The Pareto Frontier for Vehicle Fleet Purchases

Cost versus Sustainability

Daniel Reich, Sandra L. Winkler and Erica Klampﬂ

Ford Research & Advanced Engineering, Dearborn, Michigan 48124, U.S.A.

Keywords:

Integer Programming, Sustainability, Automotive.

Abstract:

Vehicle ﬂeets for large corporations can have thousands of vehicles that are replaced between every few months

and every few years. With the emergence of hybrid, plug-in hybrid, and other new vehicle technologies,

combined with an increasing focus on sustainability, planning ﬂeet purchases has and continues to become

a signiﬁcantly more complicated undertaking. This paper introduces Ford’s Fleet Purchase Planner system

designed to present ﬂeet customers with optimal purchase strategies that incorporate their companies’ cost

and sustainability considerations.

1 INTRODUCTION

Ford’s Fleet Purchase Planner (patent pending) is an

analytical system, using mathematical optimization

methodology, designed to help ﬂeet customers better

understand purchase options. It provides customized

purchase recommendations that satisfy corporate en-

vironmental goals, reduce costs, and analyze trade-

offs between company goals.

Sustainability and environmental impact are ar-

eas of growing importance to many of Ford’s ﬂeet

customers. For example, SimplexGrinnell ordered

200 Fusion Hybrids in 2010 to support a Tyco

company-wide environmental program, known as

”Vital World,” to reduce greenhouse gas emissions,

waste and water consumption by 25 percent over the

next ﬁve years (Ford Motor Company, 2010b). Kraft

also has goals with its sales ﬂeet program to reduce

fuel use and CO

emissions and purchased 4 cylinder

Fusions in 2010 to help accomplish this (Ford Motor

Company, 2010a).

In recent years, several new green vehicle tech-

nologies have emerged, e.g., battery electric vehi-

cles (BEVs), hybrid electric vehicles (HEVs), plug-

in HEVs (PHEVs), and turbocharged direct injected

gasoline engines (e.g., Ford’s EcoBoost

). These

technologies provide increasing opportunities for cus-

tomers to reduce emissions and operating costs, but

they also increase the number of purchase options

available, making planning a more complicated en-

deavor.

For example, what is the trade-off cost for pur-

chasing a Focus versus a Focus Electric (BEV)? Can

a company recover the additional cost incurred in

purchasing the BEV through fuel savings over time?

Does a BEV have the same emissions if driven in Cal-

ifornia as it does in Michigan, Texas or Florida? Deci-

sions become even more complex as customers need

to choose which vehicles in their existing ﬂeet to re-

place, which vehicles they should replace them with

(e.g. Focus, Focus Electric, Fusion, Fiesta), and how

these choices enable them to meet their cost and sus-

tainability targets.

This paper presents details on our Fleet Purchase

Planner (FPP) and is organized as follows. In Section

2, we provide background information on measuring

a vehicle’s carbon footprint. Section 3 introduces our

algorithm and integer programming models used to

generate optimal purchase recommendations. In Sec-

tion 4, we demonstrate our software application on an

example ﬂeet. Section 5 contains our summary and

conclusions.

2 CARBON FOOTPRINT

As consumers become increasingly aware of the con-

tribution of vehicle greenhouse gas (GHG) emissions

toward climate change, they seek opportunities to re-

duce their global warming footprint. Carbon dioxide

(CO

) is the primary GHG and is the main emission

from motor vehicles. CO

and water (H

O) are the

end products of combustion, a chemical reaction of

hydrocarbon (HC) fuels such as gasoline, diesel, nat-

Reich D., L. Winkler S. and Klampﬂ E..

The Pareto Frontier for Vehicle Fleet Purchases - Cost versus Sustainability.

DOI: 10.5220/0004222901750182

In Proceedings of the 2nd International Conference on Operations Research and Enterprise Systems (ICORES-2013), pages 175-182

ISBN: 978-989-8565-40-2

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

ural gas, and coal with oxygen (O

HC + O

→ H

O +CO

+ energy.

