Selection of Lightweighting Strategies for Use Across an
Automaker's Vehicle Fleet
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Citation
Montalbo, T. et al. “Selection of lightweighting strategies for use
across an automaker's vehicle fleet.” Sustainable Systems and
Technology, 2009. ISSST '09. IEEE International Symposium on.
2009. 1-6. © 2009 IEEE.
As Published
http://dx.doi.org/10.1109/ISSST.2009.5156785
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Institute of Electrical and Electronics Engineers
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Wed May 25 23:20:24 EDT 2016
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http://hdl.handle.net/1721.1/60270
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Detailed Terms
Selection of Lightweighting Strategies for Use
Across an Automaker’s Vehicle Fleet
Trisha Montalbo, Theresa M. Lee, Richard Roth, and Randolph E. Kirchain
Abstract—Vehicle lightweighting, or mass reduction, via
materials substitution is a common approach to improve fuel
economy. The many subsystems in a vehicle, choices of
materials, and manufacturing processes available, though, lead to
numerous paths to achieving the mass reduction and identifying
the best ones for an automaker to implement can be a challenge.
In this paper, that challenge is addressed through the
development of a selection model designed to inform the
lightweighting strategy decision for an automaker’s fleet. The
model, implemented with a genetic algorithm, identifies the
strategies that enable an automaker to optimize the net present
value of its cash flow, as well as to meet its CAFE obligations over
the coming years. A case study of various strategies implemented
in three vehicles over a three-year timeframe is used to
demonstrate application of the genetic algorithm selection model
and contrast it to an alternative period-by-period search
implementation.
Index
Terms—fuel
economy,
lightweighting, materials selection
genetic
algorithms,
I. INTRODUCTION
Lightweighting, or mass reduction, is an important design
strategy in vehicle development. By reducing vehicle mass,
designers can not only improve a vehicle’s performance or
fuel economy, but also offset the mass of additional vehicle
features, such as a hybrid powertrain, in order to maintain
performance.
Vehicles are typically lightweighted by
reducing part size, integrating multiple parts into a single unit,
or replacing heavier materials with lighter weight alternatives.
Materials substitution alone is associated with many options:
for instance, a designer may have to choose between
lightweighting the vehicle body, front end, closures, engine
cradle, or seats, and whether to use aluminum, magnesium,
composites, or high strength steel to achieve the weight
reduction.
With all the available strategies for lightweighting a vehicle
via materials substitution, identifying the preferred ones for
T. Montalbo is with the Department of Materials Science and Engineering
at the Massachusetts Institute of Technology, Cambridge, MA 02139 USA
(corresponding author phone: 617-253-6467; fax: 617-258-7471; e-mail:
trisha@mit.edu).
T. M. Lee is with General Motors, Warren, MI 48090 USA (e-mail:
theresa.m.lee@gm.com).
R. Roth is with the Materials Systems Laboratory at the Massachusetts
Institute of Technology, Cambridge, MA 02139 USA (e-mail:
rroth@mit.edu).
R. E. Kirchain is with the Department of Materials Science and
Engineering and the Engineering Systems Division at the Massachusetts
Institute of Technology, Cambridge, MA 02139 USA (e-mail:
kirchain@mit.edu).
implementation on the vehicle can be challenging. The
problem is only further complicated if the automaker desires
to select strategies for each vehicle model in its fleet, not only
because of the larger problem scale, but also because the
automaker may have multiple—and possibly conflicting—
objectives which it uses to identify the preferred strategies.
To address this challenge, we developed a technology
selection model to inform an automaker’s decision of which
lightweighting strategies to implement on each vehicle in its
fleet. The model assumes the automaker identifies strategies
based on which enable it to meet its fuel economy target as
dictated by the Corporate Average Fuel Economy (CAFE)
regulation and to optimize the net present value (NPV) of its
cash flow over some specified time horizon. Lightweighting a
vehicle affects both objectives. First, it allows an automaker
to improve that vehicle’s fuel economy, which in turn affects
the automaker’s CAFE number. Reducing vehicle mass also
affects the automaker’s cash flow through incurred costs (e.g.
additional manufacturing equipment) and altered revenue (e.g.
consumers are willing to pay more for improved fuel
economy). The period in which a strategy is implemented
makes a difference as well: the CAFE target can change over
time and implemented strategies that rely on emerging
technologies can see their costs evolve as automakers learn
and become more familiar with the manufacturing processes.
