Organizational Structure, Subsystem Centrality, and ... · subsystems. urthermore,F the system adapts by making either incremental or long-jump searches to nd a (possibly local) optimal

Organizational Structure, Subsystem Centrality, and

Misalignments in Complex NPD Projects

Mohsen Jafari SonghoriDepartment of Computer Science, School of Computing, Tokyo Institute of Technology, Midori-ku, Kanagawa, Japan.

[email protected]

Javad NasiryInformation Systems, Business Statistics and Operations Management Department, Hong Kong University of Science and

Technology, Clear Water Bay, Kowloon, Hong Kong. [email protected]

Developing a complex new product requires the �rm both to deconstruct that product into subsystems and

to create an organizational structure aligned with the product architecture. However, empirical evidence

indicates that misalignments do occur and are usually one of two general forms: a �hidden dependency�,

which is a missing link between teams responsible for two interacting subsystems; or �spurious communica-

tions� between two teams that interact even though their respective subsystems are not linked. We model

the product development process as a search on a rugged landscape and study how misalignments a�ect

the performance of the process in both �nal design's quality and convergence time. We �nd that the e�ects

are mediated by the organizational decision-making structure. In particular, in comparison to an aligned

system, misalignments of either type worsen the performance in a polyarchy while, in a hierarchy, only

hidden dependencies do so. Spurious communications in a hierarchical structure do not necessarily dete-

riorate the performance. Further, in comparison between polyarchies and hierarchies, polyarchies obtain a

higher �nal design quality. We also �nd that, in a hierarchy, misalignments in subsystems characterized by

medium centrality (with respect to product architecture) negatively a�ect the performance while those in

high-centrality subsystems are inconsequential. In contrast, in a polyarchy, misalignments in high-centrality

subsystems deteriorate the performance the most. We discuss the implications of our �ndings in managing

complex product development project.

Key words : complexity, misalignments, hidden dependency, spurious communication, organizational

structure, subsystem centrality, NK(C) simulation

1. Introduction

The Airbus A380, heralded as the world's largest passenger jetliner, �nally began making commercial

�ights in 2007. However, the delays in its development had required Airbus to reschedule orders,

pay out penalties to customers, and lay o� part of its workforce. Wiring of the plane was the source

of most of the problems. About 500 kilometers of wiring is needed for the A380. The wiring task was

allocated to two teams, one each in Germany and France, who independently made slight design

1

Jafari Songhori and Nasiry: Organizational Structure and Centrality in Misaligned Projects2

changes but without always informing the other team. Some incompatibilities in wiring were not

discovered until the �nal assembly stage, which resulted in production delays. As a senior Airbus

manager put it: �We perhaps underestimated the complexity of the aircraft� (Landler 2006).

Developing complex new products such as an aircraft requires that �rms break down the products

into physical subsystems that must interact properly to make the product functional. These subsys-

tems and their interactions constitute the product or technical architecture. A team of designers is

responsible for developing each subsystem. These product development (PD) teams interact within

an organizational architecture toward the goal of developing the product by a given deadline and

within a budget. These PD teams should coordinate and manage the subsystems and their interde-

pendencies properly. To achieve coordination, product and organizational architectures should be

aligned. That is if a technical interdependency exists between two subsystems, then there should be

a corresponding communication between the teams responsible for developing them and vice versa

(Le and Panchal 2012). This process is known as socio-technical coordination (Herbsleb 2007), and

the extent of alignment is known as socio-technical congruence (Kwan et al. 2011).

Though these ideas are intuitive, empirical studies generally �nd product and organizational archi-

tectures misaligned. Misalignments occur when two subsystems interact while their corresponding

teams do not (an unmatched interface or a hidden dependency) and when two teams interact while

the subsystems they are developing do not (an unmatched interaction or spurious communication)

(see Sosa et al. 2004, Gokpinar et al. 2010). We study the consequences of such misalignments on

the performance of PD teams in a model of product development as a search process by a num-

ber of teams on rugged interdependent landscapes. Misalignments may deteriorate or improve the

quality of the �nal design and the time it takes for teams to converge to this design. Understand-

ing these potential consequences helps managers to allocate limited resources e�ectively to manage

misalignments and improve the performance of the design process.

We conceptualize a PD project as PD teams searching on a landscape to �nd the best possible

design. We simulate the search process by an NK(C) �tness landscape model. In other words, there

are n subsystems each under the control of one team and with ne elements that form a system

with N = n∗ne elements. Each element of a subsystem has an average of K interactions with other

elements of that same subsystem. The parameter C represents the average number of interactions

between the elements of one subsystem with those of other subsystems; thus changing the status

of one element in the design of one subsystem a�ects C other elements in the design of other

subsystems. Furthermore, the system adapts by making either incremental or long-jump searches

to �nd a (possibly local) optimal point (Kau�man 1993). Because complex PD systems are often

�nearly decomposable� (Simon 1962), we choose the parameters K and C to re�ect such systems in

our study.


We assume that misalignments occur across the boundaries of teams and subsystems rather

than within them (Sosa et al. 2004). The misalignments may be due to unknown interactions

between subsystems or to lack of appropriate coordination mechanisms between teams (Srikanth

and Puranam 2011). In each stage of the search, if a hidden dependency occurs then we assume

that an interface between two subsystems is overlooked with a certain probability. This means that

an interface may be known to teams yet those teams may fail to update themselves on the current

status or may ignore the interdependency owing to overcon�dence or workload. From a resource

management point of view, the resources that should have been allocated to in-between interactions

of subsystems are diverted towards within-subsystem interactions. Spurious communication between

teams with independent subsystems anchors the teams on other teams' design ideas which may cause

information overload and hurt a teams' performance or provide new design alternatives and improve

the performance. We model spurious communication in a similar approach to hidden dependencies.

In this case, the resources that should have been spent on within-subsystem interaction are focused

instead on in-between teams' interactions.

Our goal is to study the performance implications of misalignments in the complex PD project.

Performance in our study is de�ned as the �nal design's quality and also the time it takes for

teams to converge to this design. These two dimensions of performance capture the key factors in

evaluating a PD project especially in competitive markets. The design quality is the average of �nal

design qualities of all teams when convergence have been achieved. Convergence occurs whenever

no team can increase its �tness value by further local search; that is a local optimum design or a

sticking point has been reached (Mihm et al. 2003, Rivkin and Siggelkow 2002).

In this setup, we seek to address the �rst of our three main research questions: [1] Do mis-

alignments degrade PD project performance?�and, if so, which type of misalignment generates a

larger e�ect? Spurious communications may facilitate coordination among homogeneous teams and

increase performance (O'Reilly et al. 1989, Zenger and Lawrence 1989). They may also have the

opposite e�ect to the extent that teams' limited attention is consumed by unnecessary communi-

cation and information (Bantel and Jackson 1989, Ancona and Caldwell 1992). Our results show

that the answer to this question is conditional on the organizational structure of the PD project,

i.e., how decisions are made in the design process. We consider two decision-making structures:

hierarchy and polyarchy. In a hierarchy, the project manager considers only those alternatives by a

team that improve the �tness value of all design teams (or leave them unchanged). That is, if an

alternative reduces the �tness value of any team, it is eliminated from the consideration set. In a

polyarchy however all the design proposals by teams are taken into account and go through further

development. A polyarchical organization then has an inherent exploration tendency.


We show that a PD project without misalignments outperforms one with either type of misalign-

ment in a polyarchy while, in a hierarchy, this holds only when hidden dependencies exist in the

project. In other words, misalignments in a polyarchical decision-making structure deteriorate the

design quality and delay the convergence more when compared to an aligned system. In a hierar-

chical structure, spurious communication does not have a negative impact on the design quality or

the convergence time. Resources should instead be allocated to identifying and managing hidden

dependencies to improve the performance of the project. In line with previous studies, we also �nd

that, independent of the misalignment type, polyarchies are conducive to better design qualities

when compared to hierarchies. Our results on the comparison of the convergence time in these two

structures however are not conclusive.

Overall, our results highlight that the e�ect of misalignments on a PD project's performance is

mediated by the organizational structure. Managing subsystems' interactions and teams' communi-

cations are more important when design alternatives are evaluated in a polyarchy to bridge the gap

in performance in comparison to an aligned project.