Consumers can reduce vehicle CO

emissions by us-

ing less fuel. This can be accomplished by select-

ing vehicles that have better fuel efﬁciency, using less

carbon-intensive fuels, or by driving fewer miles.

We use a well-to-wheels (WTW) approach to

quantify the CO

emissions from a vehicle ﬂeet.

WTW CO

includes both the direct emissions from

the combustion of fossil fuel by the vehicle, also

known as tailpipe emissions or tank-to-wheel (TTW)

emissions, as well as the upstream, or well-to-tank

(WTT), emissions. WTT emissions are introduced

when the feedstock for the ﬁnished fuel is extracted

or grown, transported, and reﬁned into a usable fuel or

used to generate electricity. The WTW emissions rep-

resent up to 80% of the vehicle life cycle CO

, while

raw materials, manufacturing and assembly, mainte-

nance, and end of life account for the remainder of

vehicle life cycle CO

emissions (Notter et al., 2010;

Ma et al., 2012). Conventional internal combustion

engine vehicles (ICEVs) have about 80% of the life

cycle CO

in the WTW phase (Notter et al., 2010;

Ma et al., 2012). With advanced technologies such

as HEVs becoming more prevalent, vehicle fuel efﬁ-

ciency improves, reducing the WTW CO

. However,

the manufacturing or raw materials become more car-

bon intense; for example, the WTW share of life cycle

for BEVs can decrease to 50-60% (Notter et al.,

2010; Ma et al., 2012).

Vehicle WTT and TTW CO

emissions are calcu-

lated based on the vehicle fuel economy (miles per

gallon, MPG) reported by the U.S. EPA and DOE

at fueleconomy.gov. Common liquid fuels are gaso-

line and diesel, which may be blended with the biofu-

els ethanol and biodiesel, respectively. A mixture of

10% ethanol and 90% gasoline (by volume) is called

E10. E10 is sold as gasoline in most U.S. states.

E85 contains 85% ethanol by volume and is used

only by ﬂex-fuel vehicles (FFVs), which can oper-

ate on any blend from E0 (gasoline) to E85. Each

fuel has known TTW CO

emissions, calculated from

the physical and chemical properties of the fuel. The

WTT CO

emissions for each fuel are provided by

GREET 1.8d.0, a fuel life cycle assessment tool de-

veloped at Argonne National Labs (Wang, 1999).

Other GHGs are emitted in smaller quantities, primar-

ily during the WTT phase. The GHGs methane (CH

)

and nitrogen dioxide (N

O) have 25 and 298 times

the global warming potential (GWP) of CO

, respec-

tively, over 100 years (Solomon, 2007). Frequently,

the emissions of CH

and N

O are weighted by their

GWPs and combined with the CO

emissions to pro-

vide a single CO

-equivalent GHG metric (CO

eq).

Table 1 lists the WTT and TTW CO

eq factors for the

fuels used in the model in units of kg/gal.

Table 1: WTT and TTW fuel emission factors.

GHG (kg CO

eq/gal)

W T T

T TW

Gasoline 2.2 8.9

E10 (corn ethanol) 2.5 8.0

E85 (corn ethanol) 4.7 1.3

Diesel 2.47 10.0

B10 (soy biodiesel) 2.49 9.0

The factors in Table 1 include only fossil-based

GHG emissions. Renewable biofuels, like neat

ethanol E100, have no TTW fossil-based CO

emis-

sions because there is no net increase in atmospheric

concentrations when the fuel is burned. The CO

is repeatedly emitted and reclaimed in a closed-cycle

in which the ethanol is combusted then absorbed from

the atmosphere as the biomass (corn) grows. Fossil

fuels like gasoline produce a net increase in atmo-

spheric CO

by removing carbon stored underground

and releasing it into the atmosphere with no mecha-

nism for returning it underground. Biofuels have only

WTT fossil-based CO

emissions.

For ICEVs, the annual metric tons of GHG emis-

sions are calculated as a function of fuel economy,

distance traveled, and GHG emissions factors in (1).

