Forecasting Lecture2

7/29/2019 Forecasting Lecture2

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2007 Pearson Education

Forecasting

Chapter 13


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How Forecastingfits the Operations Management

Philosophy

Operations As a CompetitiveWeapon

Operations StrategyProject Management Process StrategyProcess Analysis

Process Performance and QualityConstraint Management

Process LayoutLean Systems

Supply Chain StrategyLocation

Inventory ManagementForecasting

Sales and Operations PlanningResource Planning

Scheduling


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Forecasting at Unilever

Customer demand planning (CDP), which is criticalto managing value chains, begins with accurateforecasts.

Unilever has a state-of-the-art CDP system that

blends historical shipment data with promotionaldata and current order data.

Statistical forecasts are adjusted with plannedpromotion predictions.

Forecasts are frequently reviewed and adjusted withpoint of sale data.

This has enabled Unilever to reduce its inventoryand improved its customer service.


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Demand Patterns

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.

a. Horizontal. The fluctuation of data around a constant mean.

b. Trend. The systematic increase or decrease in the mean ofthe series over time.

c. Seasonal. A repeatable pattern of increases or decreases indemand, depending on the time of day, week, month, or

season.d. Cyclical. The less predictable gradual increases or decreases

over longer periods of time (years or decades).

e. Random. The unforecastable variation in demand.


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Demand Patterns

Horizontal Trend

Seasonal Cyclical


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Designing theForecast 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


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DecidingWhat To Forecast

Few companies err by more than 5 percent whenforecasting total demand for all their services orproducts. Errors in forecasts for individual itemsmay be much higher.

Level of Aggregation: The act of clustering severalsimilar services or products so that companies canobtain more accurate forecasts.

Units of measurement: Forecasts of sales revenue

are not helpful because prices fluctuate. Forecast the number of units of demand then translateinto sales revenue estimates

Stock-keeping unit (SKU): An individual item or productthat has an identifying code and is held in inventorysomewhere along the value chain.


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Choosing the Type ofForecasting Technique

Judgment methods: A type of qualitative method thattranslates the opinions of managers, expert opinions,consumer surveys, and sales force estimates into quantitativeestimates.

Causal methods: A type of quantitative method that useshistorical data on independent variables, such as promotionalcampaigns, 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 demandand recognizes trends and seasonal patterns.

Collaborative planning, forecasting, and replenishment(CPFR): A nine-step process for value-chain management thatallows a manufacturer and its customers to collaborate onmaking the forecast by using the Internet.


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2007 Pearson Education 2007 Pearson Education

Demand Forecast Applications

Causal Judgment

Causal Judgment

Time series Causal Judgment

ForecastingTechnique

Facility location Capacity planning Process

management

Staff planning Production

planning Master production

scheduling

Purchasing Distribution

Inventory

management Final assembly

scheduling Workforce

scheduling Master productionscheduling

Decision

Area

Total sales Total sales Groups orfamilies

of products or

services

Individual

products orservices

ForecastQuality

Long Term

(more than 2 years)

Medium Term

(3 months 2 years)

Short Term

(03 months)

Application

Time Horizon


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J udgment Methods

Sales force estimates: The forecasts that are compiled fromestimates of future demands made periodically by members ofa companys sales force.

Executive opinion: A forecasting method in which the

opinions, experience, and technical knowledge of one or moremanagers are summarized to arrive at a single forecast.

Executive opinion can also be used fortechnologicalforecasting to keep abreast of the latest advances intechnology.

Market research: A systematic approach to determineexternal consumer interest in a service or product by creatingand testing hypotheses through data-gathering surveys.

Delphi method: A process of gaining consensus from a groupof experts while maintaining their anonymity.


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Guidelines for UsingJ udgment Forecasts

Judgment forecasting is clearly needed when noquantitative data are available to use quantitativeforecasting approaches.

Guidelines for the use of judgment to adjustquantitative forecasts to improve forecast qualityare as follows:1. Adjust quantitative forecasts when they tend to be

inaccurate and the decision maker has important

contextual knowledge.

2. Make adjustments to quantitative forecasts to compensate

for specific events, such as advertising campaigns, the

actions of competitors, or international developments.


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Causal MethodsLinear Regression

Causal methods are used when historical data areavailable and the relationship between the factor tobe forecasted and other external or internal factorscan be identified.

Linear regression: A causal method in which onevariable (the dependent variable) is related to one ormore independent variables by a linear equation.

Dependent variable: The variable that one wants toforecast.

