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Journal of Cleaner Production 70 (2014) 132e144

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Journal of Cleaner Production

journal homepage: www.elsevier .com/locate/ jc lepro

Assortment planning of automotive products with considerations foreconomic and environmental impacts of technology selection

Ali Taghavi, Ratna Babu Chinnam*

Department of Industrial and Systems Engineering, Wayne State University, 4815 Fourth Street, Detroit, MI 48202, USA

a r t i c l e i n f o

Article history:Received 26 April 2013Received in revised form3 February 2014Accepted 4 February 2014Available online 12 March 2014

Keywords:Assortment planningConfigurable productsProduct substitutionTechnology selectionSustainabilityCAFE requirements

* Corresponding author. Tel.: þ1 313 577 4846.E-mail addresses: [email protected] (A. Taghavi

[email protected] (R.B. Chinnam).

http://dx.doi.org/10.1016/j.jclepro.2014.02.0040959-6526/� 2014 Elsevier Ltd. All rights reserved.

a b s t r a c t

A manufacturer’s assortment is the set of products that the company offers to its customers. Assortmentplanning considerably affects both the sales revenue and product offering costs for the company and ithad experienced growing attention across different industries over recent decades. In this study, wepropose a modeling framework that seeks to identify the optimal assortment for a manufacturer ofconfigurable products (in particular, automobiles). Our model accounts for environmental considerations(Corporate Average Fuel Economy requirements, tailpipe emissions, and greenhouse gas emissionsrelated to the production of the fuel used to power the vehicle) during assortment planning. Weformulate the economic and environmental requirements in the model through a mixed-integer pro-gramming framework and present a hypothetical product case study motivated by an American auto-maker that involves 120 potential configurations employing different engine technologies (gasoline,diesel, and hybrid technologies). Notwithstanding consideration for consumer perceptions and accep-tance, the results of this research work show that diesel technologies are a better choice to satisfyaverage fuel economy requirements compared to hybrid and conventional powertrains with currenttechnology maturity.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

A manufacturer’s assortment is the set of products that thecompany builds and offers to its customers. Kök et al. (2008)describe the goal of assortment planning as finding an assort-ment that maximizes company’s profit subject to various con-straints such as limited budget to purchase products and limitedshelf space to display products. For configurable products such asautomobiles, which are a combination of required and/or optionalcomponents (Rodriguez and Aydin, 2011), each model comes in anumber of configurations; the set of configurations and the asso-ciated logic for a configurable product is sometimes termed productdefinition. Assortment planning requires a tradeoff between salesrevenue and product offering costs for the company (MacDuffieet al., 1996). The automotive product offerings and configurationshave steadily grown in the U.S. until recent years. For example, thenumber of car models available in the U.S. market increased from30 models in 1955 to 142 models in 1989 (Womack et al., 1990).Including nameplates, body styles, and special performance

), [email protected],

editions, the industry is offering 394 newmodels in the U.S. marketin 2013 (Baumann, 2013). However, growing awareness for thecosts associated with increasing manufacturing complexity andplant productivity issues under large product configuration as-sortments is compelling major volume-driven automotive originalequipment manufacturers (OEMs) to consider controlling theirconfiguration variety to decrease their operational costs whilemaintaining their sales andmarket shares. For example, FordMotorCompany reduced the ordering complexity (i.e., number of order-able configurations) of the 2009 F-150 truck by more than 90%. Asfor cars, it planned for the 2010 Ford Focus to have just 150 “major”(or “core entity”) combinations, a drop of 95% from the 2008 model(Wilson, 2008). OEM data from Pil and Holweg (2004) for a popularvehicle segment in Europe even suggests that there is little corre-lation between the total number of configurations offered by abrand model and the total sales experienced. While there are anumber of factors that influence sales besides product variety (e.g.,product quality, value, brand image), overall it appears that auto-makers are not necessarily driving their strategic decisionsregarding product configuration variety based on objective andholistic decision support models.

Besides economic objectives to maximize profit, there arealso other factors affecting the final assortment of an OEM.

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mailto:[email protected]



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A. Taghavi, R.B. Chinnam / Journal of Cleaner Production 70 (2014) 132e144 133

Environmental considerations are important driving forces thatimpact the automotive industry due to increasingly strict govern-mental regulations and social expectations (Geffen andRothenberg, 2000; Koplin et al., 2007). In the U.S., the main fed-eral regulations on vehicle fuel economy have been expressedthrough Corporate Average Fuel Economy (CAFE) standards by theNational Highway Traffic Safety Administration (NHTSA) and theEnvironmental Protection Agency (EPA). CAFE is the sales-weightedfleet average fuel economy of an OEM, expressed in miles per U.S.gallon (3.785 L) of vehicles for sale in the U.S., for any given modelyear. The CAFE requirements were relatively static from 1990 to2010, with a requirement of 27.5 miles per U.S. gallon (mpg) forpassenger cars. Starting in 2011, the CAFE standards are newlyexpressed as mathematical functions depending on vehicle “foot-print”, a measure of vehicle size determined by multiplying thevehicle’s wheelbase by its average track width. Going forward, theCAFE requirements are tightening: 2016 target fuel economy is35.5 mpg for car and light trucks and will further increase to54.5 mpg by model year 2025. The current penalty for failing tomeet the standards is $5.50 per tenth of a mpg for each tenth underthe target value times the total volume of vehicles manufactured. Inaddition, a Gas Guzzler Tax is also levied on individual passengercar models (but not trucks, vans, minivans, or SUVs) that get lessthan 22.5 mpg. Instead of CAFE requirements, some countriesincluding European states have imposed taxation policy on gasolineand diesel prices (Sterner, 2007; Ekins, 1999). This policy has beenconsidered one of the best ways to fiscally control the amount ofenergy consumption and emissions from the transportation sector(Steenberghen and Lopez, 2008). This policy often involves signif-icantly increasing fuel price (van Vliet et al., 2010) and motivatescustomer’s evolution toward more fuel-efficient vehicles. This dy-namic will be implicitly considered in our model through theimpact of vehicle price on primary demand fractions for distinctconfigurations. Another important measure for OEMs in decidingthe product configuration assortment is the emissions footprintfrom vehicle manufacturing as well as product use and disposal/recycling.

In this paper, while limiting our discussion to the automotiveindustry, we aim to develop configurable product assortmentplanning models that take environmental considerations intoconcern while explicitly accounting for both demand and supplyissues. In the past decades, there has been considerable workdedicated to demand aspects of assortment planning (see Kök et al.,2008, for a literature review). However, very little research has beendone that integrally considers demand and supply/manufacturingaspects in planning product assortments. This paper proposes anobjective decision support modeling framework for configurationassortment planning for individual automotive products byexploiting exogenous demand models. Moreover, and to the best ofour knowledge, this is the first work on product assortment plan-ning that takes environmental issues into consideration. The rest ofthe paper is organized as follows: Section 2 reviews the relevantliterature; Section 3 discusses the problem setting in more detailand the main assumptions behind our model. Methodology andproblem formulation are discussed in Section 4. Section 5 reportsthe results from a number of experiments. Finally, we conclude andidentify directions for further research in Section 6.

