Another AHP Example for Forecasting Goal: Forecasting Next Quarter’s Consumption Pace Criteria:...

Another AHP Example for ForecastingAnother AHP Example for Forecasting

Goal: Forecasting Next Quarter’s Consumption Pace

Criteria: Consumer Confidence; Real Disposable Income; Credit Availability;

Interest Rates; Demand for Vehicles; Stock Market Wealth Effect; Katona Effect.

Criteria: Consumer Confidence; Real Disposable Income; Credit Availability;

Interest Rates; Demand for Vehicles; Stock Market Wealth Effect; Katona Effect.

Alternatives: Very Strong; Strong; Average; Weak; or Very Weak.Alternatives: Very Strong; Strong; Average; Weak; or Very Weak.

How Might This Model Look?How Might This Model Look?

AHP Model for Forecasting Consumer Spending One-Quarter Ahead

C on fidence Incom e C red it Availab ility In te rest R ates Veh icle D em and W ealth E ffect Katona E ffect

V ery S tron g S tron g M od era te W eak V ery W eak

Rea l C onsum er S pending Pace

How Would You Quantify the Alternatives?

Exploratory Data Analysis Techniques Could be Used.

One Method: Using a ten-year horizon, determine average growth

rate and deviation. From those statistics, determine outcome bounds.

Exploratory Data Analysis Techniques Could be Used.

One Method: Using a ten-year horizon, determine average growth

rate and deviation. From those statistics, determine outcome bounds.

EDA Summary Statistics REAL CONSUMER SPENDING GROWTH (Q/Q, AR) QUARTERLY Data for 42 periods from 1989Q1 to 1999Q2 AVERAGE GROWTH RATE (Geometric Average) = 2.9%Average ABSOLUTE DEVIATION AROUND MEAN = 1.7 pp.NORMAL UPPER BOUND = 3.8%NORMAL LOWER BOUND = 2.1%Maximum value = 6.7% in 1999Q1 Minimum value = -3.1% in 1991Q1

One Approach to Determine Bounds Based on Mean and DeviationVery Strong = Greater than (mean+dev) = Greater than 4.5%Strong = (mean+0.25*dev) to (mean+dev) = 3.4% to 4.5%Moderate = (mean-0.25*dev) to (mean+0.25*dev) = 2.6% to 3.3%Weak = (mean-dev) to (mean-0.25*dev) = 1.2% to 2.5%Very Weak = Less than (mean-dev) = Less Than 1.2%

Example for Real Consumption Growth

Very Strong = Greater than or equal to (mean+dev) = Greater than or equal to 4.6%

Strong = (mean+0.25*dev) to (mean+dev) = 3.4% to 4.5%

Moderate = (mean-0.25*dev) to (mean+0.25*dev) = 2.6% to 3.3%

Weak = (mean-dev) to (mean-0.25*dev) = 1.2% to 2.5%

Very Weak = Less than (mean-dev) = Less Than 1.2%

Or, Use Midpoint ProjectionsVS = (6.7+4.6)/2 = 5.7%

S = 4.0%M = 2.9%W = 1.9%

VW = (-3.1+1.2)/2 = -1.0%

Or, Use Midpoint ProjectionsVS = (6.7+4.6)/2 = 5.7%

S = 4.0%M = 2.9%W = 1.9%

VW = (-3.1+1.2)/2 = -1.0%

Or, Run Model for High and Low Ranges

Scenario 1 Scenario 2

Risk of High Growth Risk of Low Growth

VS = 6.7% 4.6%

S = 4.5 3.4

M = 3.3 2.6

W = 2.5 1.2

VW = 1.1 -3.1

Or, Run Model for High and Low Ranges

Scenario 1 Scenario 2

Risk of High Growth Risk of Low Growth

VS = 6.7% 4.6%

S = 4.5 3.4

M = 3.3 2.6

W = 2.5 1.2

VW = 1.1 -3.1

How Would You Quantify the Alternatives (Growth Rates)

Using the Saaty 9-Point Relative Comparison Scale?

