Robust Project-Based Organizations for the Design of Complex Engineered Systems

Abstract

Cost and schedule overruns have become increasingly common in projects that set out to deliver complex engineered systems. Considering the well-established relationship between systems and organizations that design them, this article compares real-world, project-based organizational forms to idealized forms using agent-based models. It identifies multiscale networks as the preferred theoretical form and structures based on military staffs as the preferred practical form for organizations that design complex engineered systems. Matrix organizations are particularly susceptible to congestion failure, whereas military staffs are more robust and better suited to meeting demands for cross-functional collaboration and communication.

Keywords

project-based organizations organizational design complex engineered systems multiscale networks agent-based modeling

Introduction

To meet demands for better performance and improved life cycle characteristics, designers of engineered systems often turn to novel and untested system architectures, with the result that today’s engineered systems have become more complex (Sinha & de Weck, 2013). Cost and schedule overruns have become increasingly common in projects that set out to deliver such complex engineered systems, because organizations fail to understand and manage the complexity associated with their design (Murray et al., 2011). System architecture is closely linked to the structure of the design organization responsible for it, and innovative and complex system architectures challenge design organizations by threatening their organizational and communication structures. It is therefore logical to examine aspects of organizational structure to better understand why organizations fail to manage the design of complex engineered systems.

Conway (1968) argued that a structure-preserving relationship exists between system architecture and the structure of the design organization: for any subsystem or component, one can identify individuals or groups in the design organization responsible for their design. Similarly, any link in the system design defines an interface, necessitating communication and coordination between the responsible organizational entities (Conway, 1968). In other words, technical dependencies in the system architecture drive the need for communication within the design organization (McCormack et al., 2008). Since many designs can satisfy requirements, the structure of the design organization affects how a design is selected from among alternatives. According to Conway’s Law, design organizations are “constrained to produce designs which are copies of the communication structures of these organizations”; thus, design efforts should be organized around the need for communication (Conway, 1968, p. 31).

Innovative and complex system architectures present a range of challenges. Innovative architectures challenge organizations by disrupting knowledge embedded in their organizational and communication structures. Over time, organizations accumulate architectural knowledge in their formal and informal reporting and teaming arrangements, establish filters to determine what information is important, and solve problems based on experience. Innovation puts a premium on exploration and integration of new knowledge, and organizations may struggle to adapt (Henderson & Clark, 1990).

Complexity also impairs organizational and communication structures. Design organizations respond to complexity by subdividing and delegating tasks. Pressure to maintain schedules incentivizes managers to bring on additional resources, leading to further subdivision and delegation. The net impact is fragmentation of the design organization’s communication structure and inability to absorb or channel information effectively (Conway, 1968). In addition, increasing complexity makes the design environment more ambiguous and uncertain, and learning and design must happen in parallel (Poire & Sabel, 1984). Problem-solving becomes a collective activity characterized by simultaneous design and collaboration (Dodds et al., 2003) Design organizations compensate by exchanging information, and the problem of coping with ambiguity and complexity becomes a problem of distributed communication, which further challenges organizational and communication structures (Watts, 2003).

The overall impact of the challenges of innovative and complex system architectures on design organizations depends on how they deal with them. Conway (1968) argued that design organizations should be arranged around the need for communication, but innovative and complex system architectures require agile and adaptive design organizations that are able to explore and learn through collaboration and can withstand fragmentation and communication failures. Organizations often turn to project-based forms, characterized by “cross-functional teams and more open organizational environments,” to improve their agility and robustness and thereby meet the perceived challenges of innovation and complexity (Henderson & Clark, 1990, p. 28).

The aim of this article is to contribute to an understanding of how project-based organizations can better manage the design of complex engineered systems. We treat organizations as networks and draw on work done by Dodds et al. (2003), who examined the dynamics of information exchange in organizational networks and identified a class of networks, which they call “multiscale networks,” that exhibit robustness to failure (Dodds et al., 2003). We argue that multiscale networks should provide the robustness desired in organizations that design complex engineered systems and hypothesize that real-world, project-based organizations may exhibit multiscale properties. We compare the performance of matrix organizations and military staffs to random and multiscale networks. Matrix organizations and military staffs represent real-world, project-based organizational networks, whereas random and multiscale represent two idealized forms; we compare them using agent-based models that represent design as an activity that simultaneously requires the creation of design artifacts and the sharing of information. We seek to answer two specific research questions:

RQ1: How do random, multiscale, military staff, and matrix organizational networks perform in information exchange and design environments, and how does increasing complexity affect performance?

RQ2: Do matrix organizations or military staffs exhibit multiscale properties and which organizational form is preferred for the design of complex engineered systems?