2. Literature review

van Ryzin and Mahajan (1999) were the first to study assort-ment planning and inventory decisions by using a multinomiallogit (MNL) model of consumer choice. They assume that eachproduct variant carried in the assortment has an identical unit costand is offered at an identical price. Later, Mahajan and van Ryzin

(2001) study the same problem with substitution under stock-outs. Smith and Agrawal (2000) study assortment planning prob-lem with the exogenous demand model by solving an inventoryoptimization problem that selects both items to stock and the stocklevels for each item in the assortment. Kök and Fisher (2007) solvean assortment planning problem with exogenous demand. Theyformulate their problem in the context of a supermarket chain andoffer a procedure for estimating the parameters of substitutionbehavior and demand for the stores’ products. They also propose aheuristic to solve the assortment planning and inventory problemwith one-level stock-out-based substitution in the presence ofshelf-space constraints. Honhon et al. (2009) propose an algorithmto determine the optimal assortment and inventory levels understock-out-based substitution for a single-period problem assumingthat each customer type has a specific preference ordering amongstproducts and chooses the product with the highest rank accordingto his type (if any), which is available at the time of purchase. Noneof these models accounts for environmental considerations, andtheir treatment of manufacturing/supply complexity is limited. Inmany industries (including auto-industry), there is an increasingawareness toward addressing environmental issues in their prod-ucts as well as the processes (see Transportation Research Board-National Research Council, 1997; Sutherland et al., 2004).Goldberg (1998) studies the effects of CAFE standards on automo-bile prices and sales and the expected environmental effects ofCAFE standards. He claims that policies oriented toward shifting themixture of the new car fleet to more fuel-efficient vehicles arepromising, and CAFE provides incentives for OEMs to developmorefuel-efficient vehicles. Maclean and Lave (2000) study the envi-ronmental implications of alternative-fueled automobiles withrespect to air quality and greenhouse gas trade-offs. They analyzedifferent fuel-powertrain options and estimate fuel efficiency, en-ergy use, pollutant discharge, and greenhouse gas emissions forinternal combustion engine automobiles and show that com-pressed natural gas (CNG) vehicles are giving the best exhaustemission performance while direct injected diesels had the worst.On the other hand, greenhouse gases can be reduced with directinjected diesels and direct injected CNG compared to a conven-tional fueled automobile. Michalek et al. (2004) study the impact offuel efficiency and emission policy on optimal vehicle design de-cisions in an oligopoly market. They evaluate several policy sce-narios for the small car market, including CAFE standards, carbondioxide (CO2) emissions taxes, and diesel technology quotas. Theresults show that imposing CO2 taxes on producers for expectedlife-cycle emissions results in diminishing returns on fuel efficiencyimprovement as the taxes increase, while CAFE standards lead tohigher average fuel efficiency per regulatory dollar. Although theirmodel decides on design parameters (such as engine size), prices,and production volumes, it is different from our approach onassortment planning by considering no substitution effects.Recently, Hoen et al. (2010) study the effect of carbon emissionregulations on transport mode selection in supply chains. Althoughthey study a different sector, their results suggest that introducing aconstraint on emissions is a more powerful tool for policymakers inreducing emissions compared to introducing an emission cost forfreight transport via a direct emission tax or a market mechanism.In this paper, similar to results of Hoen et al. (2010), we too conductexperiments constraining the average emissions allowed by theOEM during product use rather than introducing an emissions cost.

3. Assumptions

Suppose that for the product under consideration, N ¼ {1, ., I}denotes the set of potential configurations that can be madeavailable by the OEM. Assortment planning involves selecting a

A. Taghavi, R.B. Chinnam / Journal of Cleaner Production 70 (2014) 132e144134

subset of these configurations for tooling the assembly line andreadying the suppliers and dealers/retailers. Due to the long leadtimes associated with engineering parts/options and their inte-gration into the vehicle, as well as lead times associated withsupply chain readiness, the assortment planning decisions have tobe made well upfront, often several years in advance of productlaunch. This forces the planners to make a number of assumptions.The major assumptions behind our assortment planning model areas follows, categorized into assumptions related to demand, supply,costs, and environmental issues.

1. Demanda. Assumption (A1). We assume that the target market needs to

be split into different regions, and R¼ {1,., r} denotes the setof regions in the market. This is less of an assumption andmore of a model feature. Each region is allowed to have itsdistinct product configuration demand and substitutionbehavior (e.g., colder northern states generally exhibit lessdemand for convertible models and have higher demand forfeatures such as heated seats and engine block heaters). Fromour conversations with subject-matter-experts, this is howOEMs model the market.

b. Assumption (A2). Given the long lead times associated withassortment planning and the significant uncertainty in fuelprices and their impact on product demand, we considerdifferent potential scenarios for market fuel(s) price(s). Aprobability is associated with each of the scenarios and theassociated product demand mix (i.e., the demand for thedifferent configurations). We impose no restrictions on thestructure of the relationship between fuel price and theproduct demand mix within these scenarios.

c. Assumption (A3). We assume that every potential customerhas a favorite (most preferred) configuration from the set N.Under fuel price scenario f ˛ FP, the potential demand foreach configuration i˛N, at each region r˛ R, is assumed to bea known fraction of total market demand,M. The total marketdemand as well as the demand mix for different technologiescould be different across fuel price scenarios. If the customercannot find her favorite configuration i, she will decide not tosubstitute with probability dri ðsÞ; otherwise she will chooseconfiguration j with probability arji. We assume that cus-tomers in a region would only substitute available configu-rations across the region (and not between regions) if theirfavorite configuration is missing.

2. Supplya. Assumption (A4). Although there are multiple market reali-

zation scenarios (in terms of fuel price and associated de-mand), given the long lead times involved for productdevelopment and supply chain readiness the OEM has todecide on a unique product configuration assortment upfront(strategic planning process). The model also has to decideupfront the planned production volumes for each configu-ration, so that the supply chain can install the necessarymanufacturing capacity for producing the parts/optionscontent. While the OEMs can try to adjust these productioncapacities after launching the product and observing theactual realized demand, this is often a very lengthy andexpensive process for highly engineered and complex prod-ucts such as automobiles and often takes several quarters to ayear. OEMs can also rely on tactics such as price rebates toalter demand. These reactionary decisions are more tacticalin nature and outside the scope of our strategic assortmentplanning model. This being a strategic model, we model theproduction supply and consumption setting as a single-period problem, also known as the newsboy or news

vendor model, where the manufacturer would supply theregions with product configurations at the beginning of thetime period; we do not explicitly model the ongoingreplenishment process with dealers ordering and the OEMtrying to fulfill the orders.

b. Assumption (A5). We allow economies of scale for the OEM inpurchasing parts/options from the suppliers as a function ofpurchase quantity. That is, the OEM could receive discountson some parts/options if purchased in large quantities. Weassume that the information related to discounts is exoge-nous to our model and purchasing cost is assumed to follow astep-wise non-increasing function as a function of purchasequantity; we assume an all-unit quantity discount model. Ifparts are shared across models, the step-wise function isexpected to capture the incremental price benefits from usingthe part within the product under consideration. Additionalpiece-price discounts garnered from using a part within theparticular program under consideration will apply to otherprograms that employ the part as well. This is again less of anassumption and more of a flexible model feature.