Question: Which Factor Has the Greater Potential Impact on Real

Consumer Spending Growth?

Question: Which Factor Has the Greater Potential Impact on Real

Consumer Spending Growth?

Setup Matrix of PairwiseRelative Comparisons

CC INC CRED RATE CAR WLTH KAT

Consumer Confidence (CC) 1.0 1/AA 1/BB 1/CC 1/DD 1/EE 1/FFIncome (INC) AA 1.0 1/GG 1/HH 1/II 1/JJ 1/KK Credit Availability (CRED) BB GG 1.0 1/LL 1/MM 1/NN 1/OO Interest Rates (inverted impact) (RATE) CC HH LL 1.0 1/PP 1/QQ 1/RR Demand for Vehicles (CAR) DD II MM PP 1.0 1/SS 1/TT Stock Market Wealth Effect (WLTH) EE JJ NN QQ SS 1.0 1/UU Katona Effect (inverted impact) (KAT) FF KK OO RR TT UU 1.0

CC INC CRED RATE CAR WLTH KAT

Consumer Confidence (CC) 1.0 1/AA 1/BB 1/CC 1/DD 1/EE 1/FFIncome (INC) AA 1.0 1/GG 1/HH 1/II 1/JJ 1/KK Credit Availability (CRED) BB GG 1.0 1/LL 1/MM 1/NN 1/OO Interest Rates (inverted impact) (RATE) CC HH LL 1.0 1/PP 1/QQ 1/RR Demand for Vehicles (CAR) DD II MM PP 1.0 1/SS 1/TT Stock Market Wealth Effect (WLTH) EE JJ NN QQ SS 1.0 1/UU Katona Effect (inverted impact) (KAT) FF KK OO RR TT UU 1.0

Saaty Scale =Saaty Scale =

Setup Matrix of PairwiseRelative Comparisons For Alternatives

Saaty Scale =Saaty Scale =

Array the Comparisons

This does not have to be the 9-point scale.This does not have to be the 9-point scale.

Rescaled and

Rounded to Nearest

Integer.

Rescaled and

Rounded to Nearest

Integer.

This is one method to understand the process. Saaty, however, would suggest that it is not necessary and may be confusing to add the initial step -- if you do not know how to compare the

“very strong” and “weak” implications, for example, he suggests that you set them equal.

This is one method to understand the process. Saaty, however, would suggest that it is not necessary and may be confusing to add the initial step -- if you do not know how to compare the

“very strong” and “weak” implications, for example, he suggests that you set them equal.

Q&A about Pairwise Comparisons

VS S M W VW Very Strong (VS) 1.0 1/AA 1/BB 1/CC 1/DD Strong (S) AA 1.0 1/GG 1/HH 1/II Moderate (M) BB GG 1.0 1/LL 1/MM Weak (W) CC HH LL 1.0 1/PP Very Weak (VW) DD II MM PP 1.0

Question: How do you interpret the cells in the matrix?

Answer: While it may seem strange to compare, say, the “Very Strong” to the “Weak” criterion, this is precisely

what Saaty did in his forecasting application for real growth, which we discussed earlier. But the question that

you should ask is, “which outcome is more likely?”

Answer: While it may seem strange to compare, say, the “Very Strong” to the “Weak” criterion, this is precisely

what Saaty did in his forecasting application for real growth, which we discussed earlier. But the question that

you should ask is, “which outcome is more likely?”

Factor Impact on ObjectiveFactor Impact on Objective

Answer: For example, the “factor rating” Very Strong (VS) compared to the “factor rating” of Weak is given a relative weight 1/CC, which alternatively means that the factor rating Weak (W) compared to the factor of Very

Strong is the inverse or CC.

Answer: For example, the “factor rating” Very Strong (VS) compared to the “factor rating” of Weak is given a relative weight 1/CC, which alternatively means that the factor rating Weak (W) compared to the factor of Very

Strong is the inverse or CC.