We find military staffs exhibit multiscale properties over a range of situations and recommend that organizations that design complex engineered systems should organize themselves around structures similar to those used by military staffs.

The remainder of this article is structured as follows. The next section reviews literature related to the nature of design, the role of product architecture and its relationship to the structure of the product design organization; the nature of hierarchies and their importance to both system architecture and organizational structure; the characteristics of project-based organizations; and the characteristics of robust organizational networks. The third section describes the methodology employed, while the fourth, fifth, and sixth sections present results, conclusions, and recommendations, respectively.

Literature Review

Design, System Architecture, and Organizational Structure

Design is the process of devising “courses of action aimed at changing existing situations into preferred ones” (Simon, 1996, p. 111). Engineering design transforms customer requirements into a design that meets them, and the formulation, evaluation, and selection of good designs are both challenging and of significant importance, because poor designs can introduce fundamental flaws that are difficult or impossible to correct later (El-Haik & Yang, 1999). Complex engineered systems are especially hard to design because they have long life spans and uncertain operating environments that affect the system’s life cycle performance (Cardin et al., 2017).

A key step in the design of complex engineered systems is establishing system architecture, the scheme that translates functions and objectives into physical components. Designers commonly decompose the system into smaller elements—subsystems, modules, components, and the like—that must be integrated to work together and achieve performance objectives. The discipline of systems engineering focuses on planning and controlling component interactions to deliver system-level performance. Architecture identifies functional requirements and the arrangement of functional elements; maps functional requirements to physical systems and components; and defines physical interfaces between systems and components (Ulrich, 1995).

Researchers have long recognized the interplay between system architecture and organizational structure. Organizational structure identifies the people in an organization, their relationships to one another and the organization’s environment, and the principles governing the organization’s purpose and development (Eppinger & Browning, 2012). As already noted in the introduction, Conway argued a structure-preserving relationship exists between system architecture and organizational structure (of the design organization), with system elements being traceable to the members of the design team responsible for them, and system interfaces defining the needs for communication and coordination within the design organization (Conway, 1968). Likewise, the mirroring hypothesis predicts that organizations with different structures will design systems with different architectures. This has important managerial implications, because product architecture is an important predictor of organizational performance (McCormack et al., 2008).

The successful development of complex engineered systems depends on the efficient and effective flow of information, and leaders may want to enable “better communication, the free flow of ideas, and the open sharing of issues and concerns, with hopes of building consensus and preempting problems” (Eppinger & Browning, 2012, p. 80), but the free flow of information can go too far, creating information overload that actually impedes effective communication. Leaders therefore seek to manage the flow of information to facilitate effective execution of complex projects through purposeful organizational structures (Eppinger & Browning, 2012).

Hierarchies

The characteristics of hierarchies are important to system architecture, organizational structure, and the relationship between them. Modern theories of organizational structure trace back to Adam Smith’s The Wealth of Nations, which describes the division of labor principle Smith inferred from his observations of workers. The division of labor harnesses returns on specialization, but does not explain why hierarchical organizations emerged as the dominant type associated with mass production. Nevertheless, many firms did organize that way, and the consensus of economic theory has long held that hierarchies were the optimal organizational form. Hierarchies offer advantages for exercising control, accumulating knowledge, performing decentralized or distributed processing, and making decisions, but these advantages assume tasks can be easily decomposed into smaller subtasks that can be accomplished independently (Watts, 2003).

Hierarchies decompose the whole into modular parts or subsystems, where one can distinguish interactions within a subsystem from interactions between or among subsystems. A key property of hierarchies is near decomposability, which refers to the fact that intracomponent linkages and interactions are generally stronger than intercomponent interactions. This feature separates high-frequency dynamics related to internal structure from low-frequency interactions among components. In a nearly decomposable system, intercomponent interactions are weak but not negligible (Simon, 1996).

Traditional economic theory has argued that firms grow through vertical integration, the periodic absorbing or jettisoning of hierarchies, but Poire and Sabel (1984) challenged that theory, noting it came about only after hierarchy had become the dominant organizational design. They argued instead that flexible specialization, which exploits economies of scope using general purpose machinery and skilled workers, replaces hierarchy and further argued that such economies of scope are optimal when uncertainty and rapid change favor adaptability over scale (Poire & Sabel, 1984).

Project-Based Organizations

Beginning in the 1990s, large companies, especially in the aerospace domain, started to move toward integrated product development (IPD) and project-based design organizations to lower overhead costs, shorten development time, and increase cross-functional collaboration. IPD brings together representatives from relevant functions to capture collective input during design, often using integrated project teams (IPTs) to design systems, subsystems, and components throughout the product life cycle. IPTs use a variety of integrative tools, including systems engineering, interface optimization, colocation, and manager mediation (Browning, 1996).