Subsystems in a complex product have various levels of interdependencies. Some subsystems a�ect

the performance of many other subsystems or are a�ected by them. In other words, there is asym-

metry in the degree of in�uence that subsystems exert on each other (Strogatz 2001, Rivkin and

Siggelkow 2007); hence it is possible to place these systems (and their respective PD teams) on a

�centrality scale� whereby a subsystem/team with dense interdependencies scores high while one

with sparse interdependencies scores low. We employ a simple rule to develop this centrality scale

in our model and then address a second research question [2] At what level of centrality do mis-

alignments most a�ect the performance of PD teams? In a hierarchical decision-making structure, a

misalignment focus at subsystems of medium centrality reduces the performance of the PD project

but that at the high level does not deteriorate the performance. In a polyarchy, a misalignment focus

at subsystems of high centrality is the most detrimental to the performance of the PD project in

comparison to an aligned system. Given the decision-making structure, our results clearly indicate

how managers should allocate limited resources in managing misalignments in PD projects. Mis-

alignments are inconsequential in a hierarchy if they occur at the level of high-centrality subsystems.

Time and resources should be invested to identify and attend to mismatches among subsystems of

medium or low centrality. In contrast, the nature of decision making in a polyarchy renders mis-

matches at the high level critical to the quality and convergence time of the project which then

require closer monitoring by design teams.

These results shed light on the Airbus A380 design issues. The design and development of di�erent

subsystems of A380 was distributed among more than 200 �rst-tier suppliers across multiple coun-

tries. Such large-scale projects are generally organized in a polyarchy in which, as we �nd, misalign-

ments at the level of high-centrality subsystems (such as the wiring system) are most problematic to


the performance of the project. This insight is in line with the empirical �nding by Gokpinar et al.

(2013) that geographically-distributed vehicle development projects yield lower quality designs and

are often delayed and that higher-centrality of a subsystem worsens these issues.

In summary, our results yield several managerial insights on the allocation of scarce resources in

developing new products. Whether misalignments worsen the performance of a PD project depends

on the decision-making structure in the project. Hierarchical structures appear more e�ective in

managing misalignments and help achieve performance levels comparable to a project without mis-

alignments. However, misalignments in polyarchical structures considerably worsen the performance

of the PD project when compared to an aligned system. Moreover, we �nd that misalignments in

subsystems of lower centrality cause more problems in hierarchical structure while the opposite is

true in polyarchical structures.

The paper proceeds as follows. Section 2 provides a review of the relevant work. Section 3 describes

the mathematical model as well as conceptualization of the search process and of the two types of

misalignment. In that section we also de�ne the errors and the convergence characteristics that we

investigate. In Section 4 we detail the experiments and report the results. Section 5 discusses the

limitations of this research and concludes the paper.

2. Literature Review

Complex systems are �made up of a large number of parts that interact in a nonsimple way� (Simon

1962). In order to manage these systems, organizations divide them into a number of subsystems

that are handled by individuals or teams. Yet boundedly rational decision makers inevitably overlook

some relevant variables and their interactions (Schrader et al. 1993, Sommer and Loch 2004). Fur-

thermore, individuals and teams may lack full coordination and may also use obsolete information

about other subsystems when solving their own problems (Mihm et al. 2003, 2010).

To achieve coordination, it is natural to expect that organizational communications should occur

whenever there is a technical interaction (Le and Panchal 2012). This approach looks at what

is known as socio-technical coordination and measures the alignment between organizational and

product architectures by socio-technical congruence. Kwan et al. (2011) �nd that high socio-technical

congruence leads to a higher successful build rate for collocated teams but not for distributed teams.

Cataldo and Herbsleb (2013) investigate two large-scale software development projects and �nd that

low congruence increases software failures. They also report an association between high congruence

and improved development productivity.

Other studies investigate the mirroring hypothesis according to which there is a match between

the two architectures (Colfer and Baldwin 2016, MacCormack et al. 2012). The empirical �ndings

are mixed for this hypothesis. Colfer and Baldwin review 142 empirical studies and �nd that about


two thirds of this sample support the mirroring hypothesis; however it is rejected in other cases

where, for instance �collocated, highly interactive teams within a single �rm designed a modular

system made up of independent components� or �in some cases, tight-knit teams can `break the

mirror' and create modular technical architectures that do not re�ect their own communication

patterns�. As one might expect, the hypothesis �nds support mainly in projects run within a �rm

or across a few �rms but typically fails in open, collaborative projects.

Empirical studies on complex product development projects also report misaligned product and

organizational architectures. Sosa et al. (2004) investigate product and organizational architectures

of a large commercial aircraft engine development and �nd that both critical and noncritical inter-

actions may be unknown to PD teams. They argue that, although the performance implications

of such unknown interactions may be low, they can result in considerable extra expenditure dur-

ing each airplane's lifespan. Gokpinar et al. (2010) quantify the mismatches between product and

organizational architectures in an auto manufacturer by using a �coordination de�cit� metric. They

�nd an inverse-U relationship between product quality (as measured by the number of warranty

claims) and a subsystem's centrality in the product architecture. That is, subsystems of intermediate

complexity cause more quality problems. In a subsequent study, Gokpinar et al. (2013) �nd that

geographically-distributed vehicle development projects yields lower quality designs and are often

delayed. They also �nd that higher-centrality of a subsystem worsens these issues.

These observations are consistent with our �ndings if one can argue that globally-distributed

development teams are more likely to be organized in polyarchical decision-making structures. Our

results show that in a polyarchy, misalignments at the level of higher centrality subsystems cause

more performance loss�lower quality and longer convergence time�than misalignments at the level

of medium-centrality subsystems. We observe the reverse in PD projects with hierarchical decision

making such that misalignments at the medium-centrality subsystems result is lower quality designs

than those at the high-centrality subsystems.

Sosa et al. (2007) propose two di�erent types of misalignments in the design and development of

complex products. On the one hand, unmatched interfaces occur when the designers of two subsys-

tems do not have organizational ties (i.e., do not communicate even though the two subsystems are

functionally interactive). On the other hand, unmatched interactions occur when PD teams of two

unrelated subsystems nonetheless interact. We refer to unmatched interfaces as hidden dependencies

and to unmatched interactions as spurious communications.

With hidden dependencies, the lack of communication between teams on these dependencies can

cause two problems. First, because of interdependencies among subsystems, the overall performance

depends on how well the teams can assess the consequences of their decisions on other teams'

decisions. This dynamic is re�ected in the notion of teams' payo� functions being dependent on the


�trans-specialty understanding� (Postrel 2002). Such understanding helps members of one specialty

assess the role played by other specialties in solving a problem, which increases the odds that a

team's decisions will be aligned with those of other teams for the bene�t of the overall project.

Second, �glitches� occur often in product development projects (Hoopes and Postrel 1999, Hoopes

2001). A glitch is a costly mistake that may occur in a multi-agent project owing to lack of shared

knowledge about problem constraints. Glitches are not limited to highly complex projects. Hoopes

and Postrel provide an example of a new executive information software which took the design-

ers months to create with the capability to generate reports for di�erent categories of customers,

products, and years. When the design was being coded by programmers however, they realized that

the relevant databases could not be searched for products. The time spent by designers and pro-

grammers to solve that problem makes this mistake a costly glitch. In short, hidden dependencies

are likely to degrade the performance of PD teams through either the reduction of trans-specialty

understanding or by causing glitches.

Spurious communication among PD teams exposes them to new ideas and may establish infor-

mal communication channels that managers and designers in charge of developing subsystems �nd

useful in the PD process. It however increases the teams' workload, which in turn may increase the

error rate and create unexpected problems (Rahmandad and Repenning 2008). The extra workload

alters the dynamics and expected performance of PD projects through �re�ghting: the allocation

of scarce resources to unexpected problems (Repenning et al. 2001, Repenning 2001). Operating in

a �re�ghting mode causes rework that leads to budget and cost overruns. Spurious communication

increases the PD teams' workload; hence it is likely to generate more ��res� or unexpected problems,

which has a negative e�ect on the performance of product development projects.

Although one may expect misalignments in product and organizational architectures to degrade

complex PD performance, the literature is unclear on extent of this e�ect. Much research on dis-

tributed design (Mihm et al. 2003, Braha and Bar-Yam 2007, Mihm et al. 2010) and on distributed

search in complex systems (Lazer and Friedman 2007, Baumann 2015) implicitly assumes that

product and organization architectures are aligned. Some authors do acknowledge the existence

of misalignments and their negative consequences (e.g., Sosa et al. (2004, 2007), Gokpinar et al.