Thus, the proposed model takes multiple periods and
multiple vehicle models into account when identifying
preferred lightweighting strategies along with the period each
strategy is first implemented on its respective vehicle. For the
purposes of this paper, the strategies are limited to those that
achieve weight reduction via materials substitution, but in
reality, any lightweighting approach—or for that matter, any
technology that improves fuel economy—can be used in the
selection model.
II. MATERIALS AND TECHNOLOGY SELECTION
A review of literature shows that materials and technology
selection is a well-researched topic, partly because of its
importance in product design. The typical selection method
identifies the preferred material or technology for a particular
product given criteria or design parameters that are important
to the designer (e.g. [1] – [5]). The majority of these selection
methods are developed to identify a single best material or
technology for a single product. Selecting lightweighting
strategies across a fleet of vehicles however requires a multiproduct model that is capable of choosing a portfolio of
technologies for each product because any single vehicle
model can implement multiple lightweighting strategies and
any single strategy can be shared across models. Such an
approach is also needed because of CAFE, which imposes a
system-wide constraint by requiring that the fleet average fuel
economy meet a specified target. Only a few methods—for
example, the genetic algorithm proposed by Roth [6], and the
technology packages studied by DeCicco [7]—are capable of
choosing multiple technologies for implementation on a single
product. Likewise, only a few studies (e.g. Michalek [8])
include multiple products in their selection decisions.
Besides selecting lightweighting strategies for multiple
products, the model presented in this paper must also evaluate
the selection decision over multiple time periods, especially if
criteria or strategy parameters evolve over time. Most
methods found in the literature evaluate the selection decision
at a single point in time; one exception though is Gupta, who
uses a recourse method to re-evaluate the selection decision
after a single period [9]. Ultimately, no single method
matches what we require in a selection model.
III. SELECTION MODEL DESIGN
To inform the lightweighting strategy selection decision, we
designed a multi-period, multi-product model capable of
identifying the preferred strategies for each vehicle. The
model takes as inputs lightweighting strategies and their
respective attributes, vehicles in the automaker’s fleet, and the
number of periods in the timeframe of interest. Strategies and
implementation dates are then chosen based on which enable
the automaker to optimize NPV and meet its CAFE targets.
For this paper, the lightweighting strategies are limited to
those that use materials substitution to achieve reduction in
vehicle mass. A strategy represents a vehicle part or
subsystem and the manufacturing processes and lightweight
materials used to manufacture that part or subsystem.
Strategies can apply to the same subsystem but be
distinguished by the materials or processes that they use.
Also, the same strategy can be applied to different vehicles,
each vehicle representing a separate selection decision.
Implemented lightweighting strategies reduce vehicle mass,
which in turn affects vehicle fuel economy. These strategies
also alter the automaker’s cash flow because each is associated
with a cost of implementation, as well as added revenue
because a consumer is theoretically willing to pay more for the
improved vehicle. The selection model takes all this into
account when identifying the preferred strategies.
A. Multi-Period Selection
As mentioned above, a multi-period timeframe is
appropriate because both the CAFE target and lightweighting
strategy attributes can change over time. In the case of CAFE,
NHTSA (National Highway Traffic Safety Administration) is
planning to set interim standards for CAFE in preparation for
a required 35-mpg target by 2020 [10]. Strategy cost,
especially for strategies that rely on emerging technologies, is
likewise expected to evolve as manufacturers work their way
down the learning curve.
To handle the multi-period nature of the selection problem,
the model has the option to select additional strategies at the
beginning of each period. The selection decision is simplified
by requiring strategy continuity so that once a strategy is
implemented, it stays implemented and cannot be replaced—at
least within the timeframe of the model. While continuity is
not strictly true, replacing a strategy comes with a cost and
automakers cannot freely switch between options.
