It requires a lot of experience Judgment Technical expertise
FEATURES COMMON TO ALL FORECASTS
Most forecasting techniques assume that the same underlying causal system (explanatory variables) that existed in the past will continue to exist in future Example of a hurricane
Forecast are rarely perfect, in some situations the actual values might differ from the forecasted values by a great extent Allowances should be made for forecast
errors Forecast for group of items tend to be
more accurate than individual item Cancellation effect of forecast error Forecasting parts in an automobile
company Accuracy of forecast decreases as the
time horizon covered increases Uncertainties for short-range forecast
Vs. long-range forecast
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ELEMENTS OF A GOOD FORECAST Forecasts should be timely
Enough time should be provided for the managers to respond to the situation
Forecasts should be accurate Minimum forecast error
Forecasts should be reliable and consistent Forecasts should be expressed in meaningful
units Dollars, number of units of inventory, number of
workers etc. Entire process of forecasting should be well
documented Helps in knowing the mistakes and making
improvements Simple to understand and easy to use
Also must account for the trade-off Cost-effective: benefits should outweigh the costs
STEPS IN FORECASTING PROCESS
Step 1: What is the purpose of the forecast? Step 2: Time horizon Step 3: Select a forecasting technique Step 4: obtain, clean and analyze the data
This will be the major step Sometimes it is not easy to obtain/clean the data
Step 5: Making the forecast This the easiest step
Step 6: Monitor the forecast Important step in performance evaluation Check the forecast error
FORECASTING TECHNIQUES AND COMMON MODELS Qualitative: Subjective, Judgmental; based on
estimates and opinions Grass roots – build forecast from bottom Market research – market surveys etc. Panel consensus – group of experts Historical analogy – look at a closer analogy Delphi method
Opinions of managers and staff Achieves a consensus forecast
Time Series Analysis: Timely ordered sequence of observation (hourly, daily, monthly, yearly etc.) Simple moving average Weighted moving average Exponential smoothing Regression analysis
FORECASTING TECHNIQUES AND COMMON MODELS
Causal: tries to understand the system surrounding the item being forecasted (example: sales is dependent on advertising, quality, and competitors) Regression Analysis
Simple linear regression Multiple linear regression
Econometric models Input/output models Leading indicators – Gas price fluctuation Vs. car sales
Simulation Models: Dynamic models, computer based that allows to do simple things like:- What happens to my queue length if there is a 10%
increase in the customers
FORECASTS BASED ON TIME-SERIES DATA Time Series?
It is a time-ordered sequence of observations taken at regular intervals
It can be easily observed by plotting the data The behaviors of a time series data
Trend A long term upward or downward movement in data
Seasonality Short term regular variations related to the calendar
Cycle Wave like variations that occurs over extended period of time
Irregular variations Sudden increase or decrease, occurring due to unusual
circumstances Should not be accounted for regular behavior, should be removed
if possible Random variations
These are the remaining variations after all the behaviors are accounted
BEHAVIORS OF A TIME SERIES DATA
Trend
Irregularvariation
Seasonal variations
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Cycles
NAIVE FORECASTS
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The forecast for any period equals the previous period’s actual value.
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
Compare to other forecasting methods Example of Naïve forecast
Suppose the last two values were 50 and 53, then the next value would be:
Change in value 53 – 50 = +3 Next value: 53 + 3 = 56
NAÏVE FORECASTS
TECHNIQUES FOR AVERAGING Why would you want to average the data?
To smooth variations in data Try to remove the randomness from the data Get a better picture of the actual data by plotting
It is desirable to avoid reactions to minor variations Responding to the random changes could entail
significant increase in cost Techniques for averaging
1. Moving Average2. Weighted moving average3. Exponential smoothing
MOVING AVERAGES
Moving average – A technique that averages a number of recent actual values, updated as new values become available.
Weighted moving average – More recent values in a series are given more weight in computing the forecast. Sum of W’s = 1
Ft = MAn= n
At-n + … At-2 + At-1
Ft = WMAn= wnAt-n + … wn-1At-2 + w1At-1
SIMPLE MOVING AVERAGE
35
37
39
41
43
45
47
1 2 3 4 5 6 7 8 9 10 11 12
Actual
MA3
MA5
Ft = MAn= nAt-n + … At-2 + At-1
EXAMPLE PROBLEMS
EXAMPLE 1 Compute a three-period moving average
forecast, given demand for shopping carts for the last five periods.