Unpredictable and rapidly changing business environments drive firms to adopt project-based organizational forms and project management business practices. Holistic models of organizational design, such as the McKinsey 7 S framework and Galbraith’s star model, suggest organizational designers must consider a range of factors, including consistency and suitability. The design of project-based organizations should consider five related elements: (1) orientation, the strategic decision to be project-based; (2) project organization, which defines the relationships among projects, programs, and functions; (3) business processes, which should be project-based; (4) culture, which should be project-oriented; and (5) project working practices that recognize and accommodate the churn created when projects are formed and disbanded (Miterev et al., 2017).

Matrix Organizations

Terms like matrix or matrix organization are often used interchangeably with project-based organization to describe these kinds of organizations. Matrix organizations are characterized by a dual chain of command, where responsibilities are assigned to both functional and product or project departments. Functional departments provide specialized, internal resources, whereas project or product departments focus on outputs (Davis & Lawrence, 1978).

The common characteristic of matrix organizations is a hybrid organizational form in which a traditional, functional hierarchy is overlaid by a lateral project-based authority as shown in Figure 1. Matrix organizations can be broadly classified as heavyweight or lightweight, with heavyweight organizations having strong project managers with significant authority, who report to the general manager and control budgets and resources. Functional managers also report to the general manager and are responsible for technical excellence. In lightweight organizations, project managers play more of a coordination and administrative role and have little authority (Ulrich & Eppinger, 1995).

Figure 1

Typical matrix organization illustrating a lateral project management organization overlaid on a functional hierarchy.

Matrix organizations “attempt to create synergism through shared responsibility between project and functional management” (Kerzner, 2003, p. 103), but achieving such synergy can be quite difficult in practice. Advantages of matrix organizations include improved control over resources, independent policies and procedures for individual projects, quick adaptation to change, ability to develop a strong technical base, and improved ability to solve complex problems. Disadvantages include multidimensional work and information flow, dual reporting, changing priorities, potential for conflict, and role ambiguity (Kerzner, 2003). Early investigations suggested matrix organizations should improve information processing by “formalizing lateral communication channels and legitimizing informal communication” (Ford & Randolph, 1992, p. 273), with a corresponding increase in formal communication and decrease in informal communication. Compared to hierarchical functional organizations, matrix organizations should have greater information processing capacity and the ability to handle increased information loads because “increased contact among departments allows information to ‘permeate’ the organization, improving decision making and response time, which translates into an organization that can quickly and flexibly adapt to a dynamic situation” (Ford & Randolph, 1992, p. 273).

Military Organizations

To outside observers, military organizations, with their well-defined chains of command and lines of authority and responsibility, may seem to be the embodiment of hierarchical organizational structure. In a typical military staff, experienced senior officers oversee staff sections organized by function, such as personnel, intelligence, operations, logistics, plans, and communications, with each staff section further subdivided into specialty areas. Each functional area has subordinate staffs across multiple levels of command. Under such a hierarchy, decision-making and responsibility reside with the most experienced individuals, and clear lines of authority and responsibility maximize information flow. Ideally, this structure allows senior decision makers to focus on the most important efforts, while leaving routine tasks to skilled subordinates and also providing a suitable amount of surge capacity to deal with emergent concerns (Joint Chiefs of Staff, 2017).

The successful execution of complex military operations requires close coordination, synchronization, and information sharing; military staffs achieve this sort of cross-functional collaboration by forming boards, centers, bureaus, offices, working groups, cells, and other temporary and permanent teams to manage specific tasks or activities. These teams, sometimes shortened to “boards, centers, cells, and working groups,” facilitate planning, decision-making, and execution. Figure 2 illustrates a typical military staff organization. Teams are generally led by a senior individual from the cognizant directorate (functional hierarchy), but draw members from across the organization, depending on the role or activity performed (Wade, 2012).

Figure 2

Typical military staff organization illustrating the distribution of the functional personnel to different teams. Adapted from Joint Chiefs of Staff (2017).

The arrangement of military staffs relies on a general principle of military organizations, in that individuals and organizations have both an administrative, or functional, chain of command responsible for a wide range of administrative and logistic functions, and an operational chain of command, responsible for performing specific tasks and executing operations. It is clear that military staffs are a kind of project-based organization. Military staffs have a functional structure built around directorates with specific, enduring responsibilities and capabilities, but they also have cross-functional organizations that exist to accomplish specific tasks or projects. The principal difference between a traditional matrix organization and a military staff is that the matrix organization relies on a lateral, project-based authority separate from the functional structure, whereas military staffs embed project authorities within the existing functional structure. For example, in a military staff, the leader of a cell formed to undertake a specific planning project would likely be drawn from the planning function, whereas in a matrix organization, the leader of such a project would likely come from a separate project management organization.