(2010)). Yet our paper is the �rst to model a PD project to explicitly study misalignments and their

consequences as a function of organizational decision-making structure, interaction patterns among

product subsystems, managerial decision making capabilities, and the number of teams involved in

the development process. Our results show that misalignments are not always detrimental to the

performance of PD projects.

We study two decision-making structures: hierarchy and polyarchy. Hierarchical structures mainly

shrink convergence time while polyarchical structures typically results in higher quality designs


(Rivkin and Siggelkow 2003, Siggelkow and Rivkin 2005, Mihm et al. 2010). We also consider two

subsystem interaction patterns: cyclical and acyclical which have been empirically observed in PD

projects (MacCormack et al. 2006, Baldwin et al. 2014). These interaction patterns capture how

strongly a subsystem depends on itself through other subsystems. A lack of product architectural

knowledge results in highly cyclical interaction patterns (Sosa et al. 2013).

We further contribute to the literature by studying misalignments in conjunction with a subsys-

tem's centrality in the product architecture. The concept of subsystem centrality has been studied

under di�erent names in the literature. Rivkin and Siggelkow (2007) characterize asymmetric inter-

action patterns (e.g., preferential attachment, scale-free, and centralized) in complex organizations

and products. Sosa et al. (2011) develop a methodology of identifying a product architecture's

�hubs��that is, those subsystems with a �disproportional number of linkages�. Baldwin et al. (2014)

study the �core-periphery� structure in a sample of software development projects. Tushman and

Murmann (1998) observe that �products are composed of hierarchically ordered subsystems�, cat-

egorizing some of them as core and others as peripheral. In this paper, we use the term centrality

to conceptualize the asymmetric in�uence of di�erent subsystems in the architecture of a complex

system. In particular, we study whether the relative centrality of a subsystem in which misalignment

occurs has a signi�cant e�ect on the performance of the PD project.

We model the product development process as search on a rugged landscape by teams that

conduct local search until a local peak is obtained. An early paper using this approach in opera-

tions management was Mihm et al. (2003) in which the authors model a distributed design project

with interdependent subsystems. Their results illustrate that nonlinearity and complexity are both

increasing in the size of the system. Mihm et al. (2010) employ a similar model to investigate the

e�ects of organizational hierarchy on solution quality, stability, and speed in distributed search

projects. Baumann (2015) identi�es contingency factors that in�uence the value of integration among

decentralized searchers in a complex system. These studies, too, implicitly assume aligned product

and organizational architectures.

Finally, the result of our simulated search process at any time is represented by a �tness value. This

concept was �rst developed by Kau�man (1993) in the biology literature, in which a �tness landscape

function is conceived for a set of complex interactive elements governed by a number of agents.

The idea was incorporated into the engineering design and management literature by Levinthal and

Warglien (1999), Gavetti and Levinthal (2000), Rivkin (2000), and Rivkin and Siggelkow (2003). In

the next section, we elaborate on the concept of perceived versus real landscape functions and also

establish the �tness value of a subsystem on each type of landscape.


3. Model

In this section we set up the mathematical model to simulate the search process. The model has

four components: (i) characterization of the landscapes over which the teams search, (ii) the orga-

nizational structure within which the search teams and managers operate, (iii) a conceptualization

of misalignment forms, (iv) a de�nition of subsystem centrality in the product architecture, and

(v) the characterization of the search convergence. We discuss each component and describe the

measures we use to evaluate the performance of the search teams. We then formulate our hypotheses

on how misalignments a�ect the performance of the search process where performance is de�ned in

two dimensions as the quality of the �nal design and the convergence time.

3.1. The Landscape Model

Consider a product with n subsystems in which team i ∈ {1,2, . . . , n} is responsible for developing

subsystem si. We model the performance of team i at time t as the outcome of a search process over

the landscape of subsystem si. In the NK(C) terminology, the landscape of subsystem si consists of

ne interacting binary elements that are in state 0 or state 1 at any given time. The total number of

elements for n subsystems is thus N = nen.1

The state of subsystem si at time t is known when the states of its ne elements are known. Each

team has 2ne di�erent design states. For example, the state of team i at time t when ne = 5 might

be sit = (00110).

The state of subsystem si at time t is represented by a �tness value, f it , which is the average of

the contributions of its ne elements. Denote the contribution of element j of team i at time t by

f it (eijt ); then

F it =

∑nej=1 f

it (e

ijt )

ne. (1)

We need three ingredients to de�ne f it (eijt ): (i) the state of the element itself at time t, e

ijt , (ii)

the state of K other elements of team i that interact with element eij, and (iii) the state of all the

other elements of other teams that interact with element eij. The second ingredient captures the

idea that the elements under a team's control are interdependent; in particular, the contribution

of one element depends on the status of K other elements. The third ingredient is the idea that

subsystems are interdependent and so the �tness value of element eij depends on the C elements

of each subsystem that interacts with subsystem i. Denote the set of subsystems interacting with

subsystem i as DEi. For instance, if subsystem i interacts with three other subsystems and if C = 2,

then the contribution of eijt depends on 3× 2 = 6 elements under the control of those three teams.

1We assume that all subsystems have the same number of elements ne.


The �rst stage of the NK(C) model is generating the interaction patterns among the elements

which we will describe in detail in Section 4. The second stage of the NK(C) model involves generat-

ing the landscape function. Since element eij interacts with K+ |DEi|×C other elements, it follows

that there are 2K+|DEi|×C possible contribution values. The contribution of element eij at time t is

drawn from a uniform [0,1] distribution. We remark that the properties of the �tness landscape are

not sensitive to the distribution applied to generate the landscape (Weinberger 1991).

The third stage in the NK(C) model is characterization of the search process on the landscape

which depends on the organization structure and interaction patterns among search teams. We

describe these in detail in Sections 3.2 and 4.

3.2. Organizational Structure in the NK(C) Search Model

Firms di�er in their organizational structure: �[t]he structure of an organization can be de�ned

simply as the sum total of the ways in which it divides its labor into distinct tasks and then

achieves coordination among them� (Mintzberg 1979). Therefore, di�erent organizational designs

and structures exist which a�ect the �rms' approach to product development. We consider two

design variations on how the decisions are made in an organization: polyarchy and hierarchy. In a

polyarchy several independent decision makers can undertake projects or ideas while in a hierarchy,

decision making is more concentrated and only a few managers can accept or reject projects (Sah

and Stiglitz 1986). In other words, if any of the managers in a polyarchy accepts an idea, that

idea goes through further development while in a hierarchy even if one manager rejects the idea,

that idea is removed from the consideration set. The distinction between these two decision making

structures helps us to test for any association between the misalignments and the decision-making

structure. We next describe how we operationalize this distinction between the two structures in

our study.

We model the alternative generation and selection process similar to (Siggelkow and Rivkin 2005).

At time t= 0, each team is randomly assigned a state and the team's �tness value is calculated. At

each subsequent time t, the teams perform local search by changing one (or more) of their elements'

states from 0 to 1 or vice versa. This local search results in q≥ 1 alternatives. The status quo is also

one of the alternatives. These alternatives do not necessarily improve the �tness value of the team

because they are generated given the status quo of other teams. However, the alternative may prove

valuable once other teams change their status. This procedure introduces an �exploration� aspect

to teams' search whereby they take some risk in experimentation which may help them escape local

optima and �nd better peaks in their search landscapes.

After receiving the proposals from the teams, the PD project manager creates Q composite

alternatives and evaluates them. These composites consider all the alternatives proposed by teams.


For example, if there are four PD teams and each one proposes three alternatives, the manager has

34 = 81 composite alternatives. In a polyarchy, all these alternatives are eligible design proposals

among which the manager chooses Q randomly and evaluates them. This evaluation takes into

account the performance of all teams and not just one team. She selects the one composite alternative

that improves the overall �tness value the most. If none of the composite alternatives improves the

overall �tness value of the project, then all teams retain their status quo.