HEVs are treated as ICEVs since the small on-board

battery is recharged from the engine, not from an elec-

tric outlet.

GHG

W TW

= V MT

W T T

+ f

T TW

1000MPG

, (1)

where V MT is annual travel (miles); MPG is the

EPA label fuel economy (miles/gallon), f

W T T

the well-to-tank (fuel production) emission factor

(kg CO

eq/gallon) in Table 1, and f

T TW

is the

tank-to-wheel (fuel combustion) emission factor (kg

eq/gallon) in Table 1.

BEVs have only WTT CO

emissions. Like liq-

uid fuels, electricity may come from both fossil and

renewable sources. Renewable sources include hy-

dropower, solar energy, biomass, and wind power and

have no WTT CO

. Fossil fuels’ carbon intensities

combined with the efﬁciency of the power plant de-

termine the electricity WTT CO

footprint. Table

2 lists the WTT CO

factors for electricity by feed-

stock fuel including 8% transportation and distribu-

tion losses (Wang, 1999).

The electricity used to charge the BEV battery

varies across the country depending on the regional

mix of fuels used in the power plants. The GREET

1.8d.0 database provides mixes for the Northeast and

ICORES2013-InternationalConferenceonOperationsResearchandEnterpriseSystems

Table 2: WTT GHG emission factors for electricity genera-

tion, by fuel.

GHG (kg CO

eq/kWh)

elec

Coal 1.23

Natural Gas 0.64

Oil 1.03

Nuclear 0.02

Renewables 0.00

California. The mix for other regions was extracted

from the 2009 Annual Energy Outlook supplemental

tables (EIA, 2009), which use regions deﬁned by the

National Energy Modeling System (NEMS) shown

in Figure 1. Using GREET’s CO

factors and the

AEO2009 regional electricity feedstock mix, we can

calculate the weighted average WTT CO

eq emis-

sion factors for a region or state. Table 3 shows the

weighted emissions factors for each region and a list

of the states included in each region.

Figure 1: Electricity generation regions used in AEO2009

and GREET 1.8d.0. GREET combines regions 3, 6, and

7 to form the Northeast region. Region names: East Cen-

tral #1, Texas #2, Northeast #3+#6+#7), Mid-America #4,

Mid-Continent #5, Florida #8, Southeast #9, OK, KS #10,

Northwest #11, CO, AZ, NM #12, and CA #13. Graphic

from (EIA, 2009).

Table 3: Regional and state electricity GHG emission fac-

tors.

Region kg CO

eq coal natural oil nuclear renew-

# per kWh gas ables

1 1.074 84.2% 4.7% 0.3% 10.0% 0.8%

2 0.734 36.3% 44.1% 0.1% 12.5% 7.0%

3+6+7 0.412 29.9% 21.7% 2.2% 33.9% 12.3%

4 0.728 56.2% 4.2% 0.2% 35.2% 4.2%

5 0.893 71.5% 0.8% 0.3% 14.1% 13.3%

8 0.763 34.1% 42.3% 6.6% 14.1% 2.9%

9 0.743 52.3% 13.6% 0.5% 29.4% 4.2%

10 0.990 69.0% 21.0% 0.3% 4.4% 5.3%

11 0.440 31.6% 7.6% 0.1% 3.5% 57.2%

12 0.843 51.9% 31.2% 0.1% 9.0% 7.8%

13 0.338 13.3% 36.6% 0.0% 20.5% 29.6%

US Avg 0.721 50.4% 18.3% 1.1% 20.0% 10.2%

The EPA reports fuel economy for BEVs in

MPGe, miles per gallon equivalent, based on the

based on the fact that combustion of a gallon of gaso-

line releases 121 MJ (33.7 kWh) of energy (DOE,

2000). Equation 2 is used to calculate the annual met-

ric tons of CO

eq emissions for a BEV operating in a

particular state.

