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Forecasting

Chapter 13

Designing the Forecast System

- Deciding what to forecast
- Level of aggregation.
- Units of measure.
- Choosing the type of forecasting method
- Qualitative methods
- Judgment
- Quantitative methods
- Causal
- Time-series

Deciding What To Forecast

- Few companies err by more than 5 percent when

forecasting total demand for all their services

or products. Errors in forecasts for individual

items may be much higher. - Level of Aggregation The act of clustering

several similar services or products so that

companies can obtain more accurate forecasts. - Units of measurement Forecasts of sales revenue

are not helpful because prices fluctuate. - Forecast the number of units of demand then

translate into sales revenue estimates - Stock-keeping unit (SKU) An individual item or

product that has an identifying code and is held

in inventory somewhere along the value chain.

Choosing the Type ofForecasting Technique

- Judgment methods A type of qualitative method

that translates the opinions of managers, expert

opinions, consumer surveys, and sales force

estimates into quantitative estimates. - Causal methods A type of quantitative method

that uses historical data on independent

variables, such as promotional campaigns,

economic conditions, and competitors actions, to

predict demand. - Time-series analysis A statistical approach that

relies heavily on historical demand data to

project the future size of demand and recognizes

trends and seasonal patterns.

Demand Forecast Applications

Judgment Methods

- Sales force estimates The forecasts that are

compiled from estimates of future demands made

periodically by members of a companys sales

force. - Executive opinion A forecasting method in which

the opinions, experience, and technical knowledge

of one or more managers are summarized to arrive

at a single forecast. - Executive opinion can also be used for

technological forecasting to keep abreast of the

latest advances in technology. - Market research A systematic approach to

determine external consumer interest in a service

or product by creating and testing hypotheses

through data-gathering surveys. - Delphi method A process of gaining consensus

from a group of experts while maintaining their

anonymity.

Guidelines for Using Judgment Forecasts

- Judgment forecasting is clearly needed when no

quantitative data are available to use

quantitative forecasting approaches. - Guidelines for the use of judgment to adjust

quantitative forecasts to improve forecast

quality are as follows - Adjust quantitative forecasts when they tend to

be inaccurate and the decision maker has

important contextual knowledge. - Make adjustments to quantitative forecasts to

compensate for specific events, such as

advertising campaigns, the actions of

competitors, or international developments.

Forecasting Error

- For any forecasting method, it is important to

measure the accuracy of its forecasts. - Forecast error is the difference found by

subtracting the forecast from actual demand for a

given period. - Et Dt - Ft where
- Et forecast error for period t
- Dt actual demand for period t
- Ft forecast for period t

Measures of Forecast Error

- Cumulative sum of forecast errors (CFE) A

measurement of the total forecast error that

assesses the bias in a forecast. - Mean squared error (MSE) A measurement of the

dispersion of forecast errors. - Mean absolute deviation (MAD) A measurement of

the dispersion of forecast errors.

CFE ?Et

Measures of Forecast Error

Mean absolute percent error (MAPE) A measurement

that relates the forecast error to the level of

demand and is useful for putting forecast

performance in the proper perspective.

Calculating Forecast Error Example 13.6

The following table shows the actual sales of

upholstered chairs for a furniture manufacturer

and the forecasts made for each of the last eight

months. Calculate CFE, MSE, MAD, and MAPE for

this product.

Example 13.6 Forecast Error Measures

Causal Methods Linear Regression

- Causal methods are used when historical data are

available and the relationship between the factor

to be forecasted and other external or internal

factors can be identified. - Linear regression A causal method in which one

variable (the dependent variable) is related to

one or more independent variables by a linear

equation. - Dependent variable The variable that one wants

to forecast. - Independent variables Variables that are assumed

to affect the dependent variable and thereby

cause the results observed in the past.

Causal Methods Linear Regression

Linear Regression Example 13.1

The following are sales and advertising data for

the past 5 months for brass door hinges. The

marketing manager says that next month the

company will spend 1,750 on advertising for the

product. Use linear regression to develop an

equation and a forecast for this product.

Example 13.1Causal Methods Linear Regression

Sales Advertising Month (000 units) (000

) 1 264 2.5 2 116 1.3 3 165 1.4 4 101 1.

0 5 209 2.0

Regression equation for forecast Y a bx,

where

Example 13.1

Example 13.1Causal Methods Linear Regression

Sales, Y Advertising, X Month (000 units) (000

) XY X 2 Y 2 1 264 2.5 660.0 6.25 69,696 2 116

1.3 150.8 1.69 13,456 3 165 1.4 231.0 1.96 27,22

5 4 101 1.0 101.0 1.00 10,201 5 209 2.0 418.0 4.