3. Costsa. Assumption (A6). We assume that each potential configura-

tion j has a variable production/supply cost, Cvariablej . We as-

sume that prices for each product configuration, pj, are setexogenously and are available a priori for product assortmentplanning. We assume that each feature/option p, if carried inany final assortment configuration, will incur a fixed costCfixed_partp . The fixed cost can be attributable to factors such as

incremental design, integration engineering, testing, quality,warranty, and service costs from incorporating the featureinto the assortment. Similarly, we make provision for fixedcosts from adding configurations to the assortmentðCfixed_conf

j cjÞ.b. Assumption (A7). We assume that there is overage cost

ðCoveragei Þ for leftover inventory at the end of the selling

period to cover the cost of additional incentives/marketingnecessary to clear the inventory within the distributionpipeline for introduction of product from the next modelyear.

c. Assumption (A8). We assume that the prices of differentconfigurations are fixed and do not change as a function ofthe fuel prices encountered in the market.

4. Environmental Factorsa. Assumption (A9). We assume that the OEM will target a

specific average fuel economy (AFE) for the model underconsideration in the aim of meeting the CAFE or similar re-quirements for the overall company across all models. SinceCAFE requirements are only mandatory in USA, we wouldconsider our study/numerical experiments more consistentwith the U.S. market.

b. Assumption (A10). We assume that the effect of any tax andexcise policy on fuel prices (e.g., policies encouraging dieselvehicles in Europe) and/or financial incentives for purchasingfuel-efficient vehicles (e.g., recent subsidies for electric cars inthe U.S.) would only affect potential demand for eachconfiguration within these regions and does not incur anycost to the OEM.

c. Assumption (A11). We limit modeling of greenhouse gas(GHG) emissions to just product use emissions from tailpipeand upstream fuel supply chain GHG emissions.We are awarethat production impacts are also critical. However, given thatmany OEMs have global supply chains, any such analysis, inparticular the logistics footprint, requires good understand-ing for the supply chain configuration and this information isoften unavailable at the stage of the product development

Table 1Assortment planning model parameters, sets, and decision variables.

Setsi ˛ 1, ., N Set of all potential model configurations for the assortmentr ˛ 1, ., R Set of all market regionsp ˛ 1, ., P Set of all options required for assortment productionl ˛ 1, ., L Set of all discount levels for an optionf ˛ 1, ., FP Set of all fuel price scenariosParametersdi,r,f Primary (first-choice) demand for configuration i in region r

under fuel price scenario f when facing a full assortmentFuelECi Fuel economy (calculated in miles per gallon) of configuration iAFE Average fuel economy target for the vehicle model in support of

CAFE requirement for the whole companyCEi Annual CO2 equivalent emissions of configuration iMax_ACE Maximum average annual CO2 equivalent emissions allowed for

the whole assortmentaij Probability that customer switches (substitutes) to

configuration i after not finding the favorite choice,configuration j

pi Selling price of configuration iCfixed_confi Fixed cost of configuration i, if carried in the final assortment

Cfixed_partp Fixed cost of option/feature p, if carried in any final assortment

configurationCvariablei Variable cost for a unit of configuration i

Coveragei Overage cost of configuration i if not sold by the end of the

planning horizonp


cycle when assortment planning takes place. In addition,impact estimates from even methods such as the EconomicInput-Output Life-Cycle Assessment (EIO-LCA) are not veryreliable for many countries. We hope that future studies canaddress this limitation more thoroughly. The data we areusing in our numerical experiments is derived from the U.S.fueleconomy.gov website, and those estimates include CO2,methane, and nitrous oxide emitted from all steps in the useof a fuel (from production and refining to distribution andfinal usedvehicle manufacture is excluded). Methane andnitrous oxide emissions are converted into a CO2 equivalent(CO2e). Future research should also account for emissionsfrom producing the vehicle. We also assume that all vehicleunits sold will be used for the same number of years and thatany emissions limit is in average U.S. tons/year (1 U.S. tonequals 907.18 kg).

Furthermore, we assume that the regulations affecting theassortment decisions do not change during the planning horizon.We also assume that the fuel(s) prices will remain constant duringthe planning horizon based on one of the fuel price scenarios. Thereis also no explicit consideration for supply network decisions in themodel (e.g., supplier selection, facility location).

vl Amount of discount for each unit of option p if purchased atquantity level l

OPp Total units of option p used by other programs in the companyLPpl With respect to economies of scale, the minimum order

quantity limit for price level l of option pbpi Bill-of-material parameter; equal to one if configuration i

requires option p (zero otherwise)BigM A sufficiently large numberYmax Maximum production capacity of the OEMXmax Maximum number of configurations in the assortmentP(f) Probability mass function for fuel price scenario fDecision VariablesYri Number of vehicles of configuration i planned to be supplied to

market region rXconfigi A binary decision variable equal to one if configuration i is built

(zero otherwise)Xpartp A binary decision variable equal to one if option p should be

built based on assortment requirements (zero otherwise)Zp Total required units of option p for the production of the final

assortment~zpl Total required units of option p purchased at discount level lZ_Binarypl A binary decision variable equal to one if option p is purchased

at discount level l (zero otherwise)Li;r;f Leftover inventory of configuration i in region r, under fuel price

scenario fEi,r,f Effective demand for configuration i in region r, under fuel price

scenario f

4. Methodology

In this section, we present our framework to model assortmentplanning decisions for automotive products. The mathematicalmodel seeks to maximize OEM’s profit subjected to feasibility andenvironmental constraints. Note that our model only accounts forrevenues and direct cost of sales but not overhead costs such asselling/marketing, administrative, and other expenses. Prior topresenting the details of the model, we need to mention that ourmethodology uses the following inputs:

a. Primary demand fractions, substitution rates, and probabilitymass function of fuel price scenarios from demand perspective.

b. Information regarding fuel economy as well as annual CO2equivalent emissions from environmental perspective.

c. Selling prices, fixed and variable costs, economies of scale, Bill-of-material, and capacity limits from manufacturingperspective.

The model then outputs the optimal set of configurations to bebuilt, production volumes of each configuration at each marketingregion, and total units of option ‘p’ and corresponding discountlevel required for the assortment.

Before presenting the model’s objective function and con-straints, it is necessary that we introduce the structure of ourexogenous demand model. Assume that di,r,f is the primary (first-choice) demand for configuration i in region r under fuel pricescenario f. The effective (or realized) demand for configuration i inregion r under fuel price scenario f could be computed as follows:

Ei;r;f ¼ di;r;f þXcjsi

dj;r;f $�1� Xj

�$aji (1)

where aji is the probability that a customer will switch (substitute)to configuration i after not finding her favorite choice, configurationj; Xj is a binary decision variable equal to one if configuration i is apart of the final assortment (i.e., built), and zero otherwise. We cannow introduce the mathematical model to find the optimalassortment. For brevity, we introduce the notation and definition ofall parameters and decision variables in Table 1.