B. Objective Function
Evaluating a cash flow over multiple time periods means
that the model has to account for the devaluation of money
over time. This is accomplished through use of NPV for the
objective function. Preferred lightweighting strategies are
therefore those that optimize the NPV of an automaker over
the entire model timeframe, while still enabling CAFE
compliance.
1) Cash Flow Costs
The cash flow in each period of the model includes baseline
vehicle cost plus the cost of any implemented lightweighting
strategies. Revenue is generated by sales and consists of
baseline vehicle price plus any additional revenue the
strategies bring from improving fuel economy. Baseline
vehicle costs are assumed to be a simple unit cost per vehicle,
multiplied by the production volume of that vehicle in each
period and discounted appropriately.
Implemented strategy cost is somewhat more complex
because the cost is assumed to progress down the learning
curve. Also, the cost premium or cost difference of the
lightweighting strategy over that baseline is what matters
rather than the strategy cost itself because lightweighted
subsystems often replace a baseline counterpart.
Strategy cost is estimated as a unit variable cost multiplied
by the production volume of whichever vehicle the strategy is
implemented on, plus a yearly fixed cost that represents the
amortized investment costs. Learning is applied to the
variable cost only, which is assumed to follow an S-curve in
order to account for slow ramp-up time in the beginning and
asymptotic behavior to some theoretical minimum cost in the
long run. A general expression for the curve from [11] is
⎡
⎤
1− f
c p = c0 ⎢ f +
⎥.
1 + exp(αVcum, p Veq + β )⎥⎦
⎣⎢
(1)
c0 represents initial strategy variable cost and cp the variable
cost in period p. The change in cost depends on learning
scope, f, learning rate, α and β, cumulative production volume
through period p – 1, Vcum,p, and equivalent volume, Veq.
Learned knowledge can also be shared between similar
strategies so that implementing one strategy enables cost
reduction in other related strategies.
Baseline technology cost is calculated in a similar fashion
as lightweighting strategy cost with corresponding variable
and fixed components, but without learning as it presumably
uses established technologies. This cost is then subtracted
from the lightweighting strategy cost to obtain the cost
premium of implementing the strategy.
2) Cash Flow Revenue
Like vehicle cost, vehicle sales revenue in the selection
model is represented by a unit price, multiplied by the sales
volume of each period. This price, estimated with volumeneutral price (VNP), is composed of a baseline vehicle price,
plus additional revenue gained from improving fuel economy
through lightweighting. VNP represents the price at which a
market share increase arising from improved fuel economy is
offset by a market share decrease arising from a higher vehicle
price. In the end, the automaker sells the same number of
improved vehicles as baseline vehicles—just at a higher price.
The model relies on price change per change in fuel economy
(Δ$ / Δmpg) to compute VNP.
C. Constraints
The model’s objective is to select lightweighting strategies
that optimize NPV; however, these strategies also have to
satisfy certain constraints. One of these constraints is the
CAFE regulation, which sets a minimum fuel economy
standard for a manufacturer’s new vehicle sales and assesses a
monetary penalty if the automaker falls short of the target.
For some automakers, paying the penalty is not an option so
they will do whatever they can to meet the target. The current
CAFE calculation scheme can be very complex because the
regulation permits automakers to redistribute “credits” from
surplus years in which they exceed their CAFE target to
deficit years in which they fall short of the target, provided
that the deficit years occur within the three years preceding or
following the surplus year. This further complicates the
problem so instead, we opted to eliminate credit redistribution
and simply require that the CAFE target be met each year.
Additional constraints place restrictions on the use of
lightweighting strategies. For starters, conflicting strategies
(e.g. an aluminum hood and a composites hood) cannot be
implemented simultaneously, so the model has to somehow
ensure compatibility. Strategy continuity also constrains the
selection decision because strategies in use cannot be removed
or swapped out. Consequently, the model has to pick
correctly the first time around, especially when deciding
between two conflicting strategies.