00 43,681 Total 855 8.2 1560.8 14.90 164,259

Y 171 X 1.64

Example 13.1

Example 13.1Causal Methods Linear Regression

Example 13.1

Example 13.1Causal Methods Linear Regression

Example 13.1

Example 13.1Causal Methods Linear Regression

Example 13.1

Example 13.1Causal Methods Linear Regression

Example 13.1

Example 13.1Causal Methods Linear Regression

Figure 13.3

Example 13.1Causal Methods Linear Regression

Example 13.1

Example 13.1Causal Methods Linear Regression

Example 13.1

Example 13.1Causal Methods Linear Regression

Example 13.1

Example 13.1Causal Methods Linear Regression

Example 13.1

Components of a Time Series

- Time Series The repeated observations of demand

for a service or product in their order of

occurrence. - There are five basic patterns of most time

series. - Trend. The systematic increase or decrease in the

mean of the series over time. - Seasonal. A repeatable pattern of increases or

decreases in demand, depending on the time of

day, week, month, or season. - Cyclical. The less predictable gradual increases

or decreases over longer periods of time (years

or decades). - Random. The unforecastable variation in demand.

Demand Patterns

Horizontal

Trend

Seasonal

Cyclical

Time Series Methods

- Naive forecast A time-series method whereby the

forecast for the next period equals the demand

for the current period, or Forecast Dt - Simple moving average method A time-series

method used to estimate the average of a demand

time series by averaging the demand for the n

most recent time periods. - It removes the effects of random fluctuation and

is most useful when demand has no pronounced

trend or seasonal influences.

Moving Average Method Example 13.2

- a. Compute a three-week moving average forecast

for - the arrival of medical clinic patients in

week 4. - The numbers of arrivals for the past 3 weeks

were

Patient Week Arrivals 1 400 2 380 3 411

b. If the actual number of patient arrivals in

week 4 is 415, what is the forecast error

for week 4? c. What is the forecast for week 5?

Example 13.2Solution

The moving average method may involve the use of

as many periods of past demand as desired. The

stability of the demand series generally

determines how many periods to include.

Example 13.2 Solution continued

a.

b.

c.

Forecast error for week 4 is 18. It is the

difference between the actual arrivals (415) for

week 4 and the average of 397 that was used as a

forecast for week 4. (415 397 18)

Comparison of 3- and 6-Week MA Forecasts

Application 13.1

- We will use the following customer-arrival data

in this moving average application

Application 13.1a Moving Average Method

780 customer arrivals

802 customer arrivals

Weighted Moving Averages

- Weighted moving average method A time-series

method in which each historical demand in the

average can have its own weight the sum of the

weights equals 1.0.

Ft1 W1Dt W2Dt-1 WnDt-n1

Application 13.1b Weighted Moving Average

786 customer arrivals

802 customer arrivals

Exponential Smoothing

- Exponential smoothing method A sophisticated

weighted moving average method that calculates

the average of a time series by giving recent

demands more weight than earlier demands.

- Ft1 ?(Demand this period) (1 ?)(Forecast

calculated last period) - ? Dt (1?)Ft
- Or an equivalent equation Ft1 Ft ??(Dt

Ft ) - Where alpha (???is a smoothing parameter with a

value between 0 and 1.0

Exponential smoothing is the most frequently used

formal forecasting method because of its

simplicity and the small amount of data needed to

support it.

Exponential SmoothingExample 13.3

- Reconsider the medical clinic patient

arrival data. It is now the end of week 3.

a. Using ? 0.10, calculate the

exponential smoothing forecast for

week 4. Ft1 ? Dt (1-?)Ft - F4 0.10(411) 0.90(390) 392.1
- b. What is the forecast error for week 4 if the

actual demand turned out to be 415? - E4 415 - 392 23
- c. What is the forecast for week 5?
- F5 0.10(415) 0.90(392.1) 394.4

Application 13.1c Exponential Smoothing

784 customer arrivals

789 customer arrivals

Trend-Adjusted Exponential Smoothing

- A trend in a time series is a systematic increase

or decrease in the average of the series over

time. - Where a significant trend is present, exponential

smoothing approaches must be modified otherwise,

the forecasts tend to be below or above the

actual demand. - Trend-adjusted exponential smoothing method The

method for incorporating a trend in an

exponentially smoothed forecast. - With this approach, the estimates for both the

average and the trend are smoothed, requiring two

smoothing constants. For each period, we

calculate the average and the trend.

Trend-Adjusted Exponential Smoothing Formula

- Ft1 At Tt
- where At ??Dt (1 ?)(At-1 Tt-1)
- Tt ??(At At-1) (1 ?)Tt-1
- At exponentially smoothed average of the series

in period t - Tt exponentially smoothed average of the trend

in period t - ? smoothing parameter for the average
- ? smoothing parameter for the trend
- Dt demand for period t
- Ft1 forecast for period t 1

Trend-Adjusted Exponential Smoothing

Example 13.4 Medanalysis ran an average of 28

blood tests per week during the past four weeks.

The trend over that period was 3 additional

patients per week. This weeks demand was for 27

blood tests. We use ? 0.20 and ? 0.20 to

calculate the forecast for next week.