In a hierarchy, the project manager considers only those alternatives proposed by a team that

improve the �tness value of all the other teams (or leave them unchanged). That is, if an alternative

reduces the �tness value of any team it is eliminated from the consideration set. Consider our

previous example with four teams each proposing three alternatives. Assume team one and team

two have each only one alternative that improves the �tness value of all teams while all the proposals

of teams three and four are so. Therefore, the project manager considers Q alternatives out of

only 1× 1× 3× 3 = 9 composite alternatives. Among Q alternatives, the one that improves theperformance of the project the most is chosen.

3.3. Misalignment Forms in the NK(C) Search Model

Resources (e.g., time, human expertise, and funds) available to teams to manage the interfaces of

their subsystems are limited. One may expect that these resources are optimally allocated to the

existing and well-understood interfaces. In a complex NPD project however a team's performance

and reward depends highly on other teams; an instance of what Puranam et al. (2012) call broad

incentives which, they show, result in a link between two subsystems being neither necessary nor

su�cient for the teams in charge of them to interact or, even if they do, dedicate the optimal level

of resources. Misalignments then happen when there is a missing link between teams in charge of

interacting subsystems or when teams interact even though their respective subsystems are not

linked.

In the absence of misalignments, a team knows the states of all the interdependent teams' elements

and conducts an informed local search. A PD team in a project without misalignments has an

appropriate and balanced allocation of resources to within and between subsystems interactions.

However, no misalignments in a complex PD project represents an ideal scenario because it requires

a substantial amount of resources, instantaneous information broadcast, and a rigourous control

system (Mihm et al. 2003, Gokpinar et al. 2010). Misalignments distort the allocation of resources

and, as a result, a team may be more focused on managing the interactions among its own elements

or that among its elements and those of other teams. We next explain the dynamics of resource

allocation and misalignment occurrence formally.

Let Rii′indicate the actual amount of resources that team i allocates to its elements' interactions

with those of team i′. For i= i′, the value Rii indicates the resources that team i spends to attend


to its within-subsystem interactions. De�ne two values R̃ii and R̃ii′as the amount of resources to

within- and between-subsystem interactions of subsystem si, respectively, in an aligned project.

In the aligned system the probability that the interactions (within and between) of subsystem

si are unattended is pD = 0. That is, when the PD system is aligned (i.e., Rii′= R̃ii

′), we have

pii′= pii = 0 where pii

′is the probability that one of the interactions between subsystems si and si

′

is left unattended and pii is the corresponding probability for a within-subsystem interaction.

In the event of hidden dependencies, a PD team makes its design decisions with incomplete

knowledge of the current states of its interdependent teams. The team might be unaware of the

interdependencies, use outdated information, or simply ignore the connections. We suggest therefore

that hidden dependencies occur when teams tend to focus their resources on within-subsystem

interactions and so are more likely to leave some between-subsystem interactions unattended. To

model this dynamic, we assume that, at any time t, team i fails to attend to its interface with one

subsystem chosen randomly from the set of interdependent subsystems with subsystem si. All the

other interfaces with other teams are considered aligned and attended to.

Formally, there are C interactions between an element of subsystem si with that of interdependent

team i′, and hence there are C × ne interactions between the subsystems' elements. A hidden

dependency occurs when team i allocates insu�cient resourcesRii′< R̃ii

′to attend to its interactions

with team i′. We posit that the interface between two subsystems i and i′ is overlooked by the

corresponding teams with some probability. In other words, the teams are aware of the interface

but fail, with some probability, to discuss the interdependency. This has two consequences: (i) it

leaves more resources to attend to within-subsystem interactions of subsystem si which lowers the

likelihood of these interactions be unattended (i.e., pii = pD = 0); (ii) it increases the probability of

between-subsystem interactions of subsystem si with si′be unattended (i.e., pii

′> pD). To capture

(ii), we increase (homogenously) the probability with which each C × ne interactions between si

and si′is overlooked at time t from pD to a considerably higher level (e.g., to 0.99 which e�ectively

means the interface is overlooked). Our results are not sensitive to this approach because K and C

parameters in our experiments are relatively small. Further, experimentation with other approaches

to distort probabilities reveals no signi�cant shift in results.

Other between-subsystem interactions of si remain aligned at time t (i.e., at time t, the probability

of these interactions being unattended at time t is pii′′= pD = 0 for all i

′′ 6= {i, i′}). This process

is time-variant and, at time t+ 1, another subsystem may be misaligned with subsystem si. We

assume that pii′is time-invariant in the simulation model (in Section 4, we describe the process to

generate these probabilities).

Hidden dependencies result is team i conducting search over a landscape that di�ers from the

real one (i.e., the landscape without misalignments or one in which the occurrence of misalignments


is at a prede�ned level). We refer to this landscape as the �perceived� landscape and denote the

�tness value achieved by team i at time t on the perceived landscape as F i,hdt (where `hd' stands

for hidden dependency).

Spurious communications occur when two teams interact even though there is no interface between

their corresponding subsystems. Such communication between the two teams might anchor them

on irrelevant design ideas, lead to information overload, or divert the limited available time and

attention to unrelated issues. Similar to hidden dependencies, we model the occurrence of spurious

communications as a dynamic process whereby at any time t a subsystem si′is randomly selected

among the teams whose subsystems have no interface with si. This communication channel between

the two teams absorbs resources that should have been used to attend to within-subsystem inter-

actions of subsystem si which implies an increase in the likelihood of within-subsystem interactions

being left unattended (i.e., pii > pD).

Spurious communications distort the search landscape. We denote the �tness value of team i in

the presence of spurious communications as F i,sct (here `sc' stands for spurious communications).

3.4. Subsystem Centrality in the NK(C) Search Model

We assign a subsystem i (and its corresponding team) to a high, medium or low centrality level in

terms of a measure based on how many teams a�ect the �tness value of team i, i.e., |DEi|, and how

many teams' �tness values are a�ected by team i, i.e., |SIi|. Therefore, mi = |DEi|+ |SIi| captures

the overall in�uence of team i in the space of a complex PD project. We can then put all teams in

a descending order such that team i has a higher centrality level than team i+1 if mi >mi+1. We

de�ne three centrality levels as follows: team i is of high centrality if i < n3+1, medium if n

3≤ i < 2n

3,

and low otherwise. If we �nd two teams with the same measure m, then we consider the one with

a higher |SIi| as one with a higher centrality level. We will showcase how this allocation works in

Section 4.

3.5. Misaligned PD Teams in the NK(C) Search Model

To address our second research question�the level of centrality at which misalignments most a�ect

PD teams' performance�we adopt an abstract perspective toward misalignments and do not di�er-

entiate between the forms, that is, either form of misalignments can occur between interdependent

teams. Once we have assigned teams to centrality levels, we choose a level and create a misalignment

focus at that level. That means the teams at that level will be more likely to have misalignments of

either type with other (interdependent) teams.

To model the occurrence of misalignments between subsystems si and si′at time t, we draw

a random number in [0,1] and if this number is larger than 0.5 we create a hidden dependency;

otherwise, a spurious communication happens. This procedure guarantees that the misalignment


type is random and the results we report in Experiment 2 (Section 4.2) are not driven by a particular

type of misalignment.

3.6. Convergence in the NK(C) Search Model

Misalignments not only a�ect the �nal quality of a PD project, but also a�ect the convergence of the

search process. Convergence occurs whenever no team can increase its �tness value by further local

search�that is, when a locally optimal design has been reached (Mihm et al. 2003). To operationalize

the convergence behavior in a PD project, we follow Siggelkow and Rivkin (2005) and assume

convergence occurs when we observe status stability for all teams for a certain amount of time (i.e.,

2% or 4% of simulation time). That means, at each time t, we compare the status of all teams for

the past 2% (or 4%) of simulation time and if we �nd no change for any team, then we record t+1

as the convergence time; otherwise we continue the search process. We choose this approach for two

reasons: (i) it assures, given the status of other teams, every team has obtained a local optimum

in its respective search landscape, (ii) in practice, time itself is a limited resource. If the design

process does not converge in a reasonable amount of time, then project managers may remedy the

situation by, for example, reverting to previous designs or freezing the design of some teams and

letting others to continue the search until convergence (Mihm et al. 2003).

We report the results on convergence time in Section 4.3.