Independent variables: Variables that areassumed to affect the dependent variable andthereby cause the results observed in the past.


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Dependentvariable

Independent variable

X

YEstimate ofY fromregression

equation

ActualvalueofY

Value ofX usedto estimateY

Deviation,or error

{

Causal MethodsLinear Regression

Regressionequation:

Y = a + bX

Y = dependent variableX = independent variablea =Y-intercept of the lineb = slope of the line


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Sales AdvertisingMonth (000 units) (000 $)

1 264 2.52 116 1.3

3 165 1.44 101 1.05 209 2.0

a = 8.135b = 109.229Xr = 0.98r2 = 0.96

syx= 15.603

The following are sales and advertising data for the past 5 months forbrass door hinges. The marketing manager says that next month thecompany will spend $1,750 on advertising for the product. Use linearregression to develop an equation and a forecast for this product.

Linear RegressionExample 13.1

We use the computer to determinethe best values ofa, b, the correlationcoefficient (r), the coefficient ofdetermination (r2), and the standarderror of the estimate (syx).


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| | | |1.0 1.5 2.0 2.5

Advertising (thousands of dollars)

300

250

200

150

100

50 Sa

les(thousandsofunits)

Y = 8.135 + 109.229X

a = 8.135b = 109.229Xr = 0.98r2 = 0.96

syx= 15.603

Y = a + bX

Linear Regression Line forExample 13.1

Forecast for Month 6:X = $1750,Y = 8.135 + 109.229(1.75) =183,016


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The production scheduler can use thisforecast of 183,016 units to determine the

quantity of brass door hinges needed formonth 6.

If there are 62,500 units in stock, then therequirement to be filled from production is183,016 - 62,500 = 120,516 units.

Forecasting Demand forExample 13.1


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Time Series Methods

Naive forecast: A time-series method whereby theforecast for the next period equals the demand forthe current period, orForecast= Dt

Simple moving average method: A time-seriesmethod used to estimate the average of a demandtime series by averaging the demand for the n mostrecent time periods. It removes the effects of random fluctuation and is most

useful when demand has no pronounced trend or seasonalinfluences.


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Forecasting Error

For any forecasting method, it is important tomeasure the accuracy of its forecasts.

Forecast erroris the difference found bysubtracting the forecast from actual demandfor a given period.

Et= Dt- Ft

whereEt= forecast error for period t

Dt= actual demand for period t

Ft= forecast for period t


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Moving Average MethodExample 13.2

a. Compute a three-week moving average forecast forthe arrival ofmedical clinic patients in week 4.The numbers of arrivals for the past 3 weeks were:

PatientWeek Arrivals

1 4002 380

3 411b. 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?


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2007 Pearson Education Week

450

430

410

390

370

| | | | | |0 5 10 15 20 25 30

Patientarrivals

Actual patientarrivals

Example 13.2Solution

The moving average method may involve the use of as manyperiods of past demand as desired. The stability of thedemand series generally determines how many periods toinclude.


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Week Arrivals Average

1 400

2 380

3 411 3974 415 402

5 ?

Example 13.2Solution continued

Forecast for week 5is the average ofthe arrivals forweeks 2,3 and 4

Forecast error for week 4 is 18.It is the difference between theactual arrivals (415) for week 4and the average of 397 that wasused as a forecast for week 4.(415 397 = 18)

Forecast for week4 is the average ofthe arrivals for

weeks 1,2 and 3

F4 =411 + 380 + 400

3

a.

c.b.


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Comparison of3- and 6-Week MA Forecasts

Week

PatientArrivals

Actual patient arrivals

3-week movingaverage forecast

6-week movingaverage forecast


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Application 13.1

We will use the following customer-arrivaldata in this moving average application:


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Application 13.1a Moving Average Method

F5

D

4D

3D

2

3

790 810 740

3

780

780 customer arrivals

F6

D

5 D

4 D

3

3

805 790 810

3 801.667



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Weighted Moving Averages

Weighted moving average method: Atime-series method in which each historicaldemand in the average can have its own

weight; the sum of the weights equals 1.0.

Ft+1 = W1Dt + W2Dt-1+ + WnDt-n+1


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Application 13.1b Weighted Moving Average

F5

W1D

4W

2D

3W

3D

2 0.50 790 0.30 810 0.20 740 786


F6

W1D

5W

2D

4W

3D

3 0.50 805 0.30 790 0.20 810 801.5



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Exponential Smoothing

Ft+1 = (Demand this period) + (1)(Forecast calculated last period)= Dt + (1)Ft

Or an equivalent equation: Ft+1 = 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 forecastingmethod because of its simplicity and the small amount of data neededto support it.