Robust Organizations

Poire and Sabel (1984) challenged the notion, implicit in traditional theories of organizations, that the accomplishment of complex tasks is somehow centralized and controlled from above. Instead, they argued that when organizations embark on new projects, the people involved know little about how to accomplish the project’s objectives, so design, innovation, and production must occur simultaneously, and in a decentralized manner. When the environment becomes ambiguous and uncertain, learning and design must occur in parallel (Poire & Sabel, 1984). Organizations compensate by exchanging information, and the problem of managing ambiguity and complexity becomes a problem of distributed communication. Organizations are intrinsically hierarchical, and individual members of the organization are limited in the amount of work they can accomplish. Organizational networks are costly in terms of time and energy, so a robust information-processing network must balance production (i.e., work of the personnel) and information distribution (sharing of information among personnel; Watts, 2003).

Dodds et al. (2003) examined the dynamics of information exchange in organizational networks and identified a class of networks, multiscale networks that exhibit ultrarobustness, meaning they simultaneously reduce the likelihood individual nodes will experience congestion failure and the likelihood that the overall network will fail if congestion failures occur at individual nodes. They proposed a model (the Dodds-Watts-Sabel [DWS] model) of organizational networks with four components: (1) a construction algorithm that incrementally adds cross-functional team links to a pure branching hierarchy according to a stochastic rule; (2) a task environment based on the rate and distribution of messages exchanged between nodes (i.e., sources and targets) and the decomposability of those messages; (3) a method for passing messages through a chain of intermediate nodes; and (4) measures of robustness to congestion (Dodds et al., 2003)

The DWS model begins with hierarchical organizational structure defined by branching ratio, B, and number of levels, L, which yields a network with N = (B^L – 1)/(B – 1) nodes. The construction algorithm adds m nodes according to a stochastic rule, that governs the probability, P(i, j), that links will be added between nodes i and j:

P (i, j) \propto e^{- \frac{D_{i j}}{λ}} e^{- \frac{x_{i j}}{ς}}

(1)

The hierarchical backbone represents the organization’s formal structure, while additional links represent arrangements that transmit information. As illustrated in Figure 3, the rule uses two key parameters, depth, D_ij , of the lowest common node, a_ij , between nodes i and j, and organizational distance between nodes i and j, given by $x_{i j} = \sqrt{d_{i}^{2} + d_{j}^{2} - 2}$ , which is valid for d_i +d_j ≥ 2. The rule also uses two tuning parameters, λ and Ϛ, which represent characteristic lengths for D_ij and x_ij , respectively.

Figure 3

Schematic illustration of parameters in the Dodds-Watts-Sabel information exchange model (Dodds et al., 2003).

Figure 4 illustrates four classes of organizational networks for limiting values of the tuning parameters, λ and Ϛ:

Random networks (R) in which links are added uniformly at random, without regard to lowest common ancestor rank or organizational distance;

Local team (LT) in which links are added only between node pairs who share the same immediate supervisor;

Random interdivisional (RID) in which links are added between nodes in different major divisions of the hierarchical organization; and

Core-periphery (CP) in which links are added only between subordinates of the top node, resulting in a fully connected central core with pure branching hierarchies below.

Figure 4

Classes of organizational networks for the Dodds-Watts-Sabel information exchange model based on model parameters (Dodds et al., 2003).

Multiscale networks (MS) correspond to moderate values of λ and Ϛ and combine features of the four other network classes. Multiscale network connectivity is not dominated by a single factor or scale. Instead, multiscale networks show connectivity at multiple scales at the same time, but do not show uniform density at all scales, which distinguishes them from small-world networks. These features improve information exchange compared to hierarchical networks, which tend to put the burden of information sharing on nodes at higher ranks.

Stable environments correspond to low rates of information exchange, μ, defined as the average number of messages initiated per node per time step. For a given source node transmitting messages at rate μ, the model selects target nodes at random considering task decomposability. When tasks are highly decomposable, local dependencies prevail and target nodes are selected from among the nodes in the same hierarchical branch. When tasks are not decomposable, global dependencies prevail and target nodes are selected at random from among all nodes in the network. Messages are passed from source to target through intermediaries, with each node in the chain passing the message to an immediate neighbor who has the lowest common ancestor with the target. Congestion centrality, ρ_i, is the probability that node i will process any given message. The rate of information processed by node i is therefore given by:

r_{i} = μ N ρ_{i}

(2)

where μN is the total number of messages originated across a network of N nodes per unit time. A node will remain free of congestion if its capacity exceeds r_i , and the DWS model therefore adopts maximum network congestion centrality, ρ_max , as a measure of congestion robustness. Networks with lower ρ_max will be more robust to congestion.