Let p(f,Y) be the one-period (news vendor) profit for the OEM,from stocking assortment Y, when fuel price realization is f. Wehave

pðf ;YÞ ¼XNi¼1

XRr¼1

h�Pi � CVariable

i

�$�Yri �Li;r;f

�

� Coveragei $Li;r;f

i�XNi¼1

Cfixed_confi $Xconfig

i

�XPp¼1

Cfixed_partp $Xpart

p þXcp˛P

Xcl˛L

vpl $�~zpl þ OPp

�

(2)

This profit function consists of revenue associated with productsales minus any fixed and variable costs associated with offeringconfigurations as well as parts/options. The last term in equation(2) captures any savings from economies of scale in purchasing/

http://fueleconomy.gov


producing parts/option content. Then, the expected profit across allpossible fuel price scenarios would be:

EPðYÞ ¼Xf˛FP

pðf ; YÞ$Pðf Þ (3)

Our goal in finalizing the product assortment is to maximize EP(Y)with respect to capacity and feasibility constraints. The completeformulation for the optimization problem is presented as follows:

maxY ;X

EPðY ;XÞ ¼Xf˛FP

pðf ; YÞ$Pðf Þ (4)

s.t.

Ei;r;f ¼ di;r;f þXcjsi

dj;r;f $�1� Xj

�$aij ci; r; f (5)

Li;r;f ¼�Yri � Ei;r;f

�þci; r; f (6)

Xcr˛R

Yri � Ymax$X

configi ci (7)

Xconfigi �

Xcr˛R

Yri ci (8)

Xcr˛R

Xci˛N

Yri � Ymax (9)

Xci˛N

Xconfigi � Xmax (10)

Xci˛N

Xcr˛R

Yri � AFE*

Xci˛N

Pcr˛R

Yri

FuelECi(11)

Xci˛N

CEi$

Xcr˛R

Yri

!� Max_ACE*

Xci˛N

Xcr˛R

Yri (12)

Zp ¼Xci˛N

( Xcr˛R

Yri

!$bpi

)cp (13)

Zp � BigM*Xpartp cp (14)

Zp ¼Xcl

~zpl cp (15)

Xcl

Z_Binarypl ¼ 1 cp (16)

~zpl � LPplþ1 � Z_Binarypl cp; l (17)

~zpl � LPpl � BigM*�1� ZBinarypl

�cp; l (18)

~zpl � LPplþ1 þ BigM*�1� ZBinarypl

�cp; l (19)

Xconfigi ˛f0;1g ci˛N (20)

Zp˛Rþ;Xpartp ˛f0;1g cp˛P (21)

Yri ˛R

þ ci˛N;cr˛R (22)

Li;r;f ; dEi;r;f˛R

þ ci˛N;cr˛R;cf˛FP (23)

Constraint (5) captures effective demand for configuration i in re-gion r under fuel price scenario f. This constraint consists of originaldemand (di,r,f) plus any demand arising through substitution frommissing product configurations. Constraint (6) determines theleftover inventory of configuration i in region r, which is maximumof zero and production volumeminus realized demand. Constraints(7) and (8) are to ensure that there is no production for a config-uration that is not built. Constraint (9) is used to limit the totalproduction while constraint (10) limits maximum number of con-figurations supplied to the market. Constraint (11) ensures that theassortment satisfies the OEM’s target average fuel economy (AFE)for the model in support of meeting overall CAFE requirement forthe whole company and is the linearized form of this formulationPci˛N

Pcr˛R

Yri

Pci˛N

Pcr˛R

Yri

FuelECi

� AFE (24)

Constraint (12) ensures that the average annual tailpipe andupstream fuel CO2 emissions in the assortment do not exceed apredetermined threshold (Max_ACE). Constraint (13) calculatestotal units of option p required for the production of any configu-ration that entails part p based on the bill-of-materials. Constraint(14) guarantees that part p will have zero units (either manufac-tured or purchased) if it is not selected in the assortment. Con-straints (15)e(19) are required to determine the discount level fromeconomies of scale for each option in the assortment. More spe-cifically, constraint (15) links total units of part p to sum overdifferent discount levels of part p. Constraint (16) ensures that onlyone of the discount levels could be selected and constraints (17)e(19) give the lower and upper bounds of units of part p at dis-count level l. Equations (21)e(23) declare the model decision var-iable types.

5. Numerical experiments

In consultation with several subject-matter-experts from theU.S. automotive industry, we generated a set of hypotheticalproduct assortment planning problems generally representative ofthe mid-size sedan segment in the U.S. It should be noted that wehave had extensive discussions/collaborations with several subject-matter-experts from two OEMs. Some with extensive R&D experi-ence and routinely support marketing and supply chain analyticsstudies to inform management in managing product assortmentsand meeting regulations. Few others have over 30 years of expe-rience each as Chief Engineers in product development andassortment planning. These problems carried 120 potential productconfigurations for consideration and mostly involve vehicle pro-pulsion technologies and sample optional features such as thepresence/absence of sunroof and satellite radio. Note that it istypical for OEMs to limit the strategic assortment planning activityto key vehicle part/option content (e.g., body styles, engines,transmissions) to limit data collection and model formulationcomplexity and avoid considering relatively simple/cheap acces-sories such a floor mats and most other dealer-installed content.Colors are also often finalized much later. The proposed modelingframework is generic and is flexible enough to accommodate

Fig. 1. Demand fraction for 10 different powertrain technologies under different fuel price scenarios.


additional technologies/features and options (e.g., technologies fordirect injection, regenerative breaking, cylinder cut-off, and turbochargers). Space constraints were also a factor in keeping the list offeatures/options to a select minimum. The subject-matter-expertsalso provided guidance in generating cost data of each part/op-tion and, subsequently, deriving the unit costs associated with eachconfiguration. The profit margins were set between 15% and 30% ofthe unit cost (with 15% for cheapest configurations and 30% formost expensive ones) and added to the unit cost to compute theselling price for each configuration. The overage cost of leftoverinventory at the end of the selling period is assumed to be between4% and 12% of the unit cost of a configuration (4% for cheapestconfigurations and 12% for most expensive ones). Other data/pa-rameters such as substitution probabilities (aij), primary demandfractions (di,r,f), fixed costs of offering configuration ðCfixed_conf

i Þ, andfixed costs of offering options ðCfixed_part

p Þ were also generated inconsultationwith subject-matter-experts. In total, the 120 potentialconfigurations employ 15 different major parts/options, which aregrouped into powertrain technology choices (with 10 differenttypes consisting of 6 gasoline engine choices, 3 diesel enginechoices, and 1 hybrid engine choice), 3 body style choices (sedan,two-door coupe, and hatchback), sunroof option, and finally asatellite radio option. While the sunroof and satellite options aretruly optional (meaning that the customer can select a configura-tion without these options), powertrain and body style choices arechoices (e.g., the customer cannot select a configuration without apowertrain). Three different market scenarios are assumed basedon low, medium, and high but realistic fuel prices. In each of thesescenarios, the customers exhibit different demand for configura-tions with different levels of fuel economy. Given that the assort-ment planning problem is a strategic problem and the OEM cannoteasily change the product configuration assortment in response tochanges in fuel prices (though customers tend to react quickly tobig swings in fuel prices, as seen in the last decade), the model aimsto find a robust yet optimal assortment that best maximizes theexpected profit across all possible fuel-price/demand scenarios. In

