Chapter 13 (2)

© 2007 Pearson Education

Forecasting

Chapter 13Chapter 13


How Forecasting fits the Operations Management

Philosophy

Operations As a Competitive Weapon

Operations StrategyProject Management Process Strategy

Process AnalysisProcess Performance and Quality

Constraint ManagementProcess LayoutLean Systems

Supply Chain StrategyLocation

Inventory ManagementForecasting

Sales and Operations PlanningResource Planning

Scheduling


Forecasting at Unilever

Customer demand planning (CDP), which is critical to managing value chains, begins with accurate forecasts.

Unilever has a state-of-the-art CDP system that blends historical shipment data with promotional data and current order data.

Statistical forecasts are adjusted with planned promotion predictions.

Forecasts are frequently reviewed and adjusted with point of sale data.

This has enabled Unilever to reduce its inventory and improved its customer service.


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 of the series over time.

c. Seasonal. A repeatable pattern of increases or decreases in demand, 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.


Demand Patterns

Horizontal Trend

Seasonal Cyclical


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.

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

© 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 production scheduling

Decision

Area

• Total sales• Total sales• Groups or families

of products or services

• Individual products or services

Forecast Quality

Long Term(more than 2 years)

Medium Term(3 months– 2 years)

Short Term(0–3 months)

Application

Time Horizon


Judgment Methods

Sales force estimates: The forecasts that are compiled from estimates of future demands made periodically by members of a company’s 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: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.


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.


Dep

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Independent variableX

YEstimate ofY fromregressionequation

Actualvalueof Y

Value of X usedto estimate Y

Deviation,or error

{

Causal Methods Linear Regression

Regressionequation:Y = a + bX

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


SalesSales AdvertisingAdvertisingMonthMonth (000 units)(000 units) (000 $)(000 $)

11 264264 2.52.522 116116 1.31.333 165165 1.41.444 101101 1.01.055 209209 2.02.0

a = – 8.135b = 109.229Xr = 0.98r2 = 0.96syx= 15.603

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.

Linear Regression Example 13.1

We use the computer to determine the best values of a, b, the correlation coefficient (r), the coefficient of determination (r2), and the standard error of the estimate (syx).


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Y = – 8.135 + 109.229X

a = – 8.135b = 109.229Xr = 0.98r2 = 0.96syx= 15.603

Y = a + bX

Linear Regression Line for Example 13.1

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


The production scheduler can use this forecast of 183,016 units to determine the quantity of brass door hinges needed for month 6.

If there are 62,500 units in stock, then the requirement to be filled from production is 183,016 - 62,500 = 120,516 units.

Forecasting Demand for Example 13.1


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.

…


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 whereEt = forecast error for period t

Dt = actual demand for period t

Ft = forecast for period t


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:

PatientPatientWeekWeek ArrivalsArrivals

11 40040022 38038033 411411

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?

© 2007 Pearson EducationWeekWeek

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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.


Week Arrivals Average1 4002 3803 411 3974 415 4025 ?

Example 13.2 Solution continued

Forecast for week 5 is the average of the arrivals for weeks 2,3 and 4

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)

Forecast for week 4 is the average of the arrivals for weeks 1,2 and 3

FF44 = = 411 + 380 + 400411 + 380 + 40033

a.

c. b.


Comparison of 3- and 6-Week MA Forecasts

Week

Pat

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Actual patient arrivals

3-week moving average forecast

6-week moving average forecast


Application 13.1

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


Application 13.1a Moving Average Method

F5 D4 D3 D2

3790 810 740

3780

780 customer arrivals

F6 D5 D4 D3

3805 790 810

3801.667



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.

Ft+1 = W1Dt + W2Dt-1 + …+ WnDt-n+1


Application 13.1b Weighted Moving Average

F5 W1D4 W2D3 W3D2 0.50 790 0.30 810 0.20 740 786


F6 W1D5 W2D4 W3D3 0.50 805 0.30 790 0.20 810 801.5



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 1.0is a smoothing parameter with a value between 0 and 1.0Exponential smoothing is the most frequently used formal forecasting method because of its simplicity and the small amount of data needed to support it.

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.


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.

Ft+1 = 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

Exponential SmoothingExample 13.3

Week Arrivals1 4002 3803 4114 4155 ?


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



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.


Ft+1 = 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 trendDt = demand for period tFt+1 = forecast for period t + 1

Trend-Adjusted Exponential Smoothing Formula


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

Ft+1 = At + Tt

F2 = 30.2 + 2.8 = 33 blood tests

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

week’s demand was for 27 blood tests. We use = 0.20 and

= 0.20 to calculate the forecast for next week.


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Trend-adjusted Trend-adjusted forecastforecast

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 season’s forecast for next year.


QuarterQuarter Year 1Year 1 Year 2Year 2 Year 3Year 3 Year 4Year 4

11 4545 7070 100100 10010022 335335 370370 585585 72572533 520520 590590 830830 1160116044 100100 170170 285285 215215

TotalTotal 10001000 12001200 18001800 22002200

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

Multiplicative pattern Additive pattern


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.

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

Et2

nMSE =

MAD =|Et |n

== ((EEtt – E – E ))22

nn – 1– 1

CFE = Et


MAPE = MAPE = [[ ||EEt t | / | / Dt Dt ]](100)(100)

nn

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.

Tracking signal: A measure that indicates whether a method of forecasting is accurately predicting actual changes in demand.

Tracking signal = Tracking signal = CFECFE

MADMAD


Absolute Error 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 5.0 4 270 290 –20 400 20 7.4 5 230 250 –20 400 20 8.7 6 260 240 20 400 20 7.7 7 210 250 –40 1600 40 19.0 8 275 240 35 1225 35 12.7

Total –15 5275 195 81.3%

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

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 = = = -0.6148 CFEMAD

-1524.4


% 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

57.6276.9889.0495.4498.3699.4899.86

± 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 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.


Tracking signal = Tracking signal = CFECFEMADMAD

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Computer Support

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


OM Solver Output for Medical Clinic Patient Arrivals


Results SheetMoving Average

Forecast for 7/17/06


Results SheetWeighted Moving Average



Results SheetExponential Smoothing



Results SheetTrend-Adjusted

Exponential Smoothing

Forecast for 7/17/06 Forecast for 7/24/06Forecast for 7/31/06Forecast for 8/7/06Forecast for 8/14/06Forecast 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

1. minimizing bias

2. minimizing MAPE, MAD, or MSE

3. meeting managerial expectations of changes in the components of demand

4. 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.


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 and customers.

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

•The best way to improve forecast accuracy is to focus on reducing 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 and

communicating well than by using the most advanced forecasting technique or model.


Denver Air-Quality Discussion Question 1

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Chapter 13 (2)

Business

quantitative forecasts

pearson education guidelines

historical demand data

quantitative data

total demand

type of forecasting

technological forecasting

forecasts of sales revenue