Figure 5 presents congestion results for a hierarchy defined by branching ratio B = 5 and depth L = 6, and a task environment with moderate decomposability. Multiscale networks reduce maximum congestion centrality with fewer team links than other networks. Core-periphery networks exhibit lower values of maximum congestion centrality, but also exhibit greater variability and sensitivity to initial conditions. Multiscale networks do not exhibit this volatility, making them a more reliable solution for improving congestion robustness.

Figure 5

Congestion centrality as a function of team links added for random (R), random interdivisional (RID), local team (LT), core-periphery (CP), and multiscale (MS) networks (Dodds et al., 2003).

Multiscale networks “display a remarkable combination of properties,” including low likelihood of congestion failures over a range of environmental conditions and resistance to disconnection. They achieve these benefits when only a small number of team links are added to the hierarchical backbone, and one should expect to find networks resembling multiscale networks in real-world organizations (Dodds et al., 2003, p. 12521). Indeed, the practical relevance of multiscale networks depends on whether real-world organizations exhibit multiscale properties (Magee, 2010). If real-world, project-based organizations exhibit multiscale properties, they would then represent a preferred form for the design of complex engineered systems.

Methodology

Approach

We used agent-based models to compare the performance of matrix and military staff organizations to random and multiscale organizations and to determine if matrix or military staff organizations exhibit multiscale properties. Agent-based models represent phenomena using agents, their environment, and rules governing agent-to-agent and agent-to-environment interactions. Organizational networks satisfy the criteria for selecting agent-based models proposed by Wilensky and Rand (2015) in that they have a moderate number of heterogeneous, interacting agents; are characterized by local agent-to-agent interactions; exhibit time-dependent behavior; and adapt over time (Wilensky & Rand, 2015). We used the NetLogo agent-based modeling environment to implement models. NetLogo is an open source, cross-platform modeling environment authored by Uri Wilensky and has been continuously developed at the Center for Connected Learning and Computer-Based Modeling at Northwestern University since 1999 (Northwestern University, 2017).

We used a phased, building block approach that first implemented the DWS model of information exchange for random and multiscale networks in NetLogo and cross-validated it against a model implemented in MATLAB to confirm the DWS model could be successfully implemented in NetLogo. We then progressively extended the model to implement matrix and military staff organizational networks; account for the effects of complexity; and address the design environment, which requires both information exchange and the processing of work products.

At each step, we verified and validated models and performed experiments to characterize network behavior. All experiments started with a pure branching hierarchy composed of L = 5 levels and branching ratio B = 4, resulting in a network of N = 341 nodes. All experiments varied the number of team links added, m, from −2.5 to 0.5 as log m/N, as well as other parameters, as described below. We analyzed experimental results using the following hypothesis test to compare network performance:

\begin{matrix} H_{0} : μ_{i d e a l} = μ_{r e a l} \\ H_{1} : μ_{i d e a l} \neq μ_{r e a l} \end{matrix}

(3)

where μ represents a measure of performance and the ideal and real subscripts refer to random or multiscale networks and matrix or military staff networks respectively.

Information Exchange Environment

We first examined how organizational networks behaved in the information exchange environment. We implemented the DWS information exchange model for random and multiscale networks in NetLogo, cross-validated the model against a similar model implemented in MATLAB, and then extended the model to matrix and military staff organizational networks by altering the network construction algorithm. For matrix organizations, the model adds an additional major branch to the hierarchy to represent a project management organization and then adds m team links at random between project managers and workers in the functional hierarchy. For military staffs, the model first identifies team leads from among nodes near the top of the hierarchy (i.e., managers and supervisors), and then adds m team links at random between team leaders and other workers.

We further extended the information exchange model to account for the effect of complexity by linking message distribution to complexity using a numerical complexity scale (1–10) in which lower values (e.g., 2) represented low complexity, and higher values (e.g., 8) represented higher complexity. Use of a numerical scale simplified modeling but does not imply a quantitative relationship. For example, a complexity rating of 8 does not imply the environment is four times more complex than an environment assigned a complexity rating of 2. At low complexity, most tasks are decomposable and local dependencies prevail, so target nodes are selected at random from among workers in the same major hierarchical division as the source node. At high complexity, most tasks are not decomposable and global dependencies prevail, so target nodes are selected at random from across the hierarchy. We compared network performance at low (2), medium (5), and high (8) complexity taking maximum network congestion centrality, ρ_max , as our measure of performance, consistent with the DWS model.