IV. MODEL IMPLEMENTATION VIA GENETIC ALGORITHM
While constraints reduce the possible ways an automaker
can choose to lightweight its vehicles, they also make the
selection process more difficult because they fragment the
search space and require additional checks on the selected
strategies. Therefore, any selection model implementation
needs a reasonable approach to handling constraints, as well as
a way to optimize the objective function and cope with the
multi-period, multi-product scale. The rapid scaling of the
selection model, in particular, is an issue because the number
of ways of selecting lightweighting strategies grows
exponentially with each added strategy.
With these requirements in mind, we chose to implement
the selection model with a genetic algorithm (GA). Although
GAs cannot guarantee they will find the global optimum to the
problem, they are appropriate for large-scale problems and
problems that restrict decision variables to binary values. GAs
begin with a set or population of randomly generated
candidate solutions, known as chromosomes, to the
optimization problem. This population represents the first
generation of chromosomes. The best or fittest solutions, as
dictated by the objective function, are identified and the others
discarded. The remaining solutions become the parents and
are combined via crossover and mutated to create a new
generation of chromosomes. The process then repeats until
the solutions converge or a specified generation limit has been
reached. Since only the fitter chromosomes survive and are
used to create each new generation, the algorithm is able to
improve the selection decision.
In our particular case, the candidate solutions are strings of
binary decision variables that represent combinations of
implemented lightweighting strategies as well as the period
each strategy is first implemented on the automaker’s vehicles.
The strategy continuity assumption is built into the
chromosomes. NPV serves as the objective function of the
model and is used to assess each candidate’s fitness.
A. Constraints
Constraints are handled as additional objective functions to
be optimized rather than as actual binding constraints in order
to preserve the genetic diversity of the candidate solutions.
Since GAs are best suited to solving single-objective
problems, some modification is required. One option is to
assign each objective function a weight and combine all
objective functions into a single parameter that is then
optimized. Another approach, described by Roth [6], is to
compare a randomly chosen objective between two candidate
solutions. The fitter solution (according to the objective) is
kept and the other discarded to be later replaced in the next
generation. Our selection model uses the latter option because
of the more explicit treatment of the objective functions.
Under this approach, NPV is maximized and the CAFE
penalty and the number of conflicting strategies are minimized
for a total of three objectives.
A few assumptions are made to simplify the calculations
involved in computing each objective.
For starters,
lightweighting strategies are taken to be entirely independent
of each other so their weight savings can be summed and
converted to fuel economy improvement. Change in fuel
economy itself is also assumed to be linear with change in
vehicle mass. Finally, production volume is treated as a
model input and assumed to equal sales volume—that is, all
vehicles produced are sold in the period that they are
produced.
B. Genetic Algorithm Parameters
Choosing appropriate values for algorithm parameters is
important as these parameters govern the GA’s performance
and its ability to optimize the objective function. Unsuitable
values may lead to wasted computational effort or prevent the
algorithm from finding a reasonable solution. A dynamic
mutation rate was used, following the same approach as Roth
[6] in his technology selection GA and as Bäck and Schütz
[12].
Rate, r, varies based on generation number, t,
chromosome length, n, and the maximum number of
generations, T, according to the equation:
−1
n−2 ⎤
⎡
⋅t .
rt = ⎢2 +
T − 1 ⎥⎦
⎣
(2)
Strictly following this equation, though, leads to
comparatively high mutation rates, so n was set to 500 in order
to bring the mutation rate in the final generations more in line
with rates used in canonical GAs [13]. Population size is
defined as ten times the number of decision variables.
Ideally, the number of generations should also vary with
problem size because it can be difficult to predict exactly how
many generations are necessary for the problem to converge.
The proposed selection model opts to use a fixed number of
generations because of (2).
Crossover rate, which determines the number of candidate
solutions replaced in each generation, is another key
parameter. For our GA, this was set to 0.5 or half the
population size; higher rates are commonly used, but can lead
to pre-mature convergence with small population sizes [13].
Also, two-point crossover was chosen as the method for
generating new chromosomes [14].