GHGe

W TW

= V MT

elec,region

1000MPGe

33.7kWh

gal

, (2)

where V MT is annual travel (miles), MPGe is

the EPA label mile/gallon equivalent fuel economy,

elec,region

is the electricity generation emission factor

(kg CO

eq/kWh) for a state (Table 3), and there are

33.7 kWh/gallon of gasoline.

PHEVs operate using a combination of electricity

from the grid and internal combustion energy. PHEV

emissions are calculated as a weighted average

of WTW CO

from electric mode and internal com-

bustion mode based on the shares of travel that take

place in each mode. The utility factor (λ) is the share

of travel in electric mode, often referred to as battery

charge-depleting mode. The fuel economy label pro-

vides the all-electric range (AER) in miles. Assuming

one charge per day, we estimate the annual λ as the

AER multiplied by 365 and divided by the annual to-

tal mileage. Like BEVs, the carbon intensity of elec-

tricity used by PHEVs varies by region of operation.

Equation 3 provides the annual metric tons of GHGs

emitted by a PHEV operating in a particular state.

GHGp

W TW

= λGHGe

W TW

+ (1 − λ)GHG

W TW

, (3)

where λ is the share of travel in electric (charge-

depleting) mode, GHG

W TW

from (1) is the emissions

from gasoline and GHGe

W TW

from (2) is the emis-

sions from electricity generation.

Figure 2 compares the CO

eq emissions of a 2012

Ford Focus, ICEV versus BEV. We can see that the

WTW emissions for the ICEV are about the same as a

BEV driven in Michigan with coal-intense electricity,

but are nearly 3 times higher than a BEV driven in

California with large shares of nuclear and renewable

electricity.

3 MATHEMATICAL MODEL

There are two main goals that we aim to achieve

in identifying ﬂeet purchase options through opti-

mization: minimizing cost and minimizing emissions.

Rather than optimizing to obtain a single purchase

recommendation, we aim to present points from the

Pareto frontier from which customers can select their

preferred levels of sustainability and cost.

Pareto frontier visualization is a classic technique

for addressing multi-objective optimization problems.

TheParetoFrontierforVehicleFleetPurchases-CostversusSustainability

Figure 2: 2012 Ford Focus: ICEV vs BEV, 15000 miles,

55% city, Michigan (MI) and Calfornia (CA) electric grids

for BEV.

In the context of sustainability and cost, it has re-

cently been applied to supply chain network design

problems (Wang et al., 2011).

To calculate the Pareto frontier for ﬂeet purchases,

we developed an algorithm that repeatedly solves the

following two optimization problems:

• Cost | Emissions Bound: this IP minimizes the

cost while satisfying the emissions bound e

which is initialized to ∞ and is then iteratively

reduced until the problem becomes infeasible, at

which point the algorithm terminates. The objec-

tive function value {c

∗

}

, is used as the required

cost in the next IP.

• Emissions | Cost: this IP minimizes the emissions

∗

}

, by selecting the best replacement strategy

given the previously calculated cost {c

∗

}

. The

optimal emissions {e

∗

}

are then reduced by a

predetermined step size h to set the emissions

bound e

k+1

= {e

∗

}

− h for the next iteration.

The algorithm is outlined in Figure 3. The result

is a Pareto frontier of purchase options that include

the types and quantities of vehicles to purchase as

replacements for currently owned vehicles in a cus-

tomer’s ﬂeet.

We deﬁne the notation that we will use to formu-

late the IPs and provide a corresponding example, de-

noted with , as follows:

• R is the set of currently owned vehicles being re-

placed.

 R = {2010 Ford Fusion 3.5L - 17K miles/year

Florida, 2010 Ford Fusion 3.5L - 51K miles/year

Michigan}.

• q

is the number of units of vehicle r ∈ R being

replaced.

 ~q = [4,6].

• V is the set of vehicles available for purchase.

 V = {2012 Ford Fusion 2.5L, 2012 Ford Fusion

Hybrid, etc.}.

Figure 3: Flowchart for optimizations to produce the Pareto

frontier.