Answer: So, for example, if you think that the factor intensity is “Strong” (5) for, say income, relative to its

impact on consumption and the factor rating for “weak” income is 2, then the cell entry is “5/2”. Do not confuse the rating scale with the magnitude categories in the forecast

objective.

Answer: So, for example, if you think that the factor intensity is “Strong” (5) for, say income, relative to its

impact on consumption and the factor rating for “weak” income is 2, then the cell entry is “5/2”. Do not confuse the rating scale with the magnitude categories in the forecast

objective.

Answer: Therefore, pairwise-comparison cell (VS,W) or 1/CC is 5/2. Alternatively, the cell (W, VS), which is CC is

2/5, which simply suggests that a very strong gain in income will have a larger impact of strong consumption

than a weak income gain.

Answer: Therefore, pairwise-comparison cell (VS,W) or 1/CC is 5/2. Alternatively, the cell (W, VS), which is CC is

2/5, which simply suggests that a very strong gain in income will have a larger impact of strong consumption

than a weak income gain.

Answer: The numbers in the Saaty scale are independent of the measurement units used. If you enter 2, you mean the larger factor has two times the impact as the smaller

factor.

Answer: The numbers in the Saaty scale are independent of the measurement units used. If you enter 2, you mean the larger factor has two times the impact as the smaller

factor.

Q&A about Pairwise ComparisonsQuestion: What if we believe that all choices in the

matrix should have the same impact on the objective?

Answer: That’s fine and the matrix can be collapsed.

Question: What if we believe that all choices in the matrix should have the same impact on the objective?

Answer: That’s fine and the matrix can be collapsed.

VS S M W VW WEIGHT Very Strong (VS) 1.0 1/1 1/1 1/1 1/1 = 0.20 Strong (S) 1 1.0 1/1 1/1 1/1 = 0.20 Moderate (M) 1 1 1.0 1/1 1/1

= 0.20Weak (W) 1 1 1 1.0 1/1 = 0.20 Very Weak (VW) 1 1 1 1 1.0 = 0.20

VS S M W VW WEIGHT Very Strong (VS) 1.0 1/1 1/1 1/1 1/1 = 0.20 Strong (S) 1 1.0 1/1 1/1 1/1 = 0.20 Moderate (M) 1 1 1.0 1/1 1/1

= 0.20Weak (W) 1 1 1 1.0 1/1 = 0.20 Very Weak (VW) 1 1 1 1 1.0 = 0.20

Example Where the Evaluation of the Factor Intensity is 1 for all comparisons.

Q&A about Pairwise ComparisonsQuestion: What if a factor that typically has a positive impact on the objective will be a negative factor during

the horizon of the problem?

Answer: That should be reflected in the weights. For example, if income is declining, then you might give it a

strong weight for a “weak” reading.

Question: What if a factor that typically has a positive impact on the objective will be a negative factor during

the horizon of the problem?

Answer: That should be reflected in the weights. For example, if income is declining, then you might give it a

strong weight for a “weak” reading.

Example for Determining Weights for Declining Income on Consumption

Q&A about Pairwise ComparisonsQuestion: What if you want an absolute scale instead of

this relative comparison?

Answer: There are various techniques that you can use to develop a quantitative scale. Here is one (known as

the Holmes Method): Calculate the correlation (or R2 is better) between a very strong change in the factor (such as, income) with a very strong change in consumption.

Then do the same for a strong change change in the factor with a very strong change in consumption. Use

those correlation coefficients to assess the absolute impact. Be careful of timing (leads and lags)

relationships.

Question: What if you want an absolute scale instead of this relative comparison?

Answer: There are various techniques that you can use to develop a quantitative scale. Here is one (known as

the Holmes Method): Calculate the correlation (or R2 is better) between a very strong change in the factor (such as, income) with a very strong change in consumption.

Then do the same for a strong change change in the factor with a very strong change in consumption. Use

those correlation coefficients to assess the absolute impact. Be careful of timing (leads and lags)

relationships.