- A0 28 patients and Tt 3 patients
- At ??Dt (1 ?)(At-1 Tt-1)
- A1 0.20(27) 0.80(28 3) 30.2
- Tt ??(At At-1) (1 ?)Tt-1
- T1 0.20(30.2 2.8) 0.80(3) 2.8
- Ft1 At Tt
- F2 30.2 2.8 33 blood tests

Example 13.4 Medanalysis Trend-Adjusted

Exponential Smoothing

Forecast for Medanalysis Using the

Trend-Adjusted Exponential Smoothing Model

Application 13.2

- The forecaster for Canine Gourmet dog breath

fresheners estimated (in March) the sales average

to be 300,000 cases sold per month and the trend

to be 8,000 per month. - The actual sales for April were 330,000 cases.
- What is the forecast for May,
- assuming ? 0.20 and ? 0.10?

Application 13.2 Solution

thousand

thousand

To make forecasts for periods beyond the next

period, multiply the trend estimate by the number

of additional periods, and add the result to the

current average

Seasonal Patterns

- Seasonal patterns are regularly repeated upward

or downward movements in demand measured in

periods of less than one year. - An easy way to account for seasonal effects is to

use one of the techniques already described but

to limit the data in the time series to those

time periods in the same season. - If the weighted moving average method is used,

high weights are placed on prior periods

belonging to the same season. - Multiplicative seasonal method is a method

whereby seasonal factors are multiplied by an

estimate of average demand to arrive at a

seasonal forecast. - Additive seasonal method is a method whereby

seasonal forecasts are generated by adding a

constant to the estimate of the average demand

per season.

Multiplicative Seasonal Method

- Step 1 For each year, calculate the average

demand for each season by dividing annual demand

by the number of seasons per year. - Step 2 For each year, divide the actual demand

for each season by the average demand per season,

resulting in a seasonal index for each season of

the year, indicating the level of demand relative

to the average demand. - Step 3 Calculate the average seasonal index for

each season using the results from Step 2. Add

the seasonal indices for each season and divide

by the number of years of data. - Step 4 Calculate each seasons forecast for next

year.

Using the Multiplicative Seasonal Method

Example 13.5 Stanley Steemer, a carpet cleaning

company needs a quarterly forecast of the number

of customers expected next year. The business is

seasonal, with a peak in the third quarter and a

trough in the first quarter. Forecast customer

demand for each quarter of year 5, based on an

estimate of total year 5 demand of 2,600

customers.

Demand has been increasing by an average of 400

customers each year. The forecast demand is found

by extending that trend, and projecting an annual

demand in year 5 of 2,200 400 2,600 customers.

Example 13.5 OM Explorer Solution

Application 13.3 Multiplicative Seasonal Method

1320/4 quarters 330

Comparison of Seasonal Patterns

Tracking Signal

Tracking signal A measure that indicates whether

a method of forecasting is accurately predicting

actual changes in demand.

Forecast Error Ranges

Forecasts stated as a single value can be less

useful because they do not indicate the range of

likely errors. A better approach can be to

provide the manager with a forecasted value and

an error range.

Computer Support

Computer support, such as OM Explorer, makes

error calculations easy when evaluating how well

forecasting models fit with past data.

Results SheetMoving Average

Forecast for 7/17/06

Results SheetWeighted Moving Average

Forecast for 7/17/06

Results SheetExponential Smoothing

Forecast for 7/17/06

Results SheetTrend-Adjusted Exponential

Smoothing

Forecast for 7/17/06 Forecast for

7/24/06 Forecast for 7/31/06 Forecast for

8/7/06 Forecast for 8/14/06 Forecast for 8/21/06

Criteria for Selecting Time-Series Methods

- Forecast error measures provide important

information for choosing the best forecasting

method for a service or product. - They also guide managers in selecting the best

values for the parameters needed for the method - n for the moving average method, the weights for

the weighted moving average method, and ? for

exponential smoothing. - The criteria to use in making forecast method and

parameter choices include - minimizing bias
- minimizing MAPE, MAD, or MSE
- meeting managerial expectations of changes in the

components of demand - minimizing the forecast error last period

Using Multiple Techniques

- Research during the last two decades suggests

that combining forecasts from multiple sources

often produces more accurate forecasts. - Combination forecasts Forecasts that are

produced by averaging independent forecasts based

on different methods or different data or both. - Focus forecasting A method of forecasting that

selects the best forecast from a group of

forecasts generated by individual techniques. - The forecasts are compared to actual demand, and

the method that produces the forecast with the

least error is used to make the forecast for the

next period. The method used for each item may

change from period to period.

Forecasting as a Process

The forecast process itself, typically done on a

monthly basis, consists of structured steps. They

often are facilitated by someone who might be

called a demand manager, forecast analyst, or

demand/supply planner.

Denver Air-Quality Discussion Question 1