Exponential smoothing method: A sophisticatedweighted moving average method that calculatesthe average of a time series by giving recent

demands more weight than earlier demands.


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Reconsider the medical clinic patientarrival data. It is now the end of week 3.a. Using = 0.10, calculate theexponential smoothing forecast for

week 4. Ft+1 = Dt+ (1-)FtF4 = 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

Exponential SmoothingExample 13.3

Week Arrivals1 400

2 380

3 411

4 415

5 ?


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Application 13.1c Exponential Smoothing

Ft1 Ft Dt Ft 783 0.20 790 783 784.4


Ft1 Ft Dt Ft 784.4 0.20 805 784.4 788.52



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Trend-AdjustedExponential Smoothing

A trend in a time series is a systematic increase ordecrease in the average of the series over time. Where a significant trend is present, exponential smoothing

approaches must be modified; otherwise, the forecasts tendto 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.


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Ft+1 = At +Tt

whereAt= Dt+ (1)(At-1+ Tt-1)

Tt= (AtAt-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 trendDt= demand for period tFt+1 = forecast for period t+ 1

Trend-Adjusted ExponentialSmoothing Formula


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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= (AtAt-1) + (1)Tt-1T1 = 0.20(30.2 2.8) + 0.80(3) = 2.8

Ft+1 =At+ Tt

F2 = 30.2 + 2.8 = 33 blood tests

Trend-AdjustedExponential Smoothing

Example 13.4 Medanalysis ran an average of 28blood tests per week during the past four weeks. The trendover 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.


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| | | | | | | | | | | | | | |0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

80

70

60

50

40

30

Patientarrivals

Week

Actual bloodtest requests

Trend-adjustedforecast

Example 13.4 MedanalysisTrend-Adjusted Exponential Smoothing

F t f M d l i U i th


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Forecast for Medanalysis Using theTrend-Adjusted Exponential Smoothing Model


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Application 13.2

The forecaster for Canine Gourmet dog breathfresheners estimated (in March) the salesaverage 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?


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Application 13.2 Solution

thousand

thousand

To make forecasts for periods beyondthe next period, multiply the trendestimate by the numberof additional periods, and add the result to the

current average


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Seasonal Patterns

Seasonal patterns are regularly repeated upwardor downward movements in demand measured inperiods 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 belongingto the same season.

Multiplicative seasonal method is a method wherebyseasonal factors are multiplied by an estimate of averagedemand to arrive at a seasonal forecast.

Additive seasonal method is a method wherebyseasonal forecasts are generated by adding a constant tothe estimate of the average demand per season.


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Multiplicative SeasonalMethod

Step 1: For each year, calculate the averagedemand for each season by dividing annualdemand by the number of seasons per year.

Step 2: For each year, divide the actual demand foreach season by the average demand per season,

resulting in a seasonal indexfor each season of theyear, indicating the level of demand relative to theaverage demand.

Step 3: Calculate the average seasonal index foreach season using the results from Step 2. Add the

seasonal indices for each season and divide by thenumber of years of data.

Step 4: Calculate each seasons forecast for nextyear.


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Quarter Year 1 Year 2 Year 3 Year 4

1 45 70 100 1002 335 370 585 7253 520 590 830 1160

4 100 170 285 215

Total 1000 1200 1800 2200

Using the Multiplicative

Seasonal Method

Example 13.5: Stanley Steemer, a carpet cleaning companyneeds a quarterly forecast of the number of customers expected nextyear. The business is seasonal, with a peak in the third quarter and atrough 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 forecastdemand is found by extending that trend, and projecting an annual demand in year 5 of 2,200

+ 400 = 2,600 customers.


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Example 13.5 OM Explorer Solution


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Application 13.3 Multiplicative Seasonal Method

1320/4 quarters = 330

C i f


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Comparison ofSeasonal Patterns

Multiplicative pattern Additive pattern


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Measures ofForecast Error

Cumulative sum of forecast errors (CFE): Ameasurement of the total forecast error thatassesses the bias in a forecast.

Mean squared error (MSE): A measurement of thedispersion of forecast errors.

Mean absolute deviation (MAD): A measurement

of the dispersion of forecast errors.

Standard deviation (): A measurementof the dispersion of forecast errors.

