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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.
mj2417@gmail.com
Javad NasiryInformation Systems, Business Statistics and Operations Management Department, Hong Kong University of Science and
Technology, Clear Water Bay, Kowloon, Hong Kong. nasiry@ust.hk
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.
Jafari Songhori and Nasiry: Organizational Structure and Centrality in Misaligned Projects3
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.
Jafari Songhori and Nasiry: Organizational Structure and Centrality in Misaligned Projects4
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
Jafari Songhori and Nasiry: Organizational Structure and Centrality in Misaligned Projects5
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
Jafari Songhori and Nasiry: Organizational Structure and Centrality in Misaligned Projects6
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
Jafari Songhori and Nasiry: Organizational Structure and Centrality in Misaligned Projects7
�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
Jafari Songhori and Nasiry: Organizational Structure and Centrality in Misaligned Projects8
(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.
Jafari Songhori and Nasiry: Organizational Structure and Centrality in Misaligned Projects9
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.
Jafari Songhori and Nasiry: Organizational Structure and Centrality in Misaligned Projects10
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.
Jafari Songhori and Nasiry: Organizational Structure and Centrality in Misaligned Projects11
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
Jafari Songhori and Nasiry: Organizational Structure and Centrality in Misaligned Projects12
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
Jafari Songhori and Nasiry: Organizational Structure and Centrality in Misaligned Projects13
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
Jafari Songhori and Nasiry: Organizational Structure and Centrality in Misaligned Projects14
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.
Jafari Songhori and Nasiry: Organizational Structure and Centrality in Misaligned Projects15
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
Jafari Songhori and Nasiry: Organizational Structure and Centrality in Misaligned Projects16
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
Jafari Songhori and Nasiry: Organizational Structure and Centrality in Misaligned Projects17
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
Jafari Songhori and Nasiry: Organizational Structure and Centrality in Misaligned Projects18
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
Jafari Songhori and Nasiry: Organizational Structure and Centrality in Misaligned Projects19
(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.
Jafari Songhori and Nasiry: Organizational Structure and Centrality in Misaligned Projects20
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.
Jafari Songhori and Nasiry: Organizational Structure and Centrality in Misaligned Projects21
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?
Jafari Songhori and Nasiry: Organizational Structure and Centrality in Misaligned Projects22
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
Jafari Songhori and Nasiry: Organizational Structure and Centrality in Misaligned Projects23
(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
Jafari Songhori and Nasiry: Organizational Structure and Centrality in Misaligned Projects24
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
Pattern n ne Q t-value t-value t-value t-value
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.
Jafari Songhori and Nasiry: Organizational Structure and Centrality in Misaligned Projects25
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
Jafari Songhori and Nasiry: Organizational Structure and Centrality in Misaligned Projects26
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.
Pattern n ne Q t-value t-value t-value t-value
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
Jafari Songhori and Nasiry: Organizational Structure and Centrality in Misaligned Projects27
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.
Jafari Songhori and Nasiry: Organizational Structure and Centrality in Misaligned Projects28
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
Pattern n ne Q t-value t-value t-value t-value
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
Jafari Songhori and Nasiry: Organizational Structure and Centrality in Misaligned Projects29
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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