• c

is the cost of vehicle v ∈ V (e.g. total cost of

ownership or purchase price with or without fuel

costs).

 ~c = [$20705,$28775, etc.] (starting MSRP price).

• V

⊆ V is the subset of vehicles available for pur-

chase that are suitable replacements for currently

owned vehicle r ∈ R.

 V

= V

= {2012 Ford Fusion 2.5L, 2012 Ford Fu-

sion Hybrid}.

• e

v,r

is the emissions produced by vehicle v ∈ V

when replacing vehicle r ∈ R, which is a function

of the fuel economy of v and the annual mileage

of r, as described in Section 2.

 e

1,1

= 6.9, e

2,1

= 4.8, e

1,2

= 20.7, e

2,2

= 14.3

(metric tons CO

• e

is the maximum emissions allowed at iteration

 e

= ∞ (no limit initially, to minimize price).

• F is the set of vehicle features and categories be-

ing considered, for example, moonroof, hybrid,

leather, manual, Fusion 2.5L, Focus, etc.

 F = {hybrid}.

• f

is a lower-bound on the number of vehicles to

be purchased with feature f ∈ F.

 hybrid

= 2.

• f

is an upper-bound on the number of vehicles to

be purchased with feature f ∈ F.

 hybrid

= 8.

• f

is a boolean parameter that indicates whether

or not vehicle v ∈ V contains feature f ∈ F.



hybrid = [false, true].

ICORES2013-InternationalConferenceonOperationsResearchandEnterpriseSystems

The decision variables in both integer programs are

the same: x

v,r

is the number of units of vehicle v ∈ V

to purchase to replace vehicle r ∈ R.

We formulate Cost | Emissions Bound as follows:

Cost | Emissions Bound

∗

}

= min

∑

r∈R

∑

v∈V

v,r

(4)

s.t.

∑

r∈R

∑

v∈V

v,r

≤ e

(5)

∑

v∈V

= q

∀r ∈ R (6)

≤

∑

r∈R

∑

v∈V

: f

=true

v,r

≤ f

∀ f ∈ F (7)

~x ∈ {0,1, ···}, (8)

where (4) minimizes the total purchase cost, (5) sets

the emissions limit, (6) is a ﬂow-balance constraint

that ensures exactly one vehicle is purchased for each

vehicle being replaced, (7) provides lower and upper

bounds on features or vehicle types, and (8) requires

non-negative integer solutions for the number of ve-

hicles purchased.

Continuing our example, we ﬁrst ﬁnd the minimal

purchase cost with no emissions bound (e

= ∞), so

we have

∗

}

=min 20705(x

1,1

+ x

1,2

) + 28775(x

2,1

+ x

2,2

)

(9)

s.t. 6.9x

1,1

+ 4.8x

2,1

+ 20.7x

1,2

+ 14.3x

2,2

≤ ∞

(10)

1,1

+ x

2,1

= 4 (11)

1,2

+ x

2,2

= 6 (12)

2 ≤ x

2,1

+ x

2,2

≤ 8 (13)

~x ∈ {0,1, ···}, (14)

where (9) minimizes purchase price, constraint (10)

that sets the initial emissions bound e

= ∞ is auto-

matically satisﬁed, constraint (11) replaces the 4 ve-

hicles in Florida, constraint (12) replaces the 6 vehi-

cles in Michigan, constraint (13) includes between 2

and 8 hybrids, and constraint (14) ensures integrality.

An optimal solution (not unique) is x

1,1

= 2, x

2,1

= 2,

1,2

= 6, x

2,2

= 0, which achieves the lower limit on

hybrids of 2 and thereby minimizes purchase cost.

The optimal objective value is {c

∗

}

= $223190. The

emissions level achieved in the left-hand side of (10)

is 147.6 metric tons of CO

. However, this emissions

level is not the lowest one achievable for a purchase

of 2 hybrids and 8 conventional engine vehicles. This

is why we need one more integer program that opti-

mizes emissions for a given cost.