Design Environment

The design of complex engineered systems requires organizations to develop a wide range of work products, in other words, artifacts, such as drawings, specifications, analyses, reports, correspondence, and other documents. We modeled the design environment using an artifact network model that extended the information exchange model to include processing of artifacts by modifying the task environment, methods of information exchange, and measures of performance. Workers, supervisors, and managers in the design organization must create, review, and approve artifacts to meet design and schedule objectives. In general, the review and approval of artifacts follows functional, hierarchical lines, but the creation of artifacts also requires cross-functional collaboration, so the design organization must share information and produce artifacts simultaneously.

The artifact model describes the task environment in terms of the rate and distribution of artifacts to be processed and the rate and distribution of messages that must be exchanged to accomplish cross-functional collaboration. The artifact rate, μ_A , is the average number of artifacts originated by each node at each time step, and μ_AN is the total number of artifacts originated across the network at each time step. Artifact routing follows the functional hierarchy. Workers at the lowest level of the hierarchy originate artifacts and then pass them up the functional chain of command to a manager near the top of the hierarchy for approval. For simple tasks, the originating worker likely has sufficient information to complete the artifact without the need for cross-functional collaboration. For complex tasks, however, the worker likely lacks sufficient information and requires additional information from other workers. In this case, the originating worker places the artifact on hold and originates a request for information (RFI) to acquire the additional information required to complete the artifact. RFIs pass from source to target through a chain of intermediate nodes as with messages in the information exchange model. Upon receipt, the RFI target provides the information requested and returns the RFI directly to the originator. When the originator receives an answered RFI, they complete the associated artifact and route it for approval.

Complexity affects the rate and distribution of RFIs. At low complexity, few RFIs are created and, because tasks are decomposable, RFIs are routed to other workers in the same functional organization. At high complexity, many RFIs are created. Since tasks are not decomposable, RFIs are routed to other workers across the organization. The artifact model uses the same complexity scale used in the information exchange models implemented before.

During a given time step, workers process a number of artifacts and information requests up to their capacity. If a given worker has only RFIs or only artifacts available, they process them, but if both are available, they decide which to process by comparing a random number to an artifact preference rating, in the range [0,1]. When the artifact preference rating is higher, it is more likely the worker will select an artifact than an RFI. An artifact rating of 0.5 represents a situation where the worker chooses RFIs half the time, and artifacts the other half.

The artifact model adopts artifact completion rate (number of artifacts completed divided by the total number of artifacts created) as a measure of organizational network performance. If the organizational network is able to keep pace with the demand for artifact processing and information sharing, artifact completion rate will tend to 1.0, with a small deviation resulting from the number of artifacts being processed in the network during any particular time step. However, if the organizational network fails to keep pace with demands for artifact processing and information sharing, the artifact completion rate will drop and the organization will fall further and further behind.

Congestion centrality remains an important indicator of network performance, but separate centralities must be considered. For any node:

r_{A} = μ_{A} N ρ_{A}

(4)

r_{R F I} = μ_{R F I} N ρ_{R F I}

(5)

The A subscript refers to artifacts, whereas the RFI subscript refers to RFIs. In addition, an overall or effective congestion centrality, ρ_eff , can be defined. On average, the network will remain free of congestion when, for any node, R > r_A + _rRFI , where R is the node’s capacity. Noting that total RFI rate is proportional to artifact arrival rate, $μ_{R F I} N = k μ_{A} N$ leads to:

r_{A} + r_{R F I} = μ_{A} N ρ_{A} + k μ_{A} N ρ_{R F I}

(6)

Letting $ρ_{e f f} = ρ_{A} + k ρ_{R F I}$ leads to:

ρ_{e f f} = \frac{r_{A} + r_{R F I}}{μ_{A} N}

(7)

For the artifact model, maximum effective congestion centrality is a measure of organizational network robustness to congestion failure. We therefore compared artifact network performance at low, medium, and high complexity taking both effective congestion centrality and artifact completion rate as measures of performance.

Results

Information Exchange Environment

Figure 6 compares the performance of all organizational networks for the DWS information exchange model, without the effects of complexity, plotting maximum congestion centrality against team links added, as log m/N. Three results stand out. First, random and multiscale networks exhibit behavior consistent with that reported by Dodds et al. (2003) confirming proper implementation of the DWS model. In particular, multiscale networks showed a sharp drop in maximum congestion centrality earlier (fewer team links added) than random networks. Second, matrix organizations performed poorly compared to other networks, showing no meaningful reduction in maximum congestion centrality until a large number of team links had been added. Third, military staff networks performed well, having performance comparable to multiscale networks.