Answer :- F6 = 41.3 If actual demand in period 6 turns out to be
38, the moving average forecast for period 7 would be Answer :- F7 = 39.67
EXAMPLE PROBLEMS EXAMPLE 2
Given the following demand data, Part 1: Compute a weighted average forecast
using a weight of .40 for the most recent period, .30 for the next most recent, .20 for the next, and .10 for the next.
Part 2 If the actual demand for period 6 is 39, forecast demand for period 7 using the same weights as in part a.
Answer Part 1:- F6 = 41.0 Answer Part 2:- F7 = 40.2
EXPONENTIAL SMOOTHING
Premise--The most recent observations might have the highest predictive value. Therefore, we should give more weight to the more
recent time periods when forecasting. Weighted averaging method based on
previous forecast plus a percentage of the forecast error
A-F is the error term, is the % feedback Value of should be between 0 and 1
Ft = Ft-1 + (At-1 - Ft-1)
Period Actual Alpha = 0.1 Error Alpha = 0.4 Error1 422 40 42 -2.00 42 -23 43 41.8 1.20 41.2 1.84 40 41.92 -1.92 41.92 -1.925 41 41.73 -0.73 41.15 -0.156 39 41.66 -2.66 41.09 -2.097 46 41.39 4.61 40.25 5.758 44 41.85 2.15 42.55 1.459 45 42.07 2.93 43.13 1.87
10 38 42.36 -4.36 43.88 -5.8811 40 41.92 -1.92 41.53 -1.5312 41.73 40.92
Example 3 - Exponential SmoothingExample 3 - Exponential Smoothing
PICKING A SMOOTHING CONSTANT
35
40
45
50
1 2 3 4 5 6 7 8 9 10 11 12
Period
De
ma
nd .1
.4
Actual
• Quickness of forecast adjustment to error is determined by the smoothing constant• Closer the value to zero the slower will the forecast adjust to errors and vice-versa
EXAMPLE PROBLEM
For example, suppose the previous forecast was 42 units, actual demand was 40 units, and α = .10. What is the new forecast value? Answer:- Ft = 41.8
Then, if the actual demand turns out to be 43, the next forecast would be Answer:- Ft = 41.92
TECHNIQUES FOR TREND
Analysis for trend might involve developing a suitable equation
The trend component might be:- Linear Non-linear
A simple plot will reveal We will focus only on linear trend
Trend adjusted exponential smoothing
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COMMON NONLINEAR TRENDS
Parabolic
Exponential
Growth
LINEAR TREND EQUATION
Ft = Forecast for period t t = Specified number of time periods a = Value of Ft at t = 0 b = Slope of the line
Ft = a + bt
0 1 2 3 4 5 t
Ft
EQUATION OF A STRAIGHT LINE
EXAMPLE
For example, consider the trend equation Ft = 45 + 5t. The value of Ft when t = 0 is 45, and the slope of the line is 5, which means that, on the average, the value of Ft will increase by five units for each time period. If t = 10, the forecast?
Answer: Ft, is 45 + 5(10) = 95 units.
CALCULATING A AND B
b = n (ty) - t y
n t2 - ( t)2
a = y - b t
n
wheren = Number of periodsy = Value of the time series
LINEAR TREND EQUATION EXAMPLE
t yW e e k t 2 S a l e s t y
1 1 1 5 0 1 5 02 4 1 5 7 3 1 43 9 1 6 2 4 8 64 1 6 1 6 6 6 6 45 2 5 1 7 7 8 8 5
t = 1 5 t 2 = 5 5 y = 8 1 2 t y = 2 4 9 9( t ) 2 = 2 2 5
EXAMPLE 4
Cell phone sales for a California-based firm over the last 10 weeks are shown in the table below. Plot the data, and visually check to see if a linear trend line would be appropriate. Then determine the equation of the trend line, and predict sales for weeks 11 and 12.
EXAMPLE 4
A plot suggests that a linear trend line would be appropriate:
EXAMPLE 4
Values of Σt and Σt2
Values from table 3.1
EXAMPLE 4
From Table 3.1, for n = 10, Σt = 55 and Σt2 = 385.
b = ?; a = ?; F11 = ?; F12 = ? b = 7.51 a = 699.40 F11 = 782.01 F12 = 789.52
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