We formulate Emissions | Cost as follows:

Emissions | Cost

∗

}

= min

∑

r∈R

∑

v∈V

v,r

(15)

s.t.

∑

r∈R

∑

v∈V

v,r

= {c

∗

}

(16)

∑

v∈V

= q

∀r ∈ R (17)

≤

∑

r∈R

∑

v∈V

: f

=true

v,r

≤ f

∀ f ∈ F (18)

~x ∈ {0,1, ···}, (19)

where (15) minimizes emissions, (16) ensures the

purchase cost is the same as the optimal solution

∗

}

of Cost | Emissions Bound in (4), and con-

straints (17) - (19) are the same as (6) - (8). The result-

ing s

= ({c

∗

}

,{e

∗

}

) is added to the Pareto frontier,

and the value for e

k+1

is reduced to {e

∗

}

− h, where

h is a predetermined step size.

Continuing our example, we have

∗

}

= min 6.9x

1,1

+ 4.8x

2,1

+ 20.7x

1,2

+ 14.3x

2,2

(20)

s.t. 20705(x

1,1

+ x

1,2

) + 28775(x

2,1

+ x

2,2

) = 223190

(21)

1,1

+ x

2,1

= 4 (22)

1,2

+ x

2,2

= 6 (23)

2 ≤ x

2,1

+ x

2,2

≤ 8 (24)

~x ∈ {0,1, ···}. (25)

The optimal solution (unique) is x

1,1

= 4, x

2,1

0, x

1,2

= 4, x

2,2

= 2. While the same vehi-

cles are purchased as in Cost | Emissions Bound,

the optimal emissions level achieved of {e

∗

}

139 metric tons of CO

is 6% lower; this emis-

sions reduction emphasizes the importance of plac-

ing the vehicles optimally. s

= ({c

∗

}

,{e

∗

}

) =

($223190,139 metric tons CO

) is added to the

Pareto frontier, and the value for e

is reduced to

138 metric tons CO

, where the step size is h =

1 metric ton CO

We continue our algorithm to compute the sec-

ond point in the Pareto frontier by substituting e

138 metric tons CO

into the right-hand side of con-

straint (10) and resolving Cost | Emissions Bound.

An optimal solution (again not unique) is x

1,1

= 1,

2,1

= 3, x

1,2

= 6, x

2,2

= 0, which includes 3 hybrids.

This is the minimum number of hybrids that can be

purchased while satisfying the emissions bound of

138 metric tons CO

. The optimal objective value is

∗

}

= $231260. The emissions level achieved in

the left-hand side of (10) is 145.5 metric tons of CO

Similarly to the ﬁrst iteration (k = 1), this emissions

TheParetoFrontierforVehicleFleetPurchases-CostversusSustainability

level is not the lowest one achievable for a purchase

of 3 hybrids and 7 conventional engine vehicles.

To ﬁnd the emissions level for the second point

in the Pareto frontier, we substitute {c

∗

}

= $231260

into the right-hand side of constraint (21) and resolve

Emissions | Cost. The optimal solution (unique) is

1,1

= 4, x

2,1

= 0, x

1,2

= 3, x

2,2

= 3. While the same

vehicles are purchased as in Cost | Emissions Bound,

the optimal emissions level achieved of {e

∗

}

= 132.6

metric tons of CO

is 9% lower. The resulting s

({c

∗

}

,{e

∗

}

) = ($31260, 132.6 metric tons CO

) is

added to the Pareto frontier, and the value for e

reduced to 131.6 metric tons CO

The algorithm, summarized in Figure 3, continues

to iteratively solve the Cost | Emissions Bound and

Emissions | Cost IPs for k = 3, 4,5, 6,7 to provide us

with additional points s

. At k = 8, no

further emissions reductions are achievable due to the

limit of 8 hybrids, which yields an infeasible Cost |

Emissions Bound IP, and the algorithm terminates.

