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CHAPTER 3: FORECASTING I Lecture 3
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Page 1: Introductory Operations Management: Lecture 3 - Forecasting

CHAPTER 3: FORECASTING I

Lecture 3

Page 2: Introductory Operations Management: Lecture 3 - Forecasting

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

Page 3: Introductory Operations Management: Lecture 3 - Forecasting

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

Page 4: Introductory Operations Management: Lecture 3 - Forecasting

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.

Page 5: Introductory Operations Management: Lecture 3 - Forecasting

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

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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

I see that you willget an A this semester.

Page 7: Introductory Operations Management: Lecture 3 - Forecasting

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

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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

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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

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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

Page 11: Introductory Operations Management: Lecture 3 - Forecasting

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

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BEHAVIORS OF A TIME SERIES DATA

Trend

Irregularvariation

Seasonal variations

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Cycles

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NAIVE FORECASTS

Uh, give me a minute.... We sold 250 wheels lastweek.... Now, next week we should sell....

The forecast for any period equals the previous period’s actual value.

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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

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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

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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

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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

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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

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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

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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)

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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

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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

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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

Page 24: Introductory Operations Management: Lecture 3 - Forecasting

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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Page 26: Introductory Operations Management: Lecture 3 - Forecasting

COMMON NONLINEAR TRENDS

Parabolic

Exponential

Growth

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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

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EQUATION OF A STRAIGHT LINE

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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.

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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

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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

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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.

Page 33: Introductory Operations Management: Lecture 3 - Forecasting

EXAMPLE 4

A plot suggests that a linear trend line would be appropriate:

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EXAMPLE 4

Values of Σt and Σt2

Values from table 3.1

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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