Table 2Average margin, overage cost, fuel economy, and greenhouse green emissions for differe

Powertrain technology Averagemargin ($)

Conventional FWD 2.5 L, 4 cyl, Manual 2500FWD 2.5 L, 4 cyl, Automatic 3000FWD 3 L, 6 cyl, Automatic 3000AWD 3 L, 6 cyl, Automatic 2800FWD 3.5 L, 6 cyl, Automatic 3000AWD 3.5 L, 6 cyl, Automatic 3100

Diesel 2.0 L, 4 cyl, Manual Diesel 26002.0 L, 4 cyl, Automatic Diesel 25002.5 L, 4 cyl, Manual Diesel 2400

Hybrid 2.5 L, 4 cyl, Automatic Hybrid 1800

a Numbers are from http://www.fueleconomy.gov.b Numbers are generated based on data for similar class vehicles.

deriving the settings for our synthetic experiments, we not onlyrelied on the viewpoints of several subject-matter-experts from theNorth-American OEMs but also the official U.S. government sourcefor “fuel economy information” gathered from http://www.fueleconomy.gov to make sure that the data employed is consis-tent with the real-world situation. All generated data are presentedin detail in the Appendix.

Based on powertrain technology, we categorize the whole set ofconfigurations into conventional, diesel, and hybrid vehicles. Eachof these configurations has its specific fuel economy and productuse emission footprint, which could affect the optimal assortmentthrough either average fuel economy (AFE) requirement and/ormaximum allowed average product use emissions constraints(ACE). Fig. 1 shows the primary demand fractions for different ve-hicles (based on technology class) under different scenarios. Asexpected for the U.S. market, demand for conventional powertraintechnologies (i.e., with gasoline engines) is the highest while thereis much less demand for diesel and hybrid technologies. This is verydifferent from other markets such as Europe, where diesel power-trains carry a large market share in many vehicle segments. Asevident from the figure, the demand for hybrid and diesel tech-nologies is assumed to increase with higher fuel prices for theirhigher fuel efficiency.

Table 2 shows average profit margin, average overage cost, fuelefficiency in miles per U.S. gallon (mpg), and greenhouse gas (GHG)emissions for the different technologies. We make the simplifyingassumption that vehicle mpg and emissions are mostly dependenton the powertrain technology and that the impact of feature/optioncontent is relatively negligible. If there are significant interactionsbetween other feature/option content and configuration mpg oremissions, powertrain technology and feature/option contentcombinations can be aggregated into higher-level aggregate fea-tures/options that are part of the assortment planning model.While this comes at the cost of exponential growth in number ofaggregate options based on level of aggregation, it can be partiallymitigated only by considering combinations that are promising and

nt powertrain technologies.

Average overagecost ($)

MPG Greenhouse gasemissions (tons/year)

1200 25a 7.3a

1400 26a 7.1a

1400 23a 8.0a

1300 20a 9.1a

1400 21a 8.7a

1500 19a 9.6a

1500 26b 7.1b

1500 33b 6.3b

1600 34b 5.9b

1300 39a 4.7a

http://www.fueleconomy.gov



Fig. 3. Total manufacturer profit under different average fuel economy requirements.

Fig. 4. Average annual greenhouse gas emissions (U.S. tons/vehicle) under differentaverage fuel economy requirements.


likely to survive the assortment planning optimization process. Asis currently the case, hybrid technologies are the least profitablemodels but offer the highest fuel efficiency and lowest GHG emis-sions, while the 3.5-L automatic all-wheel drive (AWD) powertraintechnology builds the most profitable configurations that returnthe lowest fuel efficiency and release the highest GHG emissions.Our goal is to maximize total expected profit while satisfying AFErequirements and ACE emissions constraints by identifying thesupply amount (if any) of each configuration for each region. Weused ILOG-CPLEX 11.0 optimization engine to run all the experi-ments for our proposed mathematical model.

We first investigate the effect of environmental constraints onthe optimal assortment. Fig. 2 shows the optimal solution for theassortment planning problem under different AFE target levels.First, it shows the optimal solutionwhen there is no AFE constraint,and then by considering AFE requirement at different levels. Thefirst counterintuitive observation is that production shares fordifferent technologies overall look different from their primarydemand fractions. As an example, although the AWD 3 L, 6 cyl(cylinder), Automatic powertrain has the highest primary demandfraction across all technologies in all fuel price scenarios, thistechnology is only selected under two AFE requirement levels (noAFE target and AFE ¼ 25) and it has zero production for the othercases. The inconsistency between primary demand fraction andproduction share is mainly a result of environmental restrictions,product substitutions, and economies of scale. Another unexpectedobservation is seen by comparing 2.0 L, 4 cyl, Automatic Dieseltechnology with FWD 3.0 L, 6cyl, Automatic and FWD 3.5 L, 6 cyl,Automatic, and AWD 3.5 L, 6 cyl, Automatic. The diesel technologyis getting much higher production share in all AFE levels (inparticular when there is no AFE requirement) compared to thoseconventional technologies, even though the average profit marginis at least 20% less for the diesel technology. The exact reasonbehind this observation is not clear; however, we suspect that theeffect of product substitution is an important factor in determiningthe optimal share for each configuration.

In addition, one could observe that some particular technolo-gies are not profitable in most AFE scenarios (e.g., 2.5 L 4 cylManual Diesel, AWD 3.0 L Automatic, and 2.5 L Automatic hy-brids). Since there are many factors affecting the optimal assort-ment solution (substitution effects, option fixed costs, economiesof scale, etc.), it is not straightforward to predict the behavior ofthe optimal solution. However, one might consider the fact that2.5 L 5 cyl manual diesel has a lower mpg with regard to otherdiesel technologies, and hence is not getting a share in the optimalassortment.

One intuitive observation is that the optimal assortment gives ahigher share to some of the fuel-efficient technologies when weconsider environmental requirements. Also, one might observethat FWD 3.5 L Automatic powertrain technologies get smallerproduction share with regard to AWD 3.5 L Automatic

Fig. 2. Production levels for different powertrain technologi

technologies in most AFE scenarios (except when AFE ¼ 28) eventhough they have a better fuel economy, which may be the resultof having a lower than average profit margin. Another observationis that hybrid technologies seem to be non-profitable (at least withour current settings) due to low profit margins even though theyare very fuel efficient. This particular experiment suggests thatdiesel technologies are a dominant alternative for hybrid tech-nologies in order to achieve higher AFE levels. It is worthmentioning that as Goldberg (1998) and Michalek et al. (2004)discuss on the efficiency of CAFE requirements for OEMs todevelop more fuel-efficient vehicles, our experiments suggest thatdiesel powertrains work as a reliable alternative to help meetaverage fuel economy target requirements, while hybrid power-trains are not good candidates for product assortments given theircurrently low profit margins.