V. CASE STUDY
TABLE I
VEHICLE INPUTS
Compact
Midsize
Large
Rest of
fleet
Unit cost ($)
$16,300
$17,600
$18,700
$27,000
Unit price ($)
$16,500
$21,600
$23,800
$27,000
1,357
1,549
1,612
—
27.36
25.00
22.49
30.11
6%
6%
6%
—
$80
$90
$253
—
83,000
75,000
42,000
200,000
Curb weight (kg)
Initial fuel economy
(mpg)
FE improvement per
10% wt reduction (%)
Price change per FE
change (Δ$ / Δmpg)
Volume (# / yr)
ID
C. Comparison with Period-by-Period Search
In addition to the GA selection model, we also implemented
a second model using what we refer to as a period-by-period
(PBP) search. This second model serves as a basis for
comparison with the GA model in order to assess the GA’s
approach of evaluating all the periods as a single unit instead
of individually.
Like the GA model, the PBP model selects lightweighting
strategies based on which enable the manufacturer to optimize
NPV subject to CAFE and conflict constraints. In order to be
comparable, it uses the same approach to calculating NPV and
makes similar assumptions regarding strategy continuity and
learning. The difference, though, is that whereas the GA
evaluates all the periods collectively, the PBP assesses the
periods one at a time, starting with the last period to insure
CAFE compliance and stepping backwards in time to
preceding periods. Consequently, the PBP model’s selection
decision for a given period is based on the NPV and CAFE of
that period, along with continuity restrictions as dictated by
the subsequent period.
TABLE II
LIGHTWEIGHTING STRATEGY INPUTS FOR MIDSIZE CAR
Baseline
Mass
Learning
Unit
Strategy
unit cost
change
rate
costa
Learning
scope
C1 Closures 1
$320
$300
-6.2 kg
Slow
Low
C2 Closures 2
$500
$300
-29.4
Slow
Med.
C3 Closures 3
$510
$300
-33.8
Slow
High
C4 Closures 4
$450
$300
-8.3
Fast
Med.
B1 Body 1
$1,860
$1,860
-65
Slow
Low
B2 Body 2
$2,390
$1,860
-93
Slow
Med.
B3 Body 3
$2,190
$1,860
-76
Fast
Med.
B4 Body 4
$2,600
$1,860
-134
Fast
High
a. Presented costs are calculated from variable and fixed cost inputs for a
production volume of 75,000 units per year.
Application of the selection models is demonstrated with a
case study. In this study, an automaker is looking to inform
the decision of which lightweight body and closure set designs
to implement on three of its cars. (A car’s closure set consists
of its hood, doors, front fenders, and decklid.) Selection
decisions made by the GA and the PBP models are compared
and the effect of including learning curves in the NPV
calculation on the selection decision is investigated.
A. Inputs
Eight lightweighting strategies—four body and four closure
set designs—and three vehicles are used in the case study.
The model chooses which of these strategies to implement and
on which vehicles over a three-year timeframe given a CAFE
target for each year. Because of conflicts, each car can have at
most two strategies—one body and one closure set—
associated with it.
A compact, a midsize, and a large car (Table I) were chosen
for the study, with a fourth vehicle included to represent the
remainder of the automaker’s fleet and to round out the CAFE
calculation. No lightweighting strategies are associated with
the fourth vehicle. When possible, inputs for the three
primary vehicles were based on 2009 model year
specifications. Additional data such as production volume and
fuel economy dependence on vehicle mass were estimated
from other sources [15], [16]. Baseline body-in-white cost,
multiplied by a scaling factor from [17] was used to derive
vehicle cost. Finally, volume-neutral price, obtained with a
market model [18], was used to estimate price change
resulting from improved fuel economy.
The lightweighting strategies (Table II) and their baseline
counterparts are drawn from vehicle designs detailed in [19]
and [20]. Both sources rely on process-based cost models to
predict strategy cost. Since these strategies were originally
developed for different vehicles, mass reduction and costs
were adjusted to better correspond with the three car sizes
A multi-period, multi-product selection model was
developed to inform the lightweighting strategy selection
decision. Preferred strategies are identified based on which
enable the automaker to optimize NPV subject to CAFE
compliance and conflict constraints.
The model was
implemented with a genetic algorithm and applied in a case
study in which we compared it to a period-by-period search.
