4 - 1© 2014 pearson education, inc. forecasting powerpoint presentation to accompany heizer and...

4 - 1© 2014 Pearson Education, Inc.

Forecasting

PowerPoint presentation to accompany Heizer and Render Operations Management, Eleventh EditionPrinciples of Operations Management, Ninth Edition

PowerPoint slides by Jeff Heyl

44

© 2014 Pearson Education, Inc.


Outline

▶ What Is Forecasting?

▶ Seven Steps in the Forecasting System

▶ Forecasting Approaches▶ Time-Series Forecasting

▶ Associative Forecasting Methods: Regression and Correlation Analysis

▶ Accuracy of Forecasts


WHAT IS FORECASTING?


What is Forecasting?► Process of predicting a

future event

► Underlying basis of all business decisions► Production

► Inventory

► Personnel

► Facilities

??


1. Short-range forecast► Up to 1 year, generally less than 3 months

► Purchasing, job scheduling, workforce levels, job assignments, production levels

2. Medium-range forecast► 3 months to 3 years

► Sales and production planning, budgeting

3. Long-range forecast► 3+ years

► New product planning, facility location, research and development

Forecasting Time Horizons

Comprehensive

Accurate


Distinguishing Differences

1. Medium/long range forecasts deal with more comprehensive issues and support management decisions regarding planning and products, plants and processes

2. Short-term forecasting usually employs different methodologies than longer-term forecasting

3. Short-term forecasts tend to be more accurate than longer-term forecasts


Demand PatternsQ

uan

tity

Time

(a) Stable pattern: Data cluster about a horizontal line


Demand PatternsQ

uan

tity

Time

(b) Trend: Data consistently increase or decrease


Demand PatternsQ

uan

tity

| | | | | | | | | | | |J F M A M J J A S O N D

Months

(c) Seasonal: Data consistently show regular up-and-down movements in a time series that relate to recurring events such as weather or holidays

Year 1

Year 2


Seven Steps in Forecasting1. Determine the use of the forecast

2. Select the items to be forecasted

3. Determine the time horizon of the forecast

4. Select the forecasting model(s)

5. Gather the data needed to make the forecast

6. Make the forecast

7. Validate and implement results


The Realities!

► Forecasts are seldom perfect, unpredictable outside factors may impact the forecast

► Most techniques assume an underlying stability in the system

► Product family and aggregated forecasts are more accurate than individual product forecasts


FORECASTING APPROACHES


Forecasting Approaches

ForecastingMethods

Qualitative

Jury of executive opinion

Market surveyDelphi method

Sales force composite

Quantitative

Naïve approach

Average Technique

Time-seriesmodel

Associative forecasting method

Trend projection

Exponential smoothing

Simple moving average

Weighted moving average


Qualitative Forecasting Approach

► Used when situation is vague and little data exist► New products

► New technology

► Involves intuition, experience► e.g., forecasting sales on Internet

Qualitative Methods


▶Executive Opinions▶Involve small group of high-level managers

▶Group estimates demand by working together

▶Combine managerial experience with statistical models

▶Relatively quick

▶‘Group-think’ disadvantage: The view of one person may prevail



▶Market Survey▶Ask customers about purchasing plans

▶What consumers say, and what they actually do are often different

▶Surveys can be expensive and time-consuming

▶Low response rate to a mail survey

▶May be overly optimistic



▶Delphi method▶Iterative group process, continues until

consensus is reached

▶Responses are kept anonymous

▶Long-term forecast

▶Applied to a variety of situation, including forecast



▶Sales force Composite▶Sales staff are good source of information

because of their direct contact with consumer.

▶Each salesperson projects his or her sales

▶Combined at district and national levels

▶May be overly influenced by recent experiences

▶Tends to be overly optimistic




ForecastingMethods

Qualitative


Market surveyDelphi method


Quantitative

Naïve approach

Average Technique

Time-seriesmodel


Trend projection






► Used when situation is ‘stable’ and historical data exist► Existing products► Current technology

► Involves mathematical techniques► e.g., forecasting sales of color

televisions

Quantitative Methods


Time-series Forecasting

Time Market Demand1/1/2008 601/2/2008 501/3/2008 801/4/2008 70

1/11/2008 4201/18/2008 4001/25/2008 470

Not evenly spaced data

► Set of evenly spaced numerical data► Forecast based only on past values, no

other variables important► Assumes that factors influencing past and

present will continue influence in future



[Solution]: Yes, they do represent a time series since an observation was made each quarter for a period of six quarters or 1.5 years.

Year Quarter Period number Sales (yards)

2012 1 1 16,000

2 2 18,500

3 3 12,500

4 4 15,000

2013 1 5 13,500

2 6 17,500

Example 4.1: The table below shows the carpet sales in 2012 and the first half of 2013 at Hoppy Toppy in Addison, TX. Do the quarterly sales represent a time series? Why or why not?