In terms of profit, Fig. 3 shows that satisfying AFE requirementsreduces OEM’s profit from 0.77% to 6.91% for different AFE targetrequirements. This is a considerable share of the profit and suggestsa need for potential investment in developing fuel-efficient tech-nologies at lower prices. Finally, Fig. 4 shows the average annualGHG emissions under different AFE levels, which steadily reduceswhen satisfying higher AFE levels. This figure shows the potentialreduction in GHG emissions by considering more stringent AFErequirements. Considering two extreme AFE levels (AFE ¼ 28 and

es under different average fuel economy requirements.

Fig. 5. Sensitivity analysis of production volumes w.r.t different fuel price probability mass functions.

Fig. 6. Sensitivity analysis of production volumes w.r.t different profit margins.


no AFE) in Figs. 3 and 4, the net effect is a reduction of GHGemissions by about 200,000 U.S. tons per year (almost one U.S. tonper vehicle per year) and a reduced expected profit of almost 69million dollars for the OEM (which could be a potential limit on anysubsidies spent on GHG emission reduction in the auto-industry).

Besides sensitivity analysis with respect to different AFE re-quirements, we are interested to investigate the sensitivity withrespect to changes in other model inputs. For that purpose, wegenerated two sets of new scenarios to check the optimal assort-ment under: a) different fuel price scenario probability massfunctions, and b) different profit margins. In the first set, we madefive scenarios for the probability mass function of fuel price sce-nario, which can be found in Table 5 of the appendix. These runs areconsistent with our original data set and we chose the AFE targetlevel to be equal to 26 for these runs. As can be seen from the resultsin Fig. 5 and 6, the optimal production is not changing considerablyunder scenarios 1e5 and we can conclude that our results are notvery sensitive to prediction of this particular parameter althoughtotal profit is changing from one scenario to another.

In the second set, we created five other scenarios by changingthe profit margins across different powertrain technologies. Theaverage profit margins for these scenarios are reported in Table 6 ofthe appendix. These runs are consistent with our original data setand we once again chose the AFE target level to be equal to 28 forthese runs. The production volumes are very similar across the firstthree scenarios where conventional technologies have higher profitmargins compared to diesel and hybrid technologies. However, inthe last two scenarios with diesel and hybrid technologies havingmore similar profit margins compared to the conventional ones, wedo see that part of the diesel production has been shifted to hybridas it better accounts for AFE requirements. This is another indicatorthat shows necessity for investment in developing more profitablehybrid technologies to make them compatible with other tech-nologies in the optimal assortment.

6. Conclusion

We propose a strategic decision support modeling frameworkfor assortment planning of products, in particular for configurableproducts e automobiles. We use an exogenous demand model thataccounts for substitution across different product configurationswhen the customer’s first choice is not available. The modelingframework supports environmental considerations by allowingtargets for the model program’s average fuel economy and averageproduct use emissions. Given the strategic nature of the assortmentplanning process (often carried out years ahead of product launch),we account for uncertainty in market fuel prices and the resultingdemand behavior through scenarios and associated probabilities.The proposedmixed-integer programmodel seeks a robust productconfiguration assortment that maximizes expected profit across allscenarios.

Our numerical experiments that employ realistic data set-tings, developed in consultation with subject-matter-expertsfrom the automotive industry and government data sources,suggest that the optimal production volumes can be ratherdifferent from the primary demand volumes for different con-figurations. This can be attributed to product substitution effects,profit-margin differences, economies of scale, and environmentalconstraints.

The result of our research implies a need for more OEM,government, and public attention toward diesel technologies, atleast in the short term, in particular in the United States. Notethat there are health concerns regarding traditional diesel en-gines in particular for the high emissions of nitrogen oxides(NOx) and particulate matter. Although New Technology DieselExhaust (NTDE) has been shown to be dramatically cleaner thanthe Traditional Diesel Exhaust (Hesterberg and Bunn, 2012), newresearch to deliver even cleaner diesel engines seems necessaryby automotive industry. There is also need to improve public

Table 1Total demand and corresponding probabilities for different market scenarios.

Fuel pricescenario 1



Total demand 200,000 200,000 200,000Probability 0.2 0.45 0.35


perception regarding diesel health based on improved/cleanerdiesel technologies.

Another result of our research is to reveal the need for addi-tional investment in cleaner technologies (e.g., hybrids andpure electrics) to make them more cost efficient in the long-termand hence more competitive with conventional and dieseltechnologies.

Given the strategic nature of the assortment planning problem,in particular for highly engineered/complex automotive productswith long lead times for supply network design and capacityplanning, we assume a single-period single-shot supply settingwith no replenishments. As a direction for future research, wesuggest building models that account for the effects of the ongoingreplenishment process typical in the automotive industry. Anotherextension to our research could be achieved by developing modelsthat account for endogenous pricing and price-demand elasticity.Finally, the models can be further developed to consider theentire OEM fleet rather than individual vehicle programs, tobetter account for the effects of common product platforms andcommonality.

Table 2Selling price, unit cost, overage cost, and primary demand fraction for each configuratio

Configuration ID Powertraintechnology type

Selling price($1000)

Unit cost($1000)

Overagecost ($1000)

1 FWD 2.5 L, 4 cyl,Manual

17.6 14.6 1.82 18.2 15.1 1.93 15.5 13.4 0.74 15.6 13.5 0.75 16 13.9 0.76 17.6 14.6 1.87 18.6 15.5 1.98 20.4 17 2.19 15.1 13.1 0.710 15.9 13.8 0.711 16 13.9 0.712 16.1 14 0.713 FWD 2.5 L, 4 cyl,

Automatic22.8 17.5 2.1

14 14.2 12.3 0.715 17.3 14.4 1.816 19.2 16 217 18 15 1.818 14.7 12.7 0.719 15.5 13.4 0.720 22.8 17.5 2.121 15.7 13.6 0.722 17.2 14.3 1.823 15.6 13.5 0.724 17.2 14.3 1.825 FWD 3 L, 6 cyl,

Automatic23.4 18 2.2

26 19 15.8 1.927 13.7 11.9 0.628 14.5 12.6 0.729 16 13.9 0.730 14.7 12.7 0.731 23.4 18 2.232 14.8 12.8 0.733 18.6 15.5 1.934 25.4 19.5 2.4

Acknowledgments

Our special gratitude goes to Gintaras Puskorius and DeanPichette of Ford Motor Company for their valuable insights andconstructive directions, which were very helpful in shaping thisresearch. We also wish to thank the associate editor and theanonymous referees whose comments and corrections have greatlyimproved this paper.

Appendix. Data employed for case study experiments1

n under different market scenarios.