Q&A about Pairwise ComparisonsAnswer (Continued): Although this is tedious, EVIEWS can do this easily with a conditional statement. You can

also do that in EXCEL, but you must calculate the correlation only using values that meet the condition -- say, real consumption growth greater than 4.5% and

real disposable income growth greater than 6.6%(geometric mean plus 1 deviation, 1989-99) -- VERY STRONG INCOME GROWTH vs. VERY STRONG

CONSUMPTION GROWTH. Similarly that would be done for STRONG INCOME GROWTH (geometric mean plus .25* deviation, which is 4.1%, to 6.5%) vs.

VERY STRONG CONSUMPTION GROWTH and so on.

Answer (Continued): Although this is tedious, EVIEWS can do this easily with a conditional statement. You can

also do that in EXCEL, but you must calculate the correlation only using values that meet the condition -- say, real consumption growth greater than 4.5% and

real disposable income growth greater than 6.6%(geometric mean plus 1 deviation, 1989-99) -- VERY STRONG INCOME GROWTH vs. VERY STRONG

CONSUMPTION GROWTH. Similarly that would be done for STRONG INCOME GROWTH (geometric mean plus .25* deviation, which is 4.1%, to 6.5%) vs.

VERY STRONG CONSUMPTION GROWTH and so on.

Setup Matrix of Lower Pairwise Comparisons

Question: How Much Impact Does Consumer Confidence Have on Real Consumer Spending

Growth?

Question: How Much Impact Does Consumer Confidence Have on Real Consumer Spending

Growth?

This must be filled in for every alternative . . .This must be filled in for every alternative . . .

Finally, collect the individual equations into a spreadsheet.

Determine the Final Forecast Based on Mid-Point Range Estimates (or Some other

Criteria).

Determine the Final Forecast Based on Mid-Point Range Estimates (or Some other

Criteria).

ImpactWeights

Net Impact

See Next Slide for Additional BreakoutSee Next Slide for Additional Breakout

Consumer Spending Forecast =

Partial Impact of Confidence on Consumer Spending.

Consumer Spending IMPACT from CC = .031*CC

CC = 0.351*VS+0.173*S+0.106*M+0.150*W+0.220*VW

Consumer Spending IMPACT from CC = .031*CC

CC = 0.351*VS+0.173*S+0.106*M+0.150*W+0.220*VW

Limitations of AHPLimitations of AHP

1. Unicausal Modeling Only. It Does Not Incorporate Feedback Effects.

It Assumes the “Criteria” are Relatively Independent over the

Time Frame Forecasted.

2. Difficult or Impossible to Check Historical Accuracy.

1. Unicausal Modeling Only. It Does Not Incorporate Feedback Effects.

It Assumes the “Criteria” are Relatively Independent over the

Time Frame Forecasted.

2. Difficult or Impossible to Check Historical Accuracy.

Some Extensions of AHPSome Extensions of AHPNetwork Modeling with Feedback

Analytic Network Process (ANP)

Network Modeling with Feedback

Analytic Network Process (ANP)

Fast-Food Retail Industry ANP Model

Feedback Network with components having Inner and Outer Dependence among Their Elements

Feedback

Loop in a component indicates inner dependence of the elements in that component with respect to a

common property.

Arc from componentC4 to C2 indicates the

outer dependence of the elements in C2 on theelements in C4 with

respectto a common property.