▶Notation: t = Index of time period

At = Actual demand in period t, t = 1, 2, ...

Ft = Forecast for period t, t = 1, 2, ...

wt = Weight assigned to period t, t = 1, 2, …


Naive Approach

► Assumes demand in next period is the same as demand in most recent period► e.g., If January sales were 68, then

February sales will be 68

► Sometimes cost effective and efficient► Can be good starting point

Ft = At-1


Naive Approach Example 4.2: The table below shows the computers sales from 2007 to 2013. Apply the naïve approach to predict how many computers will be needed in 2014.

F8= A7 = 35,000

Year Time Period Sales

2007 1 25,000

2008 2 27,000

2009 3 30,000

2010 4 32,000

2011 5 28,000

2012 6 29,000

2013 7 35,000

2014 8 ?

the most recent period


Simple Moving Average (SMA)

▶Used if little or no trend

▶ The SMA forecast is equal to the average value of the observations in the most recent n periods, where n is the number of time periods involved and its value is determined by the decision maker

n

AAAF nt2t1t

t

Or,

© 2014 Pearson Education, Inc. 4 - 27

F8 = (A7 + A6 + A5) / 3 = (35,000 + 29,000 + 28,000) / 3 = 30,700

the 3 most recent years

Simple Moving Average (SMA)


2007 1 25,000

2008 2 27,000

2009 3 30,000

2010 4 32,000

2011 5 28,000

2012 6 29,000

2013 7 35,000

2014 8 ?

Example 4.3: Assuming that n=3, apply three-year moving average approach to predict how many computers will be needed in 2014.


Weighted Moving Average (WMA)

▶ Weights based on experience and intuition

▶ Older data less important: heavier weights are assigned to more recent observations, wt-1 wt-2 … wt-n.

nt2t1t

ntnt2t2t1t1tt w...ww

Aw...AwAwF


Or,


Weighted Moving Average (WMA)

the 4 most recent years


2007 1 25,000

2008 2 27,000

2009 3 30,000

2010 4 32,000

2011 5 28,000

2012 6 29,000

2013 7 35,000

2014 8 ?

Example 4.4: Assuming that n=4 and appropriate weights are 4, 3, 2 and 1, apply the WMA approach to predict how many computers will be needed in 2014

500,311234

1320002280003290004350008

F


Moving Average (SMA, WMA)▶ More time periods are involved, the smoother the forecasts

will be. So, the moving average approach is less sensitive to real changes in the data.


Moving Average (SMA, WMA)

▶Moving averages lag the actual value.

▶Moving averages require extensive records of past data.


Exponential Smoothing (ES)

New forecast = Last period’s forecast+ (Last period’s actual demand

– Last period’s forecast)

Ft = Ft – 1 + (At – 1 - Ft – 1)

where Ft = new forecast

Ft – 1 = previous period’s forecast

= smoothing (or weighting) constant (0 ≤ ≤ 1)

At – 1 = previous period’s actual demand

Example 4.5: In January, a car dealer predicted February demand for 142 Ford Mustangs. Actual February demand was 153 autos. Using a smoothing constant chosen by management of = 0.2, apply the ES approach to forecast March demand.

Previous forecast = 142

Previous actual = 153

= 0.2

Current forecast = Previous forecast + (Previous Actual – Previous forecast)= 142 + 0.2(153 - 142)= 144.2

Thus, the March demand forecast is rounded to 144.

Exponential Smoothing (ES)


EX 1 in classA dry cleaner uses exponential smoothing to forecast equipment usage at its main plant. August usage was forecasted to be 88 percent of capacity; actual usage was 89.6 percent of capacity. A smoothing constant of 0.1 is used. Prepare a forecast for September.


Exponential Smoothing (ES)▶ The naive forecast is a special case of the ES with = 1.

▶ Large values of are chosen when the underlying average is likely to change. Small values of are used when the underlying average is fairly stable.

▶ As increases, older values become less significant

Ex 2 in classSuppose the manager of an ice cream store is trying to forecast the pounds of ice cream that they will sell based on what they have sold in the past four days. Recent actual sales numbers are:

Day Sales (in lbs)Sunday 137.1Monday 123.6Tuesday 134.9Wednesday 160.0Thursday 140.4

1) What is a four-day moving average forecast of Friday’s demand?

2) Let’s assume the following weights. What is a four-day weighted moving average forecast of Friday’s demand?

3) Let’s say that actual sales for a given day totaled 115 pounds, while the forecast for that day was 110 pounds. With a smoothing constant of 0.1, what is the next day’s forecast?