The Pareto frontier for this example in Figure 4

shows solutions for all iterations k = 1,. .. ,7. These

solutions describe which combinations of vehicles

to purchase to replace the 10 vehicles: the solution

varies between 2 and 8 HEVs and ICEVs. While the

points in Figure 4 are spaced evenly with respect to

price, the CO

reductions become smaller when 7 and

8 HEVs are chosen for purchase; this can be explained

by the higher mileage on the 6 Michigan vehicles,

where hybrids are ﬁrst optimally placed, compared

with the lower mileage of the Florida vehicles, where

HEVs 7 and 8 are placed. This example is sufﬁciently

concise to solve with logic and intuition alone; with

large ﬂeets containing vehicles with variable mileage

and more vehicles considered as candidate replace-

ments, the Pareto frontier is quite useful in identifying

strategic purchase decisions.

Figure 4: The Pareto frontier.

While we have concentrated on formulations that

minimize purchase price in this section, additional ob-

jectives are also useful in practice; two such notewor-

thy objectives are minimizing purchase price plus fuel

costs for a given number of years and minimizing to-

tal cost of ownership.

4 SOFTWARE APPLICATION

We have developed a Microsoft Excel user interface

for the Fleet Purchase Planner. Fleet customers up-

load information on their current ﬂeets to the tem-

plate shown in Figure 5. Data collected includes year,

make, model, and powertrain, which are mapped to

EPA fuel economy data. Combining this with annual

mileage, city driving share, and region of operation,

we calculate the current state CO

, as described in

Section 2. The input for “quantity to replace” in Fig-

ure 5 is used to generate the ﬂow-balance constraints

(6), (11), (12), (17), (22) and (23).

Figure 5: Input for the set of vehicles being replaced, R,

from the example in Section 3.

To determine candidate replacements V

for those

vehicles r ∈ R listed in Figure 5, we use vehicle seg-

mentation data. For example, we look up “2010 Ford

Fusion 3.5L, V6, Auto, 2WD” in our segmentation

database and ﬁnd that this is a midsize car. We then

refer to the spreadsheet user interface in Figure 6,

which lists Fusion as a suitable candidate replacement

for midsize cars. This interface offers the ﬂexibility

to list multiple candidate replacements, so customers

can explore various options; for example, the choice

for replacement vehicles could move down in size to

a compact car or up to a crossover utility vehicle.

Figure 6: Segmentation lookup table for vehicles available

for purchase.

The interface in Figure 6 is used to narrow down

the subset of candidate replacements V

from all Ford

vehicles to all Fusion vehicles. However, in the exam-

ple from Section 3, we considered only two Fusion

vehicles as a candidate replacements: the automatic

2.5L ICEV and the HEV. In practice, we achieve this

through our feature sets F and constraints (7) and

(18). The information required to generate these con-

straints is input by the user in the spreadsheet inter-

face shown in Figure 7. For example, a maximum of

0 ”Manual” removes manual transmission Fusion ve-

hicles from consideration. This is also where we in-

ICORES2013-InternationalConferenceonOperationsResearchandEnterpriseSystems

Figure 7: Upper and lower limits, f

and f

, respectively, on

the features and categories, f ∈ F, for vehicles available for

purchase.

troduce the range of 2 to 8 HEVs for constraints (13)

and (24).

The analytical engine for the Fleet Purchase Plan-

ner is implemented in Java and CPLEX 12.4 is used

to solve the IPs. These IPs are easily solved for ﬂeets

with up to several thousand vehicles, with solve times

under 1 second on an Intel Core i5 2.5 GHz CPU with

8GB RAM running 64 bit Windows 7.

In addition to the Pareto frontier shown in Figure

4, there is other information that could be useful to the

customer. The report shown in Figure 8 highlights the

improvement in sustainability corresponding to each

point on the Pareto frontier compared with the current

state of the ﬂeet. This report may also include com-

parisons of fuel expenditure over a given time period

versus purchase price, further illustrating the relation-

ship between cost and sustainability.

Figure 8: Summary report for multiple purchase options

corresponding to points s

,·· · , s

on the Pareto frontier.