Both models provide valid results, but only the GA was able
to capture the effect of learning on the selection decision.
Method
Period
GA-I
1
2
GA-II
3
1
2
PBP
3
1
2
3
C1
C2
Compact car
C3
C4
B1
B2
B3
B4
C1
C2
C3
Midsize car
B. Selection Model Results
Selection decisions made by the GA and PBP models are
presented in Fig. 1, and objective function and constraint
results in Table III. Both modeling approaches were run under
two sets of conditions, the first with learning excluded from
the NPV calculations, and the second with it included as
described in previous sections. Results from these two runs
are represented by GA-I and GA-II, respectively. Since the
PBP model makes the same selection decision in both cases,
its results are presented only once.
The NPV results (Table III) are shown relative to the NPV
of GA-I. Because a learning curve naturally lowers the cost of
a strategy without affecting its added revenue, any NPV
calculation that includes learning will unsurprisingly be lower
than one that does not. To compensate for this, the NPV of
each selection decision was calculated twice—once with
learning incorporated and once without—in order to better
compare the results.
Without cost evolution, the PBP selection decision has the
highest NPV. This is in part because, unlike the GA model, it
is able to optimize NPV given CAFE and other constraints in
period 3. As it then steps backwards through the preceding
periods, it removes strategies as the CAFE target decreases.
The decision remains unaffected in the presence of learning
because the model evaluates one period at a time and is unable
to rethink its choices once it moves on to the next period.
In contrast to the PBP model, the GA selects strategies by
collectively evaluating all periods. This enables the model to
consider more than just the strategies that are part of the
optimal decision in period 3; consequently, it chooses
differently from the PBP model. A different selection
decision, though, may not be advantageous: when the NPV is
calculated without learning, both GA-I and GA-II are worse
off than PBP ($0 and -$127M respectively, vs. $4M) because
a GA is unable to guarantee the global optimum. However,
when learning is considered, the GA model is able to take
advantage of the cost evolution and improve NPV. It
accomplishes this by implementing strategies earlier in order
to leverage the effect of learning in later periods, and by using
the same strategy, such as B4, in multiple vehicles.
While the degree to which learning takes place may be
uncertain, learning is likely to happen, particularly for
emerging technologies which a number of lightweighting
strategies rely on. Unlike the PBP model, the GA model is
able to capture the effect of learning and use it to improve the
selection decision.
VI. CONCLUSION
C4
B1
B2
B3
B4
C1
C2
C3
Large car
chosen for this case study. Strategy learning rate and scope
represents our best guess given the current state of the
technologies each uses.
Finally, a discount rate of 8% was used for the NPV
calculation. CAFE targets were chosen according to what was
feasible given the available lightweighting strategies, but
without over-constraining the problem. The first period is
unconstrained with a target of 27.5 mpg. Subsequent periods
raise the target to 27.9 mpg and finally to 28.2 mpg.
C4
B1
B2
B3
B4
Fig. 1. Selection decisions made by GA and PBP models. Checked boxes
represent selected lightweighting strategies for a given time period.
TABLE III
SELECTION MODEL RESULTS
Modeling method
GA-I
GA-II
PBP
N
Y
N/A
Calculated w/o learning
$0 (baseline)
-$127 M
$4.0 M
Calculated w. learning
$10.8 M
$26.0 M
$12.3 M
Learning considered?
ΔNPV of decision
Constraints
CAFE satisfied?
Y
Y
Y
Conflicts present?
N
N
N
Strategy continuity?
Y
Y
Y
Although the GA model is in place, more analyses are
necessary to evaluate its performance—for example, a look at
the sensitivity of the selection decision to changes in learning
rate, among other model inputs. Another future study could
broaden the scope of the model by comparing the
lightweighting strategies discussed in this paper to other
technologies that improve fuel economy (e.g. powertrain
modifications). And since lightweighting can also improve
performance, the model could be modified to include a
decision whether to tune the engine and improve acceleration
in place of fuel economy.
ACKNOWLEDGMENT
Thanks to Joseph Donndelinger for advice on genetic
algorithms.
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