4. Experiments and Results

In this section, we describe the experimental setup and report the results. We �rst detail the sim-

ulation procedure and ingredients; then we discuss results of the three experiments outlined in

Section 3. The parameter N in the NK(C) simulation model is the total number of elements in

the landscape, so N = n × ne. In the literature on complex landscape simulations, this number

varies from 6 to 12 (see e.g., Rivkin and Siggelkow 2003, Siggelkow and Levinthal 2003, Rivkin

and Siggelkow 2007, Baumann 2013). In our experiments, we assume that the project organization

consists of three teams and that each team controls �ve elements; hence N = 3× 5 = 15. We also

study a 5-team project organization with each team controlling 3 elements. Our centrality-based

categorization of subsystems (see Section 3) allows for at least one team at each level of centrality.

Subsystems in a PD project may relate to each other in di�erent architectures (patterns). Figures

1 and 2 show the two patterns we use in our experiments for three and �ve teams, respectively.

Cyclical (or centralized) pattern is a concept also referred to as �core-periphery� in some studies of

development projects. Further, what we refer to as acyclical pattern is also known as hierarchical

pattern (MacCormack et al. 2006, 2012, Baldwin et al. 2014).2 These two patterns capture the

2We use this term in line with (Sosa et al. 2013) to avoid any confusion with the concept of hierarchical decisionmaking-structure which is a key feature in the our studies.


extent to which each subsystem depends on itself via other subsystems (Sosa et al. 2013). In a

cyclical pattern, there is a high degree of cyclicality and one team's design decisions a�ect its own

search landscape also via its impact on other teams' search landscape. This phenomenon is absent

in an acyclical subsystem interaction pattern.

Table 1 Interaction network among three teams

PD Team 1 2 31 4 4 42 4 43 4 4 4

Table 1 Cyclical

PD Team 1 2 31 42 4 43 4 4 4

Table 1 Acyclical

Table 2 Interaction network among �ve teams

PD Team 1 2 3 4 51 4 4 4 4 42 4 4 4 4 43 4 4 4 44 4 4 4 45 4 4 4Table 2 Cyclical

PD Team 1 2 3 4 51 42 4 43 4 4 44 4 4 4 45 4 4 4 4 4Table 2 Acyclical

The concept of subsystem centrality helps us to study the e�ect of misalignments as a function

of the centrality of teams. The allocation procedure we described in Section 3.4 now implies that

with three teams, team 1 is of high, team 2 medium, and team 3 low centrality. This holds for both

cyclical and acyclical network interactions. To see this, observe that in the cyclical structure, we

have m1 = 4,m2 = 3,m3 = 3. Because, 1 < 33+ 1, 3

3+ 1 ≤ 2 < 2×3

3+ 1, and �nally 2×3

3+ 1


Many complex products are nearly-decomposable or modular, that is, they can be decomposed

into subsystems which have weak interactions (Simon 1962). In other words, the subsystems are

loosely coupled together. We focus on nearly-decomposable systems in our model and choose the

parameters K and C to mirror these systems. In particular, modular products have a high level

of interactions among the elements of subsystems (a relatively high K value) while the elements

of di�erent subsystems have a low level of interactions (a relatively low C value). An element of

a team has K = ne− 1 interactions with the other elements of the team. Therefore, with 3 teams,

K = 2 and with 5 teams, K = 4. Also, we let the parameter C = 1 to capture the low number of

interactions between an element of one team with those of another team. The ratio CK

can be an

indicator of the level of modularity/decomposability. With three teams, that ratio is 12= 0.5 and,

with �ve teams, it is 14= 0.25. A high value for the ratio C

Kindicates low modularity and a low value

is indicative of high modularity.

The values we choose for parameters K and C as well as the interaction patterns among the

subsystems' elements represent plausible PD systems in the automotive, printing, semiconductor,

and power plant industries; see Table 1 in Rivkin and Siggelkow (2007) who �nd that the average

number of interactions among the elements of a subsystem is in the range [1.4,6.8]. In the same

line, the average number of interactions for each element in the PD systems we study are: (i)(3×4×5)+6=66

15= 4.4 for three teams and cyclical interaction, (ii) 63

15= 4.2 for three teams and acyclical

interaction, (iii) 4615

= 3.6 for �ve teams and cyclical interaction, and (iv) 3815

= 2.5 for �ve teams and

acyclical interaction.

The ruggedness of the search landscape depends on K and C as well as the interaction pattern

among the subsystems. Low values for the number of interactions per element imply that the

contribution of one element is rather limited and independent of the other elements; hence the

landscape is relatively smooth and a change in the state of one element does not signi�cantly a�ect

the �tness of others. At the extreme, the NK(C) landscape with entirely independent elements

(K = C = 0) has a single peak and so, unless the system has already reached that peak, �tness

can be improved from any position in the landscape. Incremental search in such landscapes may

eventually converge to the global optimum. However, if the number of interactions per element is

high, then the �tness landscape becomes more rugged; here a change in the state of one element may

have a signi�cant e�ect on the �tness values of other elements. In these landscapes, an incremental

search process may stop at a local optimum. Our setup�with the average number of interactions

per elements varying in [2.5,4.4]�then captures both smooth and rugged landscapes.

In terms of organizational decision making, we consider two arrangements: polyarchy and hier-

archy. We assume that each team proposes two alternatives in each stage of the search. In a PD

project with three teams, this means a maximum of 23 = 8 composite alternatives are available. We


consider two levels of managerial decision making capability in evaluating these alternatives: the

number of composite alternatives that are evaluated is either 2 to re�ect low or 5 to re�ect high

processing powers in the managerial team.

When the PD project consists of 5 teams, we assume 8 and 20 composite alternatives are evaluated.

We chose the number of composite alternatives in the three-team and �ve-team project structures

proportionally, that is, the managerial team evaluates 223

= 825

or 523

= 2025

fraction of the composite

alternatives.

We next elaborate on the dynamics of interaction between teams�that is, the distribution of

misalignments among teams characterized by the probability pii′. These probabilities capture the

likelihood of two teams (possibly at two di�erent centrality levels) having a misalignment. Our �rst

research question focuses on the misalignment types and their e�ect of a PD project's performance.

In addressing this question, we disregard the centrality level of teams in which misalignments hap-

pen. For instance, assume the PD project has three teams who interact in a centralized pattern and

assume at time t, we choose team 1 to have a misalignment. This misalignment may happen in its

interface with team 2 or team 3 randomly.

Our second research question investigates the e�ects of misalignments as a function of the cen-

trality of teams whose interfaces are misaligned. In this case, we do not distinguish between mis-

alignments types but change the way we distribute the probability of having misaligned interface

to make sure they have a locus at a certain centrality level.

4.1. Experiment 1: Misalignment Forms and Product Quality

Misalignment forms may di�er in their e�ects on the performance of PD projects. In our �rst set

of experiments, we investigate how the two types of misalignment a�ect the performance. Can it

ever be that misalignments of either type actually improve the performance in comparison with an

aligned system?

We compare the performance of an aligned PD project with two possible materialization of

misalignments: (i) a PD project with hidden dependencies, and (ii) a PD project with spurious

communications. We compare these based on the quality (i.e., the �tness value) of the �nal design.

We simulate each scenario for a �xed number of time periods and record the performance of all

teams. The �nal design quality is the average of the design qualities obtained by all teams once the

search has stopped. Figure 1 shows the performance of the three scenarios under two organizational

decision-making structures (hierarchy and polyarchy) and subsystems' interaction patterns (cyclical

and acyclical).

For each combination (organizational decision-making structure and subsystems' interaction pat-

tern), we generate 200 landscapes. For each landscape, we create the corresponding PD project


scenario (aligned, with hidden dependencies, and with spurious communications) and let the teams

conduct the search process for 500 simulated time periods which is su�cient, in our settings, because

by the end of the simulation, all projects achieve stability in their performance. This process is

repeated for each of the 200 landscapes. The average performance at each simulation time is the

average performance at that time period across all landscapes.

Panels (a) and (c) in Figure 1 show that in a hierarchy, and regardless of subsystems' interaction

pattern, PD projects achieve similar performances no matter which misalignment type exists in the

projects. In a polyarchy, performance di�ers across interaction patterns. With cyclical interactions,

teams with hidden dependencies and spurious communications appear to converge to similar design

qualities. In contrast, with acyclical subsystem interactions, projects with hidden dependencies

achieve higher quality designs than those with spurious communications.