The second report in Figure 9, provides the opti-

mal placement of each vehicle purchased for the var-

ious scenarios. It can also include summary statistics

for annual fuel expenditure and CO

emissions on the

individual vehicle level, compared to the current level

for the vehicle being replaced. Each new vehicle be-

ing purchased appears below the vehicle it is replac-

ing. Notice that in the min cost scenario s

, the two

HEVs purchased replace the higher mileage vehicles

in Michigan. As the upper bound on emissions e

lowered at each iteration k, more vehicles in Michigan

are replaced with HEVs. Only after all the Michigan

vehicles have been replaced with hybrids, at s

, is a

vehicle in Florida replaced with a hybrid.

Figure 9: Detailed report for multiple purchase options cor-

responding to points s

,·· · , s

on the Pareto frontier. The

vehicles being replaced are shown with a black background

and white font, with their corresponding replacements be-

low.

5 CONCLUSIONS

Ford’s Fleet Purchase Planner is a software system

designed to identify the most cost effective opportu-

nities for vehicle ﬂeets to improve their sustainability

through new purchases. FPP leverages several data

sources, including vehicle fuel economy, segmenta-

tion, customers’ current ﬂeets and driving patterns.

The IP models we have introduced generate the Pareto

frontier, which demonstrates the relationship between

cost and sustainability. This technology, for the ﬁrst

time, provides customers with current emissions lev-

els of their vehicle ﬂeets and compares that with levels

achieved by various purchase options.

FPP has already been used in collaboration with

large ﬂeet customers, with signiﬁcant demonstrated

ﬁnancial beneﬁts over more traditional vehicle re-

placements strategies. For example, one such strat-

egy is to select a single new midsize vehicle, such as

a Ford Fusion EcoBoost, to purchase for any midsize

vehicle being replaced. We can show the minimum

cost purchase to achieve the same level of sustainabil-

ity using the Pareto frontier, thereby highlighting the

value of optimization.

FPP has the potential to change the way many of

Ford’s ﬂeet customers plan their purchases, and more

importantly, the decisions they make regarding what

to purchase.

REFERENCES

DOE (2000). Electric and hybrid vehicle research, de-

velopment, and demonstration program: Petroleum-

equivalent fuel economy calculation. Technical report,

Federal Register 65, 113, 36986.

EIA, U. (2009). Annual energy outlook 2009 with projec-

tions to 2030. Technical report, DOE/EIA-0383.

Ford Motor Company (2010a). Kraft foods to re-

place U.S. sales ﬂeet. http://media.ford.com/

article

display.cfm?article id=32202.

Ford Motor Company (2010b). Simplexgrinnell or-

ders 200 ford fusion hybrids in effort to reduce

TheParetoFrontierforVehicleFleetPurchases-CostversusSustainability

greenhouse gas emissions. http://media.ford.com/

article display.cfm?article id=32710.

Ma, H., Balthasar, F., Tait, N., Riera-Palou, X., and Harri-

son, A. (2012). A new comparison between the life

cycle greenhouse gas emissions of battery electric ve-

hicles and internal combustion vehicles. Energy Pol-

icy.

Notter, D., Gauch, M., Widmer, R., W

ager, P., Stamp, A.,

Zah, R., and Althaus, H. (2010). Contribution of li-

ion batteries to the environmental impact of electric

vehicles. Environmental science & technology.

Solomon, S. (2007). Climate change 2007: the physical

science basis: contribution of Working Group I to

the Fourth Assessment Report of the Intergovernmen-

tal Panel on Climate Change. Cambridge University

Press.

Wang, F., Lai, X., and Shi, N. (2011). A multi-objective

optimization for green supply chain network design.

Decision Support Systems, 51(2):262–269.

Wang, M. (1999). Greet 1.5-transportation fuel-cycle

model-vol. 1: methodology, development, use, and

results. Technical report, Argonne National Lab., IL

(US).

ICORES2013-InternationalConferenceonOperationsResearchandEnterpriseSystems