Cluster Weights 1. Competition 2. Adverrtising 3. Quality 4. Other1. Competition 0.2146 0.2470 0.5000 0.18702. Adverrtising 0.5328 0.6223 0.0000 0.13073. Quality 0.0656 0.0000 0.0000 0.50004. Other 0.1870 0.1307 0.5000 0.1984

Fast-Food Retail Industry Model

Priority Weightings

Burger King White Collar Blue Collar Student Family PrioritiesWhite collar 1 4 5 1 / 3 0.299Blue collar 1 / 4 1 4 1 / 3 0.138Student 1 / 5 1 / 4 1 1/ 7 0.051Family 3 3 7 1 0.512

Pairwise Judgments of the Customer Group for Burger King

Local: Menu Cleanliness

Speed Service Location Price Reputation

TakeOut

Portion Taste Nutrition

Frequency

Promotion

Creativity

Wendy’s BurgerKing

McDon-ald’s

Menu Item 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.1930 0.0000 0.0000 0.0000 0.0000 0.3110 0.1670 0.1350 0.1570 0.0510 0.1590Cleanliness 0.6370 0.0000 0.0000 0.5190 0.0000 0.0000 0.2390 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.2760 0.1100 0.3330Speed 0.1940 0.7500 0.0000 0.2850 0.0000 0.0000 0.0830 0.2900 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0640 0.1400 0.0480Service 0.0000 0.0780 0.1880 0.0000 0.0000 0.0000 0.0450 0.0550 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0650 0.1430 0.0240Location 0.0530 0.1710 0.0000 0.0980 0.0000 0.5000 0.2640 0.6550 0.0000 0.0000 0.0000 0.1960 0.0000 0.7100 0.1420 0.2240 0.1070Price 0.1170 0.0000 0.0000 0.0000 0.0000 0.0000 0.0620 0.0000 0.8570 0.0000 0.0000 0.0000 0.8330 0.0000 0.0300 0.2390 0.0330Reputation 0.0000 0.0000 0.0810 0.0980 0.0000 0.0000 0.0570 0.0000 0.0000 0.0000 0.0000 0.4930 0.0000 0.1550 0.2070 0.0420 0.2230Take-Out 0.0000 0.0000 0.7310 0.0000 0.0000 0.5000 0.0570 0.0000 0.1430 0.0000 0.0000 0.0000 0.0000 0.0000 0.0590 0.0510 0.0740Portion 0.2290 0.0000 0.0000 0.0000 0.0000 0.8330 0.2800 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0940 0.6490 0.5280Taste 0.6960 0.0000 0.0000 0.0000 0.0000 0.0000 0.6270 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.2800 0.0720 0.1400Nutrition 0.0750 0.0000 0.0000 0.0000 0.0000 0.1670 0.0940 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.6270 0.2790 0.3320Frequency 0.7500 0.0000 0.0000 0.0000 0.0000 0.1670 0.5500 0.0000 0.0000 0.0000 0.0000 0.0000 0.6670 0.8750 0.6490 0.7090 0.6610Promotion 0.1710 0.0000 0.0000 0.0000 0.0000 0.8330 0.3680 0.0000 0.0000 0.0000 0.0000 0.5000 0.0000 0.1250 0.0720 0.1130 0.1310Creativity 0.0780 0.0000 0.0000 0.0000 0.0000 0.0000 0.0820 0.0000 0.0000 0.0000 0.0000 0.5000 0.3330 0.0000 0.2790 0.1790 0.2080Wendy's 0.3110 0.5000 0.0990 0.5280 0.0950 0.0950 0.1010 0.1960 0.2760 0.6050 0.5940 0.0880 0.0880 0.1170 0.0000 0.1670 0.2000Burger King 0.1960 0.2500 0.3640 0.1400 0.2500 0.2500 0.2260 0.3110 0.1280 0.1050 0.1570 0.1950 0.1950 0.2680 0.2500 0.0000 0.8000McDonald’s 0.4930 0.2500 0.5370 0.3330 0.6550 0.6550 0.6740 0.4940 0.5950 0.2910 0.2490 0.7170 0.7170 0.6140 0.7500 0.8330 0.0000

Hamburger Model Supermatrix

Cluster: Other Quality Advertising CompetitionOther 0.198 0.500 0.131 0.187Quality 0.066 0.000 0.000 0.066Advertising 0.607 0.000 0.622 0.533Competition 0.129 0.500 0.247 0.215

Cluster Priorities Matrix

AdComp

Other Quality CompetitionAdvertising

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