Day Weight4 days ago 0.13 days ago 0.22 days ago 0.2Yesterday 0.5Total 1.0



ForecastingMethods

Qualitative


Consumer market surveyDelphi method


Quantitative

Naïve approach

Average Technique

Time-seriesmodel


Trend projection





Comparison

▶Averaging Techniques -- when the time series generally varies around an average.

▶Trend Projection Method -- when the time series generally varies around a linear trend (i.e., upward and downward).


Trend Projection

Upward Linear Trend Downward Linear Trend


Trend Projection

btay ˆ

Suppose that a linear trend is present in the time series. The main goal of trend projection analysis is searching for a linear equation that best describes the trend. The best-fit trend line may be represented by the following equation:

y = Computed value of the variable to be predicted (called the dependent variable)

t = Specified number of time periods (called the independent variable)

b = Slope of the trend line (or the rate of change in y for given changes in t)

22 tnt

ytnty

a = Intercept of the trend line at the vertical axis tby n = number of data points or observations


Year Period Demand

2003 1 74

2004 2 80

2005 3 82

2006 4 74

2007 5 90

2008 6 100

2009 7 86

2010 8 94

2011 9 112

2012 10 104

2013 11 110

Example 4.6: Data on the demand for JM's computers have been accumulated for 11 years and are shown in the following table:

(1) Plot the time-series data to determine the most appropriate forecasting approach

65

75

85

95

105

115

Demand (y)

2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013year (x)

An upward linear trend is present in the time series. The trend projection approach is the most appropriate forecasting method.


t y t2 ty

1 74

2 80

3 82

4 74

5 90

6 100

7 86

8 94

9 112

10 104

11 110

66 1006

1

4

9

16

25

36

49

64

81

100

121

506

74

160

246

296

450

600

602

752

1008

1040

1210

6438

(2) How many computers will be needed in each of the coming two years?

Sum

The best-fit trend line is y = 69.49 + 3.66t

2014: F12 = 69.49 + 3.66(12) = 113.41 or about 113 units

2015: F13 = 69.49 + 3.66(13) = 117.07 or about 117 units

66.3611506

45.916116438222

tnt

ytntyb

611

66

n

tt 45.91

11

1006

n

yy

49.69666.345.91 tbya


EX3 in class

Room registrations in the Toronto Towers Plaza Hotel have been recorded for the past 9 years. To project future occupancy, management would like to determine the mathematical trend of guest registration. This estimate will help the hotel determine whether future expansion will be needed. Given the following time-series data, develop a trend equation to forecast 2014 registrations. Room registrations are in the thousands:

Year 2005 2006 2007 2008 2009 2010 2011 2012 2013Registrations(in thousands)

17 16 16 21 20 20 23 25 24



ForecastingMethods

Qualitative


Consumer market surveyDelphi method


Quantitative

Naïve approach

Average Technique

Time-seriesmodel


Trend projection





Associative Forecasting

▶ Used when changes in one or more independent variables can be used to predict the changes in the dependent variable

▶Dependent variable

▶We wish to predict

▶Example: demand for doorknobs

▶ Independent variable

▶Affect the dependent variable and thereby “cause” the results observed in the past.

▶Example: advertising expenditures and new housing starts


▶ Home values may be related to such factors as home and property size, location, number of bedrooms, and number of bathrooms

▶Dependent variable: ▶ home values

▶Independent variables: ▶ home and property size

▶ location

▶ number of bedrooms

▶ number of bathrooms



Forecasting an outcome based on predictor variables using the least squares technique

y = a + bx

where y= computed value of the variable to be predicted (dependent variable)x= the independent variable though to predict the value of the dependent variable

22 xnx

yxnxyb

xbya



▶Coefficient of determination▶How strong is the linear relationship between the variables?

▶ 0 r2 1

▶The larger the r2 value is, the more valid the linear causal model would be.

▶Physical and medical sciences, r2 0.60

▶Social sciences, r2 0.25

2222

2

2

ynyxnx

yxnxyr



Example 4.7: Chicken Palace in Spokane, WA, periodically offers carryout five-piece chicken dinners at special prices. The following table summarizes the observations over the past six weeks:

(1) Plot the price against the sales to see if an associative model is appropriate

Price ($) # of dinners sold

2.70 760

3.50 510

2.00 980

4.20 250

3.10 620

4.05 480

0200400600800

10001200

0 1 2 3 4 5

Price ($)

Sal

es (

no

. o

f d

inn

ers)

There is a negative linear relationship between the price and the sales of the chicken dinner. As such, an associative model will be appropriate.