Et2n

MSE =

MAD=|Et|n

= (Et E)2n 1

CFE = Et


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MAPE =[|Et | / Dt ](100)

n

Measures ofForecast Error

Mean absolute percent error (MAPE): Ameasurement that relates the forecast error to thelevel of demand and is useful for putting forecastperformance in the proper perspective.

Tracking signal: A measure that indicates

whether a method of forecasting is accuratelypredicting actual changes in demand.

Tracking signal =CFE

MAD


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AbsoluteError Absolute Percent

Month, Demand, Forecast, Error, Squared, Error, Error,t Dt Ft Et Et

2 |Et| (|Et|/Dt)(100)

1 200 225 -25 625 25 12.5%2 240 220 20 400 20 8.3

3 300 285 15 225 15 5.04 270 290 20 400 20 7.45 230 250 20 400 20 8.76 260 240 20 400 20 7.77 210 250 40 1600 40 19.08 275 240 35 1225 35 12.7

Total 15 5275 195 81.3%

Calculating Forecast ErrorExample 13.6

The following table shows the actual sales ofupholstered chairs for a furniture manufacturerandthe forecasts made for each of the last eight months.Calculate CFE, MSE, MAD, and MAPE for this product.


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Example 13.6 Forecast Error Measures

CFE = 15Cumulative forecast error (bias):

E = = 1.875 15

8Average forecast error (mean bias):

MSE = = 659.45275

8Mean squared error:

= 27.4Standard deviation:

MAD = = 24.4195

8Mean absolute deviation:

MAPE = = 10.2%81.3%

8Mean absolute percent error:

Tracking signal = = = -0.6148CFEMAD

-1524.4


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% of area of normal probability distribution within control limits of the tracking signal

Control Limit Spread Equivalent Percentage of Area(number of MAD) Number of within Control Limits

57.6276.98

89.0495.4498.3699.4899.86

0.80 1.20

1.60 2.00 2.40 2.80 3.20

1.0 1.5

2.0 2.5 3.0 3.5 4.0

Forecast Error Ranges

Forecasts stated as a single value can be less useful because theydo not indicate the range of likely errors. A better approach can beto provide the manager with a forecasted value and an error range.


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Tracking signal = CFEMAD

+2.0

+1.5

+1.0

+0.5

0

0.5

1.0

1.5

| | | | |0 5 10 15 20 25

Observation number

Tra

ckingsignal

Control limit

Control limit

Out of control

Computer Support

Computer support, such as OM Explorer, makes error calculationseasy when evaluating how well forecasting models fit with past data.

OM S l O f M di l Cli i P i A i l


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OM Solver Output for Medical Clinic Patient Arrivals


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Results SheetMoving Average

Forecast for 7/17/06

R l Sh


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Results SheetWeighted Moving Average



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Results SheetExponential Smoothing


Results Sheet


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Results SheetTrend-Adjusted

Exponential Smoothing

Forecast for 7/17/06Forecast for 7/24/06Forecast for 7/31/06

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

C it i f S l ti


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Criteria for SelectingTime-Series Methods

Forecast error measures provide important information forchoosing the best forecasting method for a service or product.

They also guide managers in selecting the best values for theparameters needed for the method:

n for the moving average method, the weights for the weightedmoving average method, and for exponential smoothing.

The criteria to use in making forecast method and parameterchoices include

1. minimizing bias

2. minimizing MAPE, MAD, or MSE

3. meeting managerial expectations of changes in thecomponents of demand

4. minimizing the forecast error last period


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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 methodsor different data or both.

Focus forecasting: A method of forecasting that selects thebest 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.


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Forecasting as a Process

The forecast process itself, typically done on amonthly basis, consists of structured steps. Theyoften are facilitated by someone who might be calleda demand manager, forecast analyst, or

demand/supply planner.

Some Principles for the Forecasting Process


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Some Principles for the Forecasting Process Better processes yield better forecasts.

Demand forecasting is being done in virtually every company.

The challenge is to do it better than the competition. Better forecasts result in better customer service and lower

costs, as well as better relationships with suppliers andcustomers.

The forecast can and must make sense based on the bigpicture, economic outlook, market share, and so on.

The best way to improve forecast accuracy is to focus onreducing forecast error.

Bias is the worst kind of forecast error; strive for zero bias.

Whenever possible, forecast at higher, aggregate levels.Forecast in detail only where necessary.

Far more can be gained by people collaborating andcommunicating well than by using the most advanced

forecasting technique or model.

D Ai Q lit


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Denver Air-QualityDiscussion Question 1

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Forecasting Lecture2