Figure 6

Performance of all organizational networks in the information exchange environment without considering effects of complexity.

Figure 7 compares network performance in the information exchange environment considering the effects of complexity, plotting maximum congestion centrality against team links added, as log m/N, for high complexity. At low complexity, all networks exhibited performance similar to that seen in Figure 6, but at high complexity, maximum congestion centrality varied over a greater range, with clear differences in performance for different networks. Multiscale networks perform well across the range of team links added. Military staff networks also perform well, and have maximum congestion centralities comparable to multiscale networks over the range of team links added from −2.5 to approximately −0.8 as log m/N. Military staff and multiscale networks diverge as more team links are added, with military staff networks converging with random networks as m tends to N.

Figure 7

Performance of all organizational networks in the information exchange environment at high complexity.

Design Environment

Figures 8 and 9 compare the performance of all networks in the design environment at low and high complexity, respectively, plotting artifact completion rates against team links added as log m/N. At low complexity, all networks performed well in the design environment, having comparable artifact completion rates greater than 90%. However, at high complexity, all networks experienced congestion failure, having artifact completion rates less than 90%. Multiscale and military staff networks out-perform random and matrix networks at high complexity, with comparable performance across the range of team links added. By comparison, matrix organizations perform poorly, showing no improvement in artifact completion rates until a relatively large number of team links has been added.

Figure 8

Artifact completion rate performance of all organizational networks in the design environment at low complexity.

Figure 9

Artifact completion rate performance of all organizational networks in the design environment at high complexity.

Figure 10 compares effective congestion centralities for all networks at high complexity and shows that effective congestion centrality exhibits behavior similar to that seen for maximum congestion centrality in information exchange networks. Effective congestion centrality decreases as team links are added, with a sharp decrease over a narrow range of team links. Multiscale networks exhibit this sharp decrease sooner than other networks.

Figure 10

Effective congestion centrality performance of all networks in the artifact environment at high complexity.

Analysis and Discussion

Performance of Organizational Networks

With respect to our first research question, results indicate all organizational networks perform well when the task environment is limited to information exchange. All organizational networks also perform well in the design environment at low to moderate complexity, but experience congestion failure at high complexity, with matrix organizations being particularly susceptible. Results support several observations.

First, task environment matters. All organizational networks can withstand increased complexity when the task environment is limited to information exchange, but experience congestion failure at high complexity in the design environment. Information exchange is essential to the function of a design organization, but design organizations achieve their purpose through the creation of artifacts, so a successful design organization must be able to balance both activities.

Second, complexity presents unique challenges related to task decomposability. At high complexity, it is less likely a design task can be neatly decomposed and assigned to a single functional organization. As a result, the responsible organization must seek additional information from others. Because the task is not easily decomposed, it is more likely that information is needed from an individual in another department, so it takes longer for information requests to reach their target and be answered. The combined effect is extended service times and increased congestion.

Third, matrix organizations are especially susceptible to congestion failure. Conway’s Law argues that design organizations should be organized around the need for communication, and matrix organizations implicitly assume knowledge of communication requirements. In the specific case of a design organization, the matrix structure assumes the need for communication correlates to product architecture, since architecture describes the relationship among components in the system being designed. Matrix organizations should improve communication and information processing relative to functional hierarchies, but results indicate matrix organizations do not improve performance to the same extent as other organizational networks, even random networks.

In complex engineered systems, interactions are poorly understood, so one would expect a large number of interactions would occur outside a structure based on known or predicted design relationships. Increasing complexity only exacerbates the problem because it increases the need for cross-functional collaboration and implies that tasks are not decomposable, which means collaboration must occur beyond the hierarchical or team arrangements defined by the matrix structure. Matrix organizations improve communication within the teams formed, but do not facilitate the more extensive cross-functional and cross-team communication needed when designing complex engineered systems. As a result, matrix organizations are particularly susceptible to congestion failure when complexity of the system being designed is high.

Military Staff Organizational Networks Have Multiscale Properties

With respect to our second research questions, military staff organizational networks exhibit performance comparable with multiscale networks across a range of situations. By comparison, matrix organizations do not exhibit multiscale performance. A key difference between military staff and matrix organizational networks is that military staffs embed the team leaders in the existing functional hierarchy, whereas matrix networks place them in a separate branch of the functional hierarchy. This structural difference contributes to the performance difference between them.