(2) Develop the associative model to predict future sales of the chicken dinner

x y x2 xy y2

2.70 760

3.50 510

2.00 980

4.20 250

3.10 620

4.05 480

19.55 3600Sum

258.36

55.19x

6006

600,3y

805.289

258.361925.67

600258.36713,102

22

xnx

yxnxyb

185.544,1258.3805.289600 xbya

The associative model is y = 1,544.185 – 289.805x

7.29

12.25

4

17.64

9.61

16.4025

67.1925

2052

1785

1960

1050

1922

1944

10,713

577,600

260,100

960,400

62,500

384,400

230,400

2,475,400


(3) Compute the coefficient of determination to assess the validity of model

93.0

6006400,475,2258.361925.67

600258.36713,1022

2

2222

2

2

ynyxnx

yxnxyr

As 0.93 > 0.25 (for social sciences), the associative model is valid.

x y x2 xy y2

2.70 760

3.50 510

2.00 980

4.20 250

3.10 620

4.05 480

19.55 3600Sum

7.29

12.25

4

17.64

9.61

16.4025

67.1925

2052

1785

1960

1050

1922

1944

10,713

577,600

260,100

960,400

62,500

384,400

230,400

2,475,400


(4) how many dinners can Chicken Palace expect to sell per week if the price is set at $3.90 each?

Y = 1,544.185 – 289.805X = 1,544.185 – 289.805(3.9) = 413.95 or about 414


EX4 in classHealthy Hamburgers has a chain of 6 stores in northern Illinois. Sales figures and profits for the stores are given in the following table. 1)Obtain the associative model and predict profit for a store assuming sales of $10 million.2)Determine the correlation coefficient and interpret it.

Sales, x(in $ millions)

Profits, y(in $ millions)

$6 $0.1316 0.2412 0.2020 0.4415 0.347 0.17


ACCURACY OF FORECAST


The objective is to obtain the most accurate forecast no matter the technique

We generally do this by selecting the model that gives us the lowest forecast error

Forecast error = Actual demand – Forecast value

= At – Ft

Accuracy of Forecasts


Common Measures of Error

Mean Absolute Deviation (MAD)

Mean Forecast Error (Bias)

n

Forecast - Actual

Bias

where n is the number of forecast errors involved

25

27

30

32

28

29

2

3

2

-4

1

6

10

2

3

2

4

1

6

18

Example 4.8: Given the demand data that follow, prepare a forecast by using Naïve approach, simple moving average approach and exponential approach. Compute Bias and MAD.

MAD = = 18/6 = 3 n

n

1 t

tt FA 67.1

6

10Bias

n

1 t

n

FA tt

YearTime Period

(t)Sales (At)

Forecast (Ft) et = At - Ft |et| = |At - Ft|

2007 1 25

2008 2 27

2009 3 30

2010 4 32

2011 5 28

2012 6 29

2013 7 35Sum

(1) Naïve approach


27.33

29.67

30

29.67

4.67

-1.67

-1

5.33

7.33

4.67

1.67

1

5.33

12.67

(2) Simple Moving Average (3-year SMA)

MAD = = 12.67/4 = 3.17 n

n

1 t

tt FA 83.1

4

33.7Bias

n

1 t

n

FA tt

YearTime Period

(t)Sales (At)


2007 1 25

2008 2 27

2009 3 30

2010 4 32

2011 5 28

2012 6 29

2013 7 35Sum


25

25

26.2

28.48

30.59

29.04

29

0

2

3.8

3.52

-2.59

-0.04

6

12.69

0

2

3.8

3.52

2.59

0.04

6

17.95

(3) Exponential Smoothing ( = 0.6, F1 = 25, F2 = 25)

MAD = = 17.95/7 = 2.56 n

n

1 t

tt FA 81.1

7

69.12Bias

n

1 t

n

FA tt

YearTime

Period (t)Sales (At)


2007 1 25

2008 2 27

2009 3 30

2010 4 32

2011 5 28

2012 6 29

2013 7 35Sum


▶ If Bias is used Naive approach

▶ If MAD is used Exponential smoothing approach

(4) Comparison

Naïve

Approach SMAExponential Smoothing

Bias 1.67 1.83 1.81

MAD 3 3.17 2.56


EX5 in classData collected on the annual promotional expenditure (in millions of dollars) of Fairface Cosmetics Company over the past seven years are shown in the following table:

1) Use the 2-year SMA method to develop a forecast of the promotional expenditure in each year up to 2013.

2) Repeat (1) by using the 3-year WMA method with weights of 0.5, 0.25, and 0.25.

3) Repeat (1) by using the ES method with α = 0.5 and the forecast for 2007 of $6 million.

4) Which of the three methods is most reliable on the basis of MAD?

5) Based on the findings in (4) above, provide a forecast of the promotional expenditure in 2014.

Year 2007 2008 2009 2010 2011 2012 2013Expenditure 10 8 7 9 12 14 11

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