4 - Decisions Involving Multiple Objectives MCDA- Chapter 3

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n Ivi 9 mu pi :8

....

DECISIONS INVOLVING MULTIPLE OBJECTIVES: SMART

AN OVERVIEW OF THE ANALYSIS

below:

Location of office

Addison 8ilton Village Carlisle Walk Denver Street Elton Street Filton Village Gorton

(A) (8) (C) (D) (E) (F) (G)

Annual rent ($)

30000 15000 5000 12000 30000 15000 10000

to 6.

as possible, he would also Addison is in a

but it is to rent. lt is staff to work in. In


tree can be

CONSTRUCTING A VALUE TREE

Rent Electricity Cleaning Closeness Visibility Image Size Comlort Car to customers parking

3.1 A value tree for the office location DroDlem

36 DECISIONS INVOlVING MUlTIPlE OBJECTIVES: SMART

whether it is an accurate and 2 sug-

that are concern to

a

MEASURING HOW WELL THE OPTIONS PERFORM ON EACH ATIRIBUTE

tree went

Table 3.1 Costs associated with the seven offices

Annual Annual

OHica Annual rant ($) costs ($) costs ($) Total cost

30000 3000 2000 35000 Bilton 15000 2000 800 17800 Carlsle Walk 5000 1 000 700 6700 Denver Street 12000 1 000 1 100 14100 Elton 30000 2500 2300 34800 Filton Village 15000 1 000 2600 18600 Gorton 10000 1 100 900 12000

MEASURING HOW WELL THE OPTIONS PERFORM ON EACH ATIRIBUTE

3.2 A vaJue scale for office

Value 100 I---L~~~~~

90-----~_E~lwto~nLS~t~re~e~t~

80

70-~--~JF~ilwto~n~V~illilla~e~

60

50

40

30~~--t=fD~env~e~r}S~t~re~eitJ 20 1-~~:2IU::>g:

101-~~~~~~ O L_-r-r.;;;r~W;k1

as an increase


Table 3.2 ~ Values and

Attribute

Closeness 32 26 23

Size 10 Comfort 6

3

Benefits

A B e

100 20 80 60 80 70

100 10 o 75 30 o o 100 10

90 30 100

80.8 39.4 47.4

can

strength VLU'-~O is shown below:

Addison Bilton Village Carlisle Walk Oenver Street Elton Street Filton Village Gorton

(A) (B) (C) (O) (E) (F)

Office

D

70 50 30 55 30 90

52.3

Floor area

1000 550 400 800

1500 400 700

in area froID 500 to 1000

an increase aUractive. To

E

40 60 90

100 60 70

64.8

on aa-lOO we can r>v,'"""",,,, as follows.

F G

o 60 o 100

70 20 o 50

80 50 o 80

20.9 60.2

MEASURING HOW WELL THE OPTIONS PERFORM ON EACH ATTRIBUTE 41

The owner judges that, the it is. largest Street, an area t so we can 1500 a value of 100. In

v(1500) = lOO, where v(1500) means Walk and FiIton Village) both

the office areas that faH between rptprt'pt! areas. We could ask the owner to rate the areas

under consideration the methods of the section. beca use areas involving awkward numbers are involved, it be easier to what 1S known as a methods can function, but one of the most widely 1S

requires owner to identify an office area halfway between the preferred are a (400 and the most area (1500 fe). Note area does not necessarily have to to of one of lnitially, owner suggests that the midpoint area would that an 400 to 1000 is just as aUractive as an increase 1000 to 1500 sorne he rejects this increases from smaller areas will, he reasons, reduce so be much more attrac-tive than increases areas, which would only lead to minor

"H,D1"C\,rf other candidates for the midpoint position (for as Finally, he that 700

identified the midpoint the to the 'quarter-points'. first of these will be the area that a value between the least area (400 and the midpoint area (700 fe). He decides that is 500 , so v(500) = Similarly, we ask him to identify an area has a value halfway between the midpoint area (700 fe) the best area (1500 fe). He judges this to be 1000 f which implies that v(1000) = We now have the for five fIoor areas, and this enables us to plot the function for office is shown in 3.3. value function can now be used to estimate

the actual areas of offices consideration. example, the Bilton Village office has an area 550 the curve suggests that the area is about

A applied to the 'closeness to by the variable 'distance fram town , and the

value function is shown in Note that the the distance from the town center, the lower the value will curve also suggests a move fram O to 2 miles fram the town center is more damagng to business than a move fram 6 to 8 values identified for the seven in terms

to are shown in

3.3


100

75 --- - - ---

(j) :; ~ 50 - -

Oflice floor area

a value function for office floor area

100

75

(j) :; 50 (ti >

25

00 ----L 2 4 6 Distance Irom town center (miles)

8

3.4 - A value function for distance fmm customers

DETERMINING THE WEIGHTS OF THE ATIRIBUTES

can to

Floor area

X 400 y 402

to the would

Office Fioor area

X O Y 100 Weights 5

problems. see

Distance from customers

O miles 15 miles

as follows:

Distance from customers

100 O 1

100 500

( or swing) from in another


attributes

'closeness to this change has would next choose to move to and so on,

until all the owner' s are as follows:

(1) to customers

We can now assessed as foUows. location to the most

100. a swing from

most distant location customers some decides that swing in 'visibility' is

80(X) as as the swing in 'doseness to customers', so visibility is a weight of a swing from the worst 'image' to best is considered to

as important as a swing from worst to the best location 'doseness to customers', so s assgned a weight of 70. procedure is for all the other attributes, illustrates the

obtained sum to 310, and it is conventional to to 100 (this will later stages of the analysis to

is by dividing weight the sum of the weights multiplying by 100:

Attribute

Closeness to customers Visibility

Size Comfort

facilities

100 80 70 30 20

310

Normalized w"".n"'I"'" (to nearest whole number)

32 26 23 10 6 3

100

AGGREGATING THE BENEFITS USING THE ADDITIVE MODEL

100 Bes!

80 Bes!

O Worst

Derivation of is considered to be

to customers

Wors!

Bes!

Worst

For

1"'" Worst 1 Bes! Worst Best Wors! from the worst to the best location for worst to the best location for closeness

in the 'working the appropriate lower-level weights, so

Agg

for workng conditions is 9

model We now have (1) a measure how well on weights enable us to compare the values allocated to one allocated to the The next is to how well

combining the six value scores allocated to do this, we will assume the model is

this simply adding an weighted value scores to measure of its overall benefits. model is the most widely

46 DECISIONS INVOLVING MULTIPLE OBJECTIVES: SMART

Attribute Addison values Value x

to customers 100 32 3200 Visibility 60 26 1560

100 23 2300 Size 75 10 750 Comfort O 6 O

facilities 90 3 8080

TRADING BENEFITS AGAINST COSTS

100

A "-',

J!l "

'$ x E e (!)

xD J::J 50 e

SENSITIVITY ANALYSIS

100

90

Weight placed on turnover

3.7 - for on turnover

INVOLVING MULTIPLE OBJECTIVES: SMART

4 - Decisions Involving Multiple Objectives MCDA- Chapter 3

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