By embedding team leaders in the functional hierarchy, military staff networks inherently build connectivity at multiple scales like multiscale networks. Cross-functional links arise from embedded team leaders, so the multiscale effect builds quickly as links are added, with prompt reductions in congestion centrality. Military staffs improve information exchange and performance like multiscale networks, but results also demonstrate military staff organizational networks begin to diverge from multiscale networks when many team links are added, suggesting that structural similarities between military staffs and multiscale networks become less important when many team links are added. Notably, effective congestion centrality of military staff organizational networks diverges sharply from those of multiscale organizational networks in the design environment, suggesting military staff networks are not as effective at relieving the combined congestion associated with handling artifacts and sharing information.

Military staff organizational networks are not multiscale networks, but they do have performance comparable to multiscale networks over a wide range of situations. It is likely that military staff organizational networks can be adjusted and used in ways to further realize the robust performance characteristics of multiscale networks.

Conclusions

This article set out to understand how organizations can better manage the design of complex engineered systems and sought to identify the organizational forms best suited to that task. Multiscale networks have desirable properties, including low likelihood of congestion failure and resistance to disconnection, which make them robust to fragmentation and communication failure. We used agent-based models to evaluate and compare organizational networks and found that all organizational networks perform well—or well enough—at low to moderate complexity, but experience congestion failure at high complexity. We also found that military staff organizations exhibit multiscale properties across a range of situations, making them the preferred form for the design of complex engineered systems.

Complexity results from the number and diversity of elements in the system being designed, and their interactions, which are often poorly understood. Increasing complexity challenges the design organization’s ability to keep artifacts and information-sharing in balance by increasing the frequency and extent of cross-functional collaboration required. As congestion builds, the organization falls further and further behind, leading to the cost and schedule overruns that seem to plague projects that design complex engineered systems.

Conventional wisdom argues that projects should be organized around matrix organizations because they improve communication and cross-functional collaboration relative to traditional, functional hierarchies. However, results indicate matrix organizations are particularly susceptible to congestion failure. Compared to multiscale, military staff and even random organizations, matrix organizations are not effective at exchanging information because they overlay a project management hierarchy on top of an existing functional hierarchy. The resulting structure fails to create the conditions for effective cross-functional communication when increasing complexity requires collaboration outside established channels. As a consequence, matrix-based design organizations experience congestion failure when challenged by highly complex systems.

By comparison, military staffs can withstand congestion failure and exhibit performance comparable to multiscale networks over a range of scenarios. They are not multiscale networks but build connectivity at multiple scales like multiscale networks. They therefore represent a practical approach to creating an organization with multiscale properties. Unlike matrix organizations, military staff organizations embed team leaders in the functional hierarchy, which makes them more effective at cross-functional communication.

Conway (1968) argued that design organizations should be structured around the need to communicate, but the essence of complexity is the inability to fully appreciate the interactions in the system being designed, which likewise makes it impossible to predict in advance which elements of the organization need to communicate with one another. As complexity increases, organizations must communicate outside their usual hierarchical and teaming arrangements. Military staffs are better at accommodating such demands for increased cross-functional communication than matrix organizations and therefore represent a preferred solution for project-based organizations that design complex engineered systems.

Recommendations

Organizations that set out to design complex engineered systems should organize themselves around a structure similar to that used by military staffs by embedding project managers in the functional hierarchy. Project-based organizations may find it challenging to implement this recommendation, because project management orthodoxy emphasizes a separate organizational role for project managers. Success will depend on having project managers able to balance functional and project management roles, but these are often seen as distinct areas of specialization, especially in design organizations where design demands specific technical expertise. Military organizations are more comfortable blending project and functional roles because the concept of dual chains of command is built into their culture.

The findings, conclusions, and recommendations presented in this article are based on results obtained from modeling, so it would be useful to compare the behavior of actual organizations to model predictions. For example, a case study evaluation of a military staff could confirm whether they achieve multiscale performance in practice and could also reveal important characteristics and considerations not captured by models. A comparable study of a matrixed design organization could likewise validate actual performance against model predictions.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the esearch, authorship, and/or publication of this article.

Author Biographies

Valerie Maier-Speredelozzi is an Associate Professor in the Department of Mechanical, Industrial and Systems Engineering at the University of Rhode Island. She received her PhD in Mechanical Engineering from the University of Michigan in 2003. Her research and teaching interests include lean systems, including manufacturing, service and healthcare industries; design of manufacturing systems; performance metrics for manufacturing and transportation systems; and facility layout and material handling. She can be contacted at valerie@uri.edu

Bryan Still is a retired U.S. Navy Submarine Warfare Officer who received his PhD in Industrial and Systems Engineering from the University of Rhode Island in 2018. His research and professional interests include complexity and complex engineered systems, project management, and agent-based modeling. He is currently working as the President of Basic Engineering Concepts and Technologies, Inc. (BecTech) in Alexandria, Virginia. He can be contacted at bryanstill@icloud.com

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