Primary demand fractionin fuel price scenario 1


Primary demandfraction in fuel pricescenario 3

0.0241 0.0219 0.02080.0145 0.0132 0.01250.0130 0.0118 0.01120.0097 0.0088 0.00830.0080 0.0073 0.00690.0078 0.0071 0.00670.0052 0.0047 0.00450.0048 0.0044 0.00420.0043 0.0039 0.00370.0032 0.0029 0.00280.0026 0.0024 0.00220.0017 0.0016 0.00150.0349 0.0317 0.03010.0209 0.0190 0.01810.0188 0.0171 0.01620.0139 0.0127 0.01200.0116 0.0106 0.01000.0113 0.0102 0.00970.0075 0.0068 0.00650.0070 0.0063 0.00600.0063 0.0057 0.00540.0046 0.0042 0.00400.0038 0.0034 0.00320.0025 0.0023 0.00220.0295 0.0268 0.02410.0177 0.0161 0.01450.0159 0.0144 0.01300.0118 0.0107 0.00970.0098 0.0089 0.00800.0095 0.0087 0.00780.0064 0.0058 0.00520.0059 0.0054 0.00480.0053 0.0048 0.00430.0039 0.0036 0.0032

1 Probabilities of substitution between configurations are generally derived forthese experiments based on price and content similarities between configurations;similar to the a priori substitutability concept discussed by Vaagen et al. (2011). Inother words, the more common the parts/options between any two configurations,the higher probability of substitution between the two under stock-out. The(120 � 120) cell table is not reported here due to space constraints.

Table 2 (continued )



Unit cost($1000)

Overagecost ($1000)




35 19.6 16.3 2 0.0032 0.0029 0.002636 15.1 13.1 0.7 0.0021 0.0019 0.001737 AWD 3 L, 6 cyl,

Automatic20.4 17 2.1 0.0697 0.0634 0.0570

38 18.6 15.5 1.9 0.0418 0.0380 0.034239 15.1 13.1 0.7 0.0375 0.0341 0.030740 15.2 13.2 0.7 0.0279 0.0254 0.022841 15.9 13.8 0.7 0.0232 0.0211 0.019042 17.7 14.7 1.8 0.0225 0.0205 0.018443 17.8 14.8 1.8 0.0150 0.0137 0.012344 15.9 13.8 0.7 0.0139 0.0127 0.011445 19.5 16.2 2 0.0125 0.0114 0.010246 14.2 12.3 0.7 0.0093 0.0085 0.007647 24.1 18.5 2.3 0.0075 0.0068 0.006148 19.6 16.3 2 0.0050 0.0046 0.004149 FWD 3.5 L, 6 cyl,

Automatic14.3 12.4 0.7 0.0176 0.0146 0.0117

50 22.8 17.5 2.1 0.0105 0.0088 0.007051 14.2 12.3 0.7 0.0095 0.0079 0.006352 15.1 13.1 0.7 0.0070 0.0059 0.004753 20.2 16.8 2.1 0.0059 0.0049 0.003954 15.2 13.2 0.7 0.0057 0.0047 0.003855 26 20 2.4 0.0038 0.0032 0.002556 18 15 1.8 0.0035 0.0029 0.002357 14.7 12.7 0.7 0.0032 0.0026 0.002158 20.1 16.7 2.1 0.0023 0.0020 0.001659 13.3 11.5 0.6 0.0019 0.0016 0.001360 20.2 16.8 2.1 0.0013 0.0011 0.000861 AWD 3.5 L, 6 cyl,

Automatic15.7 13.6 0.7 0.0293 0.0244 0.0195

62 17.2 14.3 1.8 0.0176 0.0146 0.011763 23.8 18.3 2.2 0.0158 0.0131 0.010564 23.4 18 2.2 0.0117 0.0098 0.007865 18.3 15.2 1.9 0.0098 0.0081 0.006566 17.1 14.2 1.8 0.0095 0.0079 0.006367 13.7 11.9 0.6 0.0063 0.0053 0.004268 19 15.8 1.9 0.0059 0.0049 0.003969 17.2 14.3 1.8 0.0053 0.0044 0.003570 13.7 11.9 0.6 0.0039 0.0033 0.002671 14.5 12.6 0.7 0.0032 0.0026 0.002172 20.1 16.7 2.1 0.0021 0.0018 0.001473 2.0 L, 4 cyl,

Manual Diesel14.1 12.8 0.7 0.0197 0.0219 0.0351

74 14.9 13.5 0.7 0.0118 0.0132 0.021175 14 12.7 0.7 0.0106 0.0118 0.018976 21.5 17.2 2.1 0.0079 0.0088 0.014077 17.3 15 1.8 0.0066 0.0073 0.011778 12.3 11.1 0.6 0.0064 0.0071 0.011379 21.7 17.3 2.1 0.0043 0.0047 0.007680 24.4 19.5 2.4 0.0039 0.0044 0.007081 18.8 16.3 2 0.0035 0.0039 0.006382 14.5 13.1 0.7 0.0026 0.0029 0.004783 21.5 17.2 2.1 0.0021 0.0024 0.003884 13.2 12 0.6 0.0014 0.0016 0.002585 2.0 L, 4 cyl,

Automatic Diesel17 14.7 1.8 0.0154 0.0171 0.0213

86 23.4 18.7 2.3 0.0092 0.0102 0.012887 23.5 18.8 2.3 0.0083 0.0092 0.011588 15.2 13.8 0.7 0.0061 0.0068 0.008589 17.9 15.5 1.9 0.0051 0.0057 0.007190 18.7 16.2 2 0.0050 0.0055 0.006991 17 14.7 1.8 0.0033 0.0037 0.004692 13.6 12.3 0.7 0.0031 0.0034 0.004393 13.7 12.4 0.7 0.0028 0.0031 0.003894 19.4 16.8 2.1 0.0020 0.0023 0.002895 15.4 14 0.7 0.0017 0.0018 0.002396 14.3 13 0.7 0.0011 0.0012 0.001597 2.5 L, 5 cyl,

Manual Diesel22.2 17.7 2.2 0.0110 0.0122 0.0152

98 17.9 15.5 1.9 0.0066 0.0073 0.009199 12.8 11.6 0.6 0.0059 0.0066 0.0082100 19.3 16.7 2.1 0.0044 0.0049 0.0061101 12.7 11.5 0.6 0.0037 0.0041 0.0051102 18.4 16 2 0.0035 0.0039 0.0049103 22.9 18.3 2.2 0.0024 0.0026 0.0033104 24 19.2 2.4 0.0022 0.0024 0.0030105 16.4 14.2 1.8 0.0020 0.0022 0.0027106 13.1 11.9 0.6 0.0015 0.0016 0.0020107 18.4 16 2 0.0012 0.0013 0.0016108 14.9 13.5 0.7 0.0008 0.0009 0.0011

(continued on next page)





Unit cost($1000)

Overagecost ($1000)




109 2.5 L, 4 cyl,Automatic Hybrid

20.2 17.5 1.6 0.0078 0.0098 0.0137110 19.8 17.2 1.6 0.0047 0.0059 0.0082111 16.5 15 1.4 0.0042 0.0053 0.0074112 14.2 13.5 0.6 0.0031 0.0039 0.0055113 11.7 11.1 0.5 0.0026 0.0033 0.0046114 18.2 16.5 1.5 0.0025 0.0032 0.0044115 21.6 18.7 1.7 0.0017 0.0021 0.0029116 17.1 15.5 1.4 0.0016 0.0020 0.0027117 20.7 18 1.7 0.0014 0.0018 0.0025118 13.7 13 0.6 0.0010 0.0013 0.0018119 17.6 16 1.5 0.0008 0.0011 0.0015120 20.2 17.5 1.6 0.0006 0.0007 0.0010

Table 3Bill-of-material for each potential configuration.