Across all the panels in Figure 1, the aligned system achieves a higher performance indicating

that misalignments of either type have an adverse e�ect on the performance. Taking the perfor-

mance of the aligned system as a reference in a hierarchy (respectively, polyarchy), we observe that

misalignments have a stronger negative e�ect on the design quality when decisions are made in a

polyarchy rather than in a hierarchy.

Comparisons across organizational structures provides further interesting insights. Given the

interaction pattern (cyclical or acyclical), misalignments have stronger negative consequences on

the performance in a hierarchy than in a polyarchy. This �nding corroborates that in (Knudsen

and Levinthal 2007) where agents with moderate/high imperfectness in evaluating alternatives �nd

better solutions when organized in a polyarchy rather than hierarchy.

These observations are con�rmed by paired t-tests to statistically compare performances across

projects. Because each type (aligned, with hidden dependencies, and with spurious communications)

is simulated on the same landscape as other types, the observations in one sample (e.g., performance

of a project with hidden dependencies) can be paired with observations in another sample (e.g.,

performance of a project with spurious communications). As project's performance oscillates over

time, we used the average PD performance in the last 25 time periods as performance measure in our

statistical tests. The null hypothesis for the �rst set of paired t-tests is that the mean of performance

of a system with hidden dependencies is equal to that of a system with spurious communications:

Hypothesis 1. PD systems with hidden dependencies achieve a higher performance than those

with spurious communications.

Spurious communications are argued to have less disruptive e�ects than hidden dependencies

(Sosa et al. 2015). However, these arguments consider dyad or triad subsystems which may not be

the case for PD projects with many subsystems whose interactions have varying degrees of criticality


(a) Hierarchy, Cyclical interaction (b) Polyarchy, Cyclical interaction

(c) Hierarchy, Acyclical interaction (d) Polyarchy, Acyclical interaction

Figure 1 The average performance for aligned (blue), with hidden dependencies (red), and with spurious

communications (green) PD projects. In this �gure, n= 3, ne = 5, q= 2 and Q= 5.

or strength. For example, consider the project with four subsystems in Figure 2 and assume that

the strength of interactions is weak for A-B, strong for B-D, and medium for C-D (the thickness of

the lines between subsystems re�ects strength). It may appear that the hidden dependency between

teams A and B is potentially more harmful than spurious communication between teams B and C.

However, spurious communication between teams B and C can alleviate the e�ect of the hidden

dependency between teams B and D which have interactions of high criticality. Hence, if team B

focuses its e�orts to manage its spurious communication with team C, the system will achieve a

higher performance than when it focuses on the hidden dependency it has with team A.

The test results for Hypothesis 1 are in Table 3.3 Clearly, in a polyarchy and with acyclical

subsystem interaction pattern, projects with hidden dependencies result in higher design qualities

3We use 1, 2, and 3 starts to indicate 10%, 5%, and 1% signi�cance levels, respectively.


Figure 2 A PD project with four subsystems.

than those with spurious communications. This result is robust and holds across our experiments

with three and �ve teams and low/high managerial decision-making capabilities. When subsystems

interact acyclically, the performance of some teams is a�ected by few (or none of) other teams (see

e.g. team 1 in Tables 1 and 2). Consequently, with hidden dependencies, those teams' attendance to

their within-team interactions, instead of their subsystems' interactions with other subsystems, is

unlikely to a�ect their performance. In contrast, with spurious communications, these teams attend

more to their subsystems' interactions with other subsystems than their own within-subsystem

interactions, and so their search process is highly in�uenced by other teams.

In a polyarchy, all design combinations are eligible design solutions which intensi�es the above

e�ects. However, a hierarchy curbs these e�ects because a design proposal becomes eligible only

when all other teams also �nd it appealing. As a result, we do not �nd any signi�cant di�erence

between systems with hidden dependencies and spurious communications in a hierarchy.

In summary, our model does not di�erentiate between misalignment forms in their e�ect on the

�nal design quality unless the PD project organization is polyarchical and its subsystems interact

acyclically. Further, we �nd that either form of misalignments reduces the project performance.

We next compare the performance of projects with hidden dependencies and spurious communi-

cations with that of aligned projects. This comparison helps to understand whether and to what

extent misalignments a�ect the PD teams' performance.

Hypothesis 2. Aligned PD projects achieve a higher performance than those with hidden depen-

dencies or spurious communications.

We examine Hypothesis 2 assuming �rst a polyarchical and then a hierarchical decision-making

structure. This results in four possible PD systems (i) a polyarchy with hidden dependencies, (ii)

a polyarchy with spurious communications, (iii) a hierarchy with hidden dependencies, and �nally

(iv) a hierarchy with spurious communications.


Table 3 Paired t-tests comparing performance of PD systems with di�erent misalignment forms. For this table,

q= 2.

Hierarchy Polyarchy Hierarchy PolyarchyH.D. vs. S.P. H.D. vs. S.P. Aligned vs. S.P. Aligned vs. H.D.

Pattern n ne Q t-value t-value t-value t-value

Cyclical

3 5 2 -1.553 -0.859 2.134∗ 9.439∗∗∗

3 5 5 -2.249∗ -0.416 1.129 9.088∗∗∗

5 3 8 -0.434 -0.411 1.681 3.831∗∗∗

5 3 20 -0.19 0.487 2.019∗ 2.996∗∗∗

Acyclical

3 5 2 1.116 2.956∗∗∗ 2.168∗ 7.621∗∗∗

3 5 5 -0.217 6.687∗∗∗ 2.056∗ 3.109∗∗∗

5 3 8 0.17 7.209∗∗∗ 1.653 5.228∗∗∗

5 3 20 0.523 7.859∗∗∗ 2.318∗∗ 4.512∗∗∗

We �nd signi�cant results when comparing aligned projects with those with hidden dependencies

in a polyarchy. We also observe signi�cant results when comparing aligned projects with those with

spurious communications in a hierarchy. For brevity, we report the signi�cant results in Table 3.

The full set of the results are in Appendix. From Table 3, and in a polyarchy, aligned projects

achieve higher quality designs than the projects with hidden dependencies at the α = 0.01 signif-

icance level. Our experiments to compare aligned projects to ones with spurious communications

result in di�erent patterns. Interestingly, misalignments are inconsequential in projects with spuri-

ous communications if decisions are made hierarchically. We observe these performance patterns in

all scenarios with di�erent levels of managers' capability in evaluating the composite alternatives

(i.e., di�erent values of Q), and di�erent modularity levels in product design (that is, for di�erent

values of CK= 1

ne−1).

Our results in Table 3 (and those in Appendix) show that, in comparison to an aligned system,

more performance loss results due to misalignments in a polyarchy, rather than in a hierarchy. We

believe that because every team's proposal is considered eligible by the PD project manager in a

polyarchy, there is no mechanism to curb the e�ects of misalignments. In a hierarchy however man-

agers' e�ort in screening out design proposals that cause performance loss for any team signi�cantly

restrains the potential consequences of misalignments.

4.2. Experiment 2: Misalignments and the E�ect of Centrality

In a second set of experiments, we study whether the e�ect of misalignments on performance depends

on the centrality level at which misalignments occur. We allocate the teams to three centrality levels

(high, medium, and low) based on the intensity of their interactions with other teams (see Section

3.4). Our allocation rule is simple and arbitrary and given the network structure in Tables 1 and

2, resembles a Pareto-like criterion in that one subsystem (i.e., 20% of the teams) is categorized as

highly central. Nonetheless, the rule allows us to answer a critical question: whether the e�ects of

misalignments depend on their centrality locus?


We create three types of PD projects depending on where misalignments are concentrated. In

this section and Section 4.3, we report the results for projects in which misalignments occur at

either high- or medium-centrality teams. We relegate the results with misalignment locus in low-

centrality teams to Appendix. This is because we observe stronger performance implications at high

and medium levels of centrality.

We measure the performance of each type by the �nal design's quality which is the average quality

of �nal designs by all teams in the project. Figure 3 shows the performance of PD projects in di�erent

scenarios. These scenarios are designed based on whether the project is aligned, or is misaligned

with the locus at high or medium levels, and under varying organizational decision-making structure

and subsystems' interaction pattern. In total, there are 8 scenarios (2 organizational structures,

2 subsystem patterns, and 2 project types). For each scenario, we generate 200 landscapes and

simulate it for 500 time periods. At each simulation time, we calculate the average performance of

all landscapes.

