Krajewski Chapter 13.ppt

© 2007 Pearson Education
Forecasting
Chapter 13

How Forecasting
fits the Operations Management
Philosophy
Operations As a Competitive
Weapon
Operations Strategy
Project Management Process Strategy
Process Analysis
Process Performance and Quality
Constraint Management
Process Layout
Lean Systems
Supply Chain Strategy
Location
Inventory Management
Forecasting
Sales and Operations Planning
Resource 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 of
Forecasting 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.

Demand Forecast Applications
• Causal
• Judgment
• Causal
• Judgment
• Time series
• Causal
• Judgment
Forecasting
Technique
• 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.

Dependent
variable
Independent variable
X
Y
Estimate of
Y from
regression
equation
Actual
value
of Y
Value of X used
to estimate Y
Deviation,
or error
{
Causal Methods
Linear Regression
Regression
equation:
Y = a + bX
Y = dependent variable
X = independent variable
a = Y-intercept of the line
b = slope of the line

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
a = – 8.135
b = 109.229X
r = 0.98
r2 = 0.96
syx= 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).

| | | |
1.0 1.5 2.0 2.5
Advertising (thousands of dollars)
300 —
250 —
200 —
150 —
100 —
50 —
Sales
(thousands
of
units)
Y = – 8.135 + 109.229X
a = – 8.135
b = 109.229X
r = 0.98
r2 = 0.96
syx= 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
where
Et = 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:
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?

Week
450 —
430 —
410 —
390 —
370 —
| | | | | |
0 5 10 15 20 25 30
Patient
arrivals
Actual patient
arrivals
Example 13.2
Solution
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 Average
1 400
2 380
3 411 397
4 415 402
5 ?
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
F4 =
411 + 380 + 400
3
a.
c.
b.

Comparison of
3- and 6-Week MA Forecasts
Week
Patient
Arrivals
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
3

790 810 740
3
 780
780 customer arrivals

F6 
D5  D4  D3
3

805 790 810
3
 801.667

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 1.0
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 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
Example 13.3
Week Arrivals
1 400
2 380
3 411
4 415
5 ?

Application 13.1c Exponential Smoothing

Ft1  Ft  Dt  Ft
  783 0.20 790 783
  784.4

Ft1  Ft  Dt  Ft
  784.4  0.20 805 784.4
  788.52

Trend-Adjusted
 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 trend
Dt = demand for period t
Ft+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
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.

| | | | | | | | | | | | | | |
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
80 —
70 —
60 —
50 —
40 —
30 —
Patient
arrivals
Week
Actual blood
test requests
Trend-adjusted
forecast
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.

Quarter Year 1 Year 2 Year 3 Year 4
1 45 70 100 100
2 335 370 585 725
3 520 590 830 1160
4 100 170 285 215
Total 1000 1200 1800 2200
Using the Multiplicative
Seasonal Method
Example 13.5: Stanley Steemer, a carpet cleaning 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.
Et
2
n
MSE =
MAD =
|Et |
n
 = (Et – E )2
n – 1
CFE = Et

MAPE =
[|Et | / Dt ](100)
n
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 =
CFE
MAD

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 = – 15
Cumulative forecast error (bias):
E = = – 1.875
– 15
8
Average forecast error (mean bias):
MSE = = 659.4
5275
8
Mean squared error:
 = 27.4
Standard deviation:
MAD = = 24.4
195
8
Mean absolute deviation:
MAPE = = 10.2%
81.3%
8
Mean absolute percent error:
Tracking signal = = = -0.6148
CFE
MAD
-15
24.4

% 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
57.62
76.98
89.04
95.44
98.36
99.48
99.86
± 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 =
CFE
MAD
+2.0 —
+1.5 —
+1.0 —
+0.5 —
0 —
–0.5 —
–1.0 —
–1.5 —
| | | | |
0 5 10 15 20 25
Observation number
Tracking
signal
Control limit
Control limit
Out of control
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 Sheet
Moving Average
Forecast for 7/17/06

Results Sheet
Weighted Moving Average

Results Sheet

Results Sheet
Trend-Adjusted
Forecast for 8/7/06

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
250 –
225 –
200 –
175 –
150 –
125 –
100 –
75 –
50 –
25 –
0 | | | | | | | | | | | | | |
22 25 28 31 3 6 9 12 15 18 21 14 27 30
Year 2
Year 1
July August
Date
Visibility
rating

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