Configuration ID Powertrain technology type 4-Door body style 2-Door body style Hatchback body style Sunroof Satellite radio

1 FWD 2.5 L, 4 cyl, Manual 1 0 0 1 12 0 1 0 1 13 1 0 0 0 14 0 0 1 1 15 1 0 0 1 06 0 1 0 0 17 0 0 1 0 18 0 1 0 1 09 1 0 0 0 010 0 0 1 1 011 0 1 0 0 012 0 0 1 0 013 FWD 2.5 L, 4 cyl, Automatic 1 0 0 1 114 0 1 0 1 115 1 0 0 0 116 0 0 1 1 117 1 0 0 1 018 0 1 0 0 119 0 0 1 0 120 0 1 0 1 021 1 0 0 0 022 0 0 1 1 023 0 1 0 0 024 0 0 1 0 025 FWD 3 L, 6 cyl, Automatic 1 0 0 1 126 0 1 0 1 127 1 0 0 0 128 0 0 1 1 129 1 0 0 1 030 0 1 0 0 131 0 0 1 0 132 0 1 0 1 033 1 0 0 0 034 0 0 1 1 035 0 1 0 0 036 0 0 1 0 037 AWD 3 L, 6 cyl, Automatic 1 0 0 1 138 0 1 0 1 139 1 0 0 0 140 0 0 1 1 141 1 0 0 1 042 0 1 0 0 143 0 0 1 0 144 0 1 0 1 045 1 0 0 0 046 0 0 1 1 047 0 1 0 0 048 0 0 1 0 049 FWD 3.5 L, 6 cyl, Automatic 1 0 0 1 150 0 1 0 1 151 1 0 0 0 152 0 0 1 1 153 1 0 0 1 054 0 1 0 0 155 0 0 1 0 156 0 1 0 1 0



Configuration ID Powertrain technology type 4-Door body style 2-Door body style Hatchback body style Sunroof Satellite radio

57 1 0 0 0 058 0 0 1 1 059 0 1 0 0 060 0 0 1 0 061 AWD 3.5 L, 6 cyl, Automatic 1 0 0 1 162 0 1 0 1 163 1 0 0 0 164 0 0 1 1 165 1 0 0 1 066 0 1 0 0 167 0 0 1 0 168 0 1 0 1 069 1 0 0 0 070 0 0 1 1 071 0 1 0 0 072 0 0 1 0 073 2.0 L, 4 cyl, Manual Diesel 1 0 0 1 174 0 1 0 1 175 1 0 0 0 176 0 0 1 1 177 1 0 0 1 078 0 1 0 0 179 0 0 1 0 180 0 1 0 1 081 1 0 0 0 082 0 0 1 1 083 0 1 0 0 084 0 0 1 0 085 2.0 L, 4 cyl, Automatic Diesel 1 0 0 1 186 0 1 0 1 187 1 0 0 0 188 0 0 1 1 189 1 0 0 1 090 0 1 0 0 191 0 0 1 0 192 0 1 0 1 093 1 0 0 0 094 0 0 1 1 095 0 1 0 0 096 0 0 1 0 097 2.5 L, 5 cyl, Manual Diesel 1 0 0 1 198 0 1 0 1 199 1 0 0 0 1100 0 0 1 1 1101 1 0 0 1 0102 0 1 0 0 1103 0 0 1 0 1104 0 1 0 1 0105 1 0 0 0 0106 0 0 1 1 0107 0 1 0 0 0108 0 0 1 0 0109 2.5 L, 4 cyl, Automatic Hybrid 1 0 0 1 1110 0 1 0 1 1111 1 0 0 0 1112 0 0 1 1 1113 1 0 0 1 0114 0 1 0 0 1115 0 0 1 0 1116 0 1 0 1 0117 1 0 0 0 0118 0 0 1 1 0119 0 1 0 0 0120 0 0 1 0 0


Table 4Fixed costs and production economies of scale information for each part/option.

Part/option name Fixed cost($1000)

Volume forall-unit quantitydiscount

Discount ($)

FWD 2.5 L, 4 cyl, Manual 10,800 37,000 180FWD 2.5 L, 4 cyl, Automatic 12,000 50,000 200FWD 3 L, 6 cyl, Automatic 13,200 40,000 220AWD 3 L, 6 cyl, Automatic 15,300 16,000 255FWD 3.5 L, 6 cyl, Automatic 16,500 12,000 275AWD 3.5 L, 6 cyl, Automatic 18,000 25,000 3002.0 L, 4 cyl, Manual Diesel 22,500 46,000 3752.0 L, 4 cyl, Automatic Diesel 24,000 36,000 4002.5 L, 5 cyl, Manual Diesel 25,500 20,000 4252.5 L, 4 cyl,

Automatic Hybrid30,000 20,000 500

4-Door Body Style 4500 95,000 752-Door Body Style 6000 72,000 100Hatchback Body Style 4500 60,000 75Sunroof 3600 130,000 60Satellite Radio 2400 135,000 40

Table 5Probabilities for different market scenarios.




Scenario 1 0.1 0.4 0.5Scenario 2 0.2 0.4 0.4Scenario 3 0.3 0.4 0.3Scenario 4 0.4 0.4 0.2Scenario 5 0.5 0.4 0.1

Table 6Average profit margin for different powertrain technologies.

Powertraintechnology

Scenario1

Scenario2

Scenario3

Scenario4

Scenario5

Conventional FWD 2.5 L, 4cyl, Manual

2900 2700 2500 2300 2100

FWD 2.5 L, 4cyl,Automatic

3400 3200 3000 2800 2600

FWD 3 L, 6cyl,Automatic

3400 3200 3000 2800 2600

AWD 3 L, 6cyl,Automatic

3200 3000 2800 2600 2400

FWD 3.5 L, 6cyl,Automatic

3400 3200 3000 2800 2600

AWD 3.5 L, 6cyl,Automatic

3500 3300 3100 2900 2700

Diesel 2.0 L, 4 cyl,ManualDiesel

2400 2500 2600 2700 2800

2.0 L, 4 cyl,AutomaticDiesel

2300 2400 2500 2600 2700

2.5 L, 4 cyl,ManualDiesel

2200 2300 2400 2500 2600

Hybrid 2.5 L, 4 cyl,AutomaticHybrid

800 1300 1800 2300 2800


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