Panels (a) and (c) in Figure 3 show that misalignments deteriorate the PD project's performance

to a greater extent (when compared to an aligned project) if decisions are made in polyarchy. With

hierarchical organizational structure, we �nd similar performances for projects with misalignment

locus at di�erent centrality levels. We also observe that, over time, the design quality in a misaligned

project is similar to that of an aligned project no matter where the misalignment locus is. Therefore,

when decisions are made in a hierarchy, misalignments do not result in the deterioration of the

project performance.

Given the subsystem interaction pattern, and comparing panels (a) and (b) or panels (c) and (d),

we also observe that the �nal design's quality is superior in a polyarchy than in a hierarchy. This is

attributable to the exploratory nature of search in a polyarchical organization.

To test our observations, we conduct paired t-tests to statistically compare the performance of

di�erent project types. Here we use the average of PD performance in the last 25 time periods as a

performance measure. Formally, the hypothesis is:

Hypothesis 3. PD projects with misalignment locus at high-centrality subsystems achieve a

higher performance than those with misalignment locus at medium-centrality subsystems.

The test results are in Table 4. In a polyarchy and with more divisionalized organizational struc-

ture (that is, �ve teams rather than three), Hypothesis 3 is rejected at the α = 0.01 signi�cance

level.

With hierarchical decision-making, and regardless of subsystem interaction pattern, we reject the

null hypothesis 3. In other words, projects with misalignment locus at high and medium centrality

levels yield similar performances. The only exception to this result is when the project organization


(a) Hierarchy, Cyclical interaction (b) Polyarchy, Cyclical interaction

(c) Hierarchy, Acyclical interaction (d) Polyarchy, Acyclical interaction

Figure 3 The performance of aligned (blue), or misaligned with the locus at high (red) and medium (green) levels.

Each point presents the average performance of 200 simulation experiments. In this �gure, n= 3, ne = 5, q= 2 and

Q= 5.

is more divisionalized, and with higher managerial capability (that is, when Q= 20). Under these

conditions, we cannot reject Hypothesis 3. These results con�rm the empirical �ndings that subsys-

tems with intermediate complexity (subsystems with medium centrality levels) are associated with

more quality problems in the vehicle development projects (Gokpinar et al. 2010).

Similar to our results for Hypothesis 1 in Section 4.1, we also �nd that misalignments exert

stronger e�ects in a polyarchy than in a hierarchy. This is because the more selective approach to

team proposals dampens the misalignments e�ects in a hierarchy.

Moreover, we see stronger results for more divisionalized projects and when managers' capability

is higher, that is, when they can evaluate more alternatives in each search stage. Both of these

conditions are known to increase the number of sticking points in the search landscape. The search

process may come to rest at sticking points that di�er from the organizational landscape's local


optima (Rivkin and Siggelkow 2002). In our setup, each team changes its subsystem design and

proposes design solutions to a PD manager who applies certain rules to choose among these proposals

(e.g., in a hierarchy the composite proposal must improve all teams' �tness values or is eliminated).

A sticking point then is an equilibrium in the game between PD managers and teams from which

there is no incentive to deviate despite the fact that it may not be a local optimum.

In our model, the set of local optima is the same in all the experiments because we keep the

landscape unchanged but change the type of misalignments or their centrality level. But the set

of sticking points changes with the number of teams involved or the capability of the managers.

Therefore, depending on these factors, the performance of two misaligned (or misaligned and aligned)

systems depends on how di�erent the corresponding sets of sticking points are.

Any point on the design landscape that is a sticking point in a polyarchy is also a sticking point

for the corresponding hierarchical system. However, the opposite is not true4. Thus, the number

of sticking points is higher in a polyarchy system than the hierarchical system. Hence, we observe

more performance variations of misaligned systems in polyarchy arrangements.

Table 4 Paired t-tests comparing performance of PD systems with misalignments at the high- and

medium-centrality levels. For this table, q= 2.

Inputs Hierarchy Polyarchy Hierarchy PolyarchyHigh vs. Medium High vs. Medium Aligned vs. High Aligned vs. Medium


Cyclical

3 5 2 0.788 -0.16 0.299 6.803∗∗∗

3 5 5 -0.904 -2.649∗∗ 1.64 1.6115 3 8 0.836 -5.68∗∗∗ 2.193∗ 6.407∗∗∗

5 3 20 1.817 -7.808∗∗∗ 1.831 4.528∗∗∗

Acyclical

3 5 2 0.382 -0.881 0.542 6.468∗∗∗

3 5 5 0.831 0.15 0.197 3.626∗∗∗

5 3 8 0.682 -4.666∗∗∗ 1.176 7.533∗∗∗

5 3 20 4.158∗∗∗ -8.202∗∗∗ -0.793 2.759∗∗

We next compare the performance of PD projects with misalignment locus at di�erent centrality

levels with the performance of an aligned PD project. In particular, we test the following hypothesis:

Hypothesis 4. An aligned PD project yields a higher performance than those with misalignments

at high or medium-centrality subsystems.

We report the statistically notable results in Table 4. The full report of results is in Appendix. In a

hierarchy, we �nd signi�cant results when comparing the performance of aligned projects and those

with misalignments focus at high-centrality levels. In a polyarchy, we observe signi�cant results

4 To understand this, consider the fact that all possible combination of design proposals are eligible in the polyarchysystem, of which a subset are eligible in the hierarchical system.


when comparing an aligned project and projects with the misalignment locus at medium-centrality

levels.

In a hierarchy, Hypothesis 4 is rejected for all scenarios at the α= 0.01 signi�cance level. Sim-

ilar to our results for Hypothesis 2 in Section 4.1, the screening nature of hierarchical structures,

dampens the negative consequences of misalignments concentrated on high-centrality levels so that

PD systems with such misalignments have a similar performance to aligned projects. However, the

negative consequences of misalignments are stronger when they are concentrated at the subsystems

of medium-centrality levels (in comparison to high-centrality levels) when decisions are made in a

polyarchy.

4.3. Experiment 3: Convergence

In this section, we study the convergence time of the search process�which is a proxy for develop-

ment time�on real versus perceived landscapes. Development time is among the most important

criteria used when evaluating the performance of a PD project (Krishnan and Ulrich 2001), and

more so in competitive markets. We examine convergence in two setups. First, we simulate aligned

PD projects and also those with a form of misalignment to see how misalignments a�ect convergence

time. Second, we manipulate the misalignment locus in a PD project to study whether subsystems'

centrality at which misalignments occur more intensely a�ects the convergence time of the PD

project.

Convergence occurs when we observe status stability for all teams for a number of time periods. In

our experiments this number is 10 and 20 simulation time periods (corresponding to 2%, and 4% of

simulation time, respectively). We report the results when this number is 10: that is, at each time t,

we compare the status of all teams for the past 10 simulation time periods and if we �nd no change

in the status of any team, then we record t+ 1 as the convergence time; otherwise we continue

the search process. We obtain similar results with 20 time periods; the corresponding tables are in

Appendix. The �rst hypothesis is that the mean convergence time for a PD project with hidden

dependencies is higher than that for a PD project with spurious communications.

Hypothesis 5. PD projects with hidden dependencies have longer convergence time than those

with spurious communications.

Table 5 reports the results. Clearly, in a polyarchy and with acyclical subsystem interactions,

projects with hidden dependencies result in shorter convergence time than those with spurious

communications. This result is robust for all projects, that is, with three or �ve teams and with

varying degree of managerial decision-making capability, at the α= 0.01 signi�cance level.

As we discussed in Section 4.1, with acyclical subsystem interaction pattern and a polyarchy

structure, PD systems with hidden dependencies conduct more e�ective search than projects with


spurious communications. This search e�ciency results not only in higher quality of the �nal

design�sticking points with higher �tness values on the perceived landscape�but also in a shorter

convergence time.

With acyclical subsystems interactions, and in a hierarchy, we observe shorter convergence time

only with high managerial decision-making capability levels (Q= 5,20). Hierarchical search organi-

zations dampen the e�ect of misalignments and so we may expect systems with hidden dependencies

and spurious communications to converge in similar times. However, higher managerial capability

is associated with a higher number of sticking points which leads to the signi�cant di�erences in

convergence time between systems with the two misalignments forms.

