169
These values for the exchange constant are based on engineering
criteria. More difficult to assess are those based on perceived value.
That for the performance/cost tradeoff for cars is an example. To
the enthusiast, a car that is able to accelerate rapidly is alluring. He
(or she) is prepared to pay more to go from 0 mph to 60 mph in 5
seconds than to wait around for 10 seconds. Figure 5.16 shows just
how much. It is a tradeoff plot of 0–60 acceleration time tâ against
all-inclusive running cost per mile, C r (the total of fuel, depreciation,
insurance, etc.), for about 2500 cars. Dominated solutions, some
labeled, lie far from the tradeoff surface. Nondominated solutions,
some of these, too, labeled, lie on or near it. They are the ones with
the most attractive combinations of acceleration and running cost.
To refine the selection further, it is necessary to assign a value to
acceleration. Suppose that the car will be driven 10,000 miles per
year. Then the penalty function describing the way the tradeoff
between acceleration and annual running cost takes the form:
Z
C
t
r
a
=
+
10 000
,
α
(5.10)
Here α describes the (perceived) value of acceleration. Two penalty
lines are shown, both tangent to the tradeoff surface. The first is for
a value of α of $500/sec. The second is for a value of α = $10,000/
Figure 5.16
A tradeoff plot for selecting cars that have high
performance but are cheap to run. The best
choices are those that lie on or near the tradeoff
surface.
Cost of ownership ($ per mile)
0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
Acceleration: time 0-60 mph (s)
0
5
10
15
20
Subaru
Impreza 2.0
Mitsubishi
Evo RS
Mercedes-Benz
CLK 55 AMG
Mercedes-Benz
SLK 32
Volvo
S60 2.5T SE
Daihatsu
Sirion 1.3
Renault
Clio 1.4
Toyota
Land cruiser
Land Rover
Defender
Nissan
Patrol GR
Land Rover
Range Rover
BMW
735Li 4dr
Audi
A8 Quattro
Mitsubishi
Shogun 2.5
Smart
Fortwo
Volkswagen
Lupo
Fiat
Punto 1.2
Toyota
Yaris 1.4
Trade-off
surface
D o m in a t e d s o lu t io n s
N o n - d o m i n a t e d
s o l u t i o n s
α = $10,000/sec
α = $500/sec
Resolving Conflicting Objectives
These values for the exchange constant are based on engineering
criteria. More difficult to assess are those based on perceived value.
That for the performance/cost tradeoff for cars is an example. To
the enthusiast, a car that is able to accelerate rapidly is alluring. He
(or she) is prepared to pay more to go from 0 mph to 60 mph in 5
seconds than to wait around for 10 seconds. Figure 5.16 shows just
how much. It is a tradeoff plot of 0–60 acceleration time tâ against
all-inclusive running cost per mile, C r (the total of fuel, depreciation,
insurance, etc.), for about 2500 cars. Dominated solutions, some
labeled, lie far from the tradeoff surface. Nondominated solutions,
some of these, too, labeled, lie on or near it. They are the ones with
the most attractive combinations of acceleration and running cost.
To refine the selection further, it is necessary to assign a value to
acceleration. Suppose that the car will be driven 10,000 miles per
year. Then the penalty function describing the way the tradeoff
between acceleration and annual running cost takes the form:
Z
C
t
r
a
=
+
10 000
,
α
(5.10)
Here α describes the (perceived) value of acceleration. Two penalty
lines are shown, both tangent to the tradeoff surface. The first is for
a value of α of $500/sec. The second is for a value of α = $10,000/
Figure 5.16
A tradeoff plot for selecting cars that have high
performance but are cheap to run. The best
choices are those that lie on or near the tradeoff
surface.
Cost of ownership ($ per mile)
0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
Acceleration: time 0-60 mph (s)
0
5
10
15
20
Subaru
Impreza 2.0
Mitsubishi
Evo RS
Mercedes-Benz
CLK 55 AMG
Mercedes-Benz
SLK 32
Volvo
S60 2.5T SE
Daihatsu
Sirion 1.3
Renault
Clio 1.4
Toyota
Land cruiser
Land Rover
Defender
Nissan
Patrol GR
Land Rover
Range Rover
BMW
735Li 4dr
Audi
A8 Quattro
Mitsubishi
Shogun 2.5
Smart
Fortwo
Volkswagen
Lupo
Fiat
Punto 1.2
Toyota
Yaris 1.4
Trade-off
surface
D o m in a t e d s o lu t io n s
N o n - d o m i n a t e d
s o l u t i o n s
α = $10,000/sec
α = $500/sec
Resolving Conflicting Objectives