We do not observe a di�erence in convergence time in projects with hidden dependencies and

those with spurious communications in other scenarios in Table 5. In particular, independent of

the organizational structure, it appears the two misalignments forms do not result in di�erent

convergence time with a cyclical subsystem interaction pattern. This is because there are a lower

number of sticking points for less modular PD systems (Rivkin and Siggelkow 2003) which appears

to make the convergence in the misaligned projects insensitive to the misalignment type.

Table 5 Paired t-tests comparing convergence time of PD systems with di�erent misalignment forms. For this table,

q= 2.

Inputs Hierarchy Polyarchy Hierarchy PolyarchyH.D. vs. S.P. H.D. vs. S.P. Aligned vs. H.D. Aligned vs. S.P.


Cyclical

3 5 2 -1.553 -0.839 -0.747 -2.07∗

3 5 5 -1.298 -0.576 -3.7∗∗∗ -6.833∗∗∗

5 3 8 0.431 -0.078 -1.118 -5.32∗∗∗

5 3 20 1.435 -2.229∗ -0.025 -8.386∗∗∗

Acyclical

3 5 2 -0.021 -2.876∗∗∗ -0.104 -1.1053 5 5 -2.816∗∗ -3.25∗∗∗ -2.736∗∗ -5.593∗∗∗

5 3 8 -1.32 -2.788∗∗ -0.424 -4.895∗∗∗

5 3 20 -3.26∗∗∗ -5.199∗∗∗ -1.975 -5.763∗∗∗

We next compare the convergence time of PD projects with a particular misalignment form to

that of aligned PD projects. The second hypothesis then is that the mean convergence time of an

aligned PD project is shorter than that of a PD project with either hidden dependencies or spurious

communications.

Hypothesis 6. Aligned PD projects have shorter convergence time than those with hidden depen-

dencies or spurious communications

The full set of text results are in Appendix. The signi�cant results which we report in Table

5 are on the (i) comparison of the aligned project and project with hidden dependencies in a


polyarchy, and (ii) comparison of the aligned projects and projects with spurious communications

in a hierarchy.

In a polyarchy, aligned PD projects in general converge faster than PD projects with hidden

dependencies. However, with a hierarchy, aligned projects converge at similar times to PD projects

with spurious communications. We observe these convergence patterns for most scenarios with

di�erent levels of managers' capability levels and low/high divisional levels.

The results in Table 5 indicate that how search is conducted on a perceived landscape a�ects

the convergence in misaligned PD systems in comparison to aligned projects. In a polyarchy, teams

consider more diverse design solutions which renders the convergence of aligned and misaligned

projects signi�cantly di�erent. In a hierarchy however fewer design proposals are conceived as eligible

by the PD manager and so the potential e�ects of misalignments are curbed which results in aligned

and misaligned projects with spurious communications to have similar convergence times.

We next compare the convergence time of PD projects with misalignment locus at high, medium,

or low levels and that of aligned projects. In our experiments, convergence occurs when the teams

do not change their designs for 10 or 20 simulation time periods corresponding to 2%, and 4%

of the simulation time, respectively. In here, we report the results with 10 time periods and only

comparisons of PD projects with misalignments at the medium and high levels. We relegate the

other results to the Appendix. The �rst hypothesis is that the mean convergence time of projects

with misalignment locus at the high level is longer than that of projects with the locus at the

medium level.

Hypothesis 7. PD systems with misalignment locus at the high level have longer convergence

time than those with the locus at the medium levels.

The results are in Table 6. For more divisionalized projects (i.e., projects with �ve teams) and

with highly capable managers (Q= 20), Hypothesis 6 is supported at the α= 0.01 signi�cance level.

That is, under these conditions, misalignments at the high level lengthen the convergence time.

These conditions increase the number of sticking points (Rivkin and Siggelkow 2002) which seem

to a�ect the convergence time of projects with misalignments at the high-centrality level more than

those with misalignments at the medium-centrality level.

We also compare the convergence of a project with misalignment locus at high or medium, with

an aligned project. In particular we test the following hypothesis:

Hypothesis 8. Aligned PD systems have shorter convergence time than those with high or

medium misalignment-locus.


Table 6 Paired t-tests comparing convergence time of PD systems with misalignments occurring at the high- and

medium-centrality levels. For this table, q= 2.

Inputs Hierarchy Polyarchy Hierarchy PolyarchyHigh vs. Medium High vs. Medium Aligned vs. High Aligned vs. Medium


Cyclical

3 5 2 0.65 0.507 -0.146 -0.793 5 5 -0.376 1.786 -2.07∗ -4.575∗∗∗

5 3 8 1.672 1.523 -0.642 -5.032∗∗∗

5 3 20 3.394∗∗∗ 6.053∗∗∗ -2.576∗∗ -4.828∗∗∗

Acyclical

3 5 2 0.21 -0.573 -0.641 -1.8683 5 5 -0.488 1.356 -1.405 -5.157∗∗∗

5 3 8 1.959 2.883∗∗∗ -0.423 -5.544∗∗∗

5 3 20 2.684∗∗ 6.42∗∗∗ -2.236∗ -4.568∗∗∗

We examine Hypothesis 8 both in a polyarchy and a hierarchy. Here we report our signi�cant

results on (i) comparison between aligned projects and PD systems with misalignment locus at

the high level in a hierarchy, and (ii) comparison between aligned projects and PD systems with

misalignment locus at the medium level in a polyarchy. These results are provided in Table 6.

In general, with a polyarchy structure, misalignments at the medium level increase the convergence

time in comparison to an aligned project. The only occasion when this observation is not signi�cant

is when the project consists of a small number of teams with low levels of managerial capability.

However, with a hierarchical decision making, we do not �nd strong support for misalignments

at the high centrality level to lengthen the convergence time in comparison to an aligned project.

Some support exists for a lengthier convergence time when the number of teams in the PD project

increases from 3 to 5 in our simulations.

Our results on Hypothesis 8 re�ect the importance of search organization on the perceived land-

scapes in comparison to the real landscape. When organized in a hierarchy, fewer solutions on

organizational landscapes are examined which decreases the e�ect of misalignments and so both

aligned and misaligned projets have similar convergence patterns. In a polyarchy however teams

consider more diverse designs and the exploratory nature of the search exacerbates the e�ects of

the misalignments and so the misaligned projects converge slower than the aligned projects.

5. Discussion and Conclusions

This paper proposes a model for studying how misalignments between product and organizational

architectures a�ect the performance of a complex PD project. According to socio-technical coordi-

nation strategy, PD teams should interact only when there are interactions among the subsystems

they develop. There is some empirical documentation on that approach being applied to complex

products and the observation that misalignments do occur.

Misalignments are expected to have a negative e�ect on the product development process (Sosa

et al. 2004, 2007, Gokpinar et al. 2010). However, neither the extent of the e�ect on the performance


nor possible strategies to manage it have been examined. We conceptualize misalignments as a cause

for PD teams to search on perceived rather than real landscapes. We then theorize the possible

consequences in PD systems organized in a hierarchical or polyarchical decision-making structure

and also in PD systems in which subsystems are in cyclical or acyclical interactions.

We study misalignments in their e�ect on time required to develop a product and the quality of

the �nal design. We also de�ne a measure of centrality, and then score subsystems in terms of their

degree of connectedness, in an e�ort to study the e�ects of misalignments as a function of subsystem

centrality.

Our notion of a real versus perceived landscape in an NK(C) search model is consistent with some

key concepts. For instance, ambiguity (Schrader et al. 1993) or unforeseeable uncertainty (Sommer

and Loch 2004) are characteristics of new projects and are de�ned as the inability to identify and

articulate the relevant variables and their e�ects. PD teams developing a new project are unlikely

to identify all of the project's possible and consequential events (Pich et al. 2002). However, these

unknown events di�er from complexity, which is the state of having (too) many interacting variables.

The concept of search on a real versus perceived landscape is also in line with (collective) cognitive

limits and bounded rationality of the PD teams. Such constraints cause PD teams to overlook the

interactions among some elements and thus to search in a space di�erent from the real one.

Tables 7 and 8 provide a summary of our results on how the two misalignment forms a�ect the

convergence and quality of the �nal design depending on the decision-making structure and the

subsystem interaction pattern.

Table 7 Comparison between aligned projects and those with either form of misalignments in a polyarchy

Measure Aligned vs. Misaligned Misaligned vs. Misaligned

Qualityaligned > hidden depen

hidden d

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