§ 4.3.1
Graph-based models
Graphs are popular tools for representing complex models, by virtue of their modelling flexibility that further offers an intuitive and creative modelling environment. Graph Theory has numerous applications in computer science, electrical engineering, and operations research. The basic module of a graph is a triple that consists of two nodes (or vertices), connected through an edge (line or arrow). Graphs are also popular in BIM research since the IFC is usually represented as a hierarchical data model i.e., in EXPRESS-G, the graphical representation of the EXPRESS modelling language. Moreover, graphs are very popular in portraying SCM concepts, e.g. block diagrams of the relations among the SC actors, e.g. in Lambert et al. (1998) (see Figure 15), O’Brien et al. (2002)
and London (2009). In Figure 15, Lambert et al. (1998) have represented a focal firm and at least three tiers of their suppliers and customers as a tree-based (hierarchical)
graph consisting of nodes (other firms) and lines (purchasing relations). In Figure 16, Pryke (Pryke, 2012) represented the AEC supply chain as a non-hierarchical network, where the various actors exchange information beyond their contractual relations. Thus, graph-based approaches have already provided powerful visual and analytic tools for representing SC complex systems, either hierarchical or of network-type.
1 1 1 1 1 1 2 2 2 2 3 3 n n n n n n 1 1 1 2 2 n n n Initial Suppliers Tier 3 to n Suppliers
Tier 3 to n Customers Customers / End Customers
Tier 3 to
Initial Suppliers SuppliersTier 2 SuppliersTier 1 CompanyFocal CustomersTier 1 CustomersTier 2 Tier 3 to Customers/End Customers
FIGURE 15 Typical representation of a Supply Chain Network Structure (adapted from Lambert et al. [1998]).
Project Manager Client Engineer A B C D E Supplier A B C D Contractual relation Information exchange
First Tier Second Tier
Contractor
Third Tier
Engineer B Architect
Subcontractor A
AEC organisationLEGEND:
Graph Theory has its roots in the 17th century when a topological puzzle – the bridges of Koningsberg – attracted the interest of Euler, who used mathematics to resolve the problem (Biggs, Lloyd, & Wilson, 1976). Since then, graphs have become natural in systems theory, software engineering, and computer science. While in OR and SCM research, graph-based approaches are popular for some decades now; they have only recently been introduced to BIM research. Graph-based methods are used in BIM applications to map topological, i.e. physical, relations within buildings or to clarify the actors’ configuration. Besides representing product-related aspects, graph-based models are used in rationalising more intangible process- and actor-related aspects of the AEC. Merschbrock (2012) created a network of collaborating actors and identifies the architect as a communication hub. BIM and graph theory have been combined for change management in construction (Isaac & Navon, 2013). Hickethier et al.
(2013) analysed the BIM-based interaction of various actors in an IPD project using graphs. From the above, the graphs could be quite eloquent for the representation and understanding of socio-technical systems, and particularly of inter-organisational BIM use. However, in BIM research the graphs are more likely to be used to represent the groups of actors are networks, rather than hierarchies, which has been customary in the SC research.
§ 4.3.2
Modelling types
Product and process modelling
A product model is a set of specification data for a given artefact – physical or conceptual. The need to formalise and structure these data in a logical way so as to represent knowledge generated the area of data modelling (Eastman, 1999). In AEC, the need to achieve a high-level definition of the building systems generated the area of product modelling by using the advancements in data modelling (Dado et al., 2010). A popular type of data model is the E-R model, where information is defined regarding entity, relation, and attribute. Within construction, the IFC model is an industry standard definition of products and processes, used for data modelling and interoperability in many proprietary applications. But, since essentially it is an E-R model, it lacks the notions of time, and it faces a “process and data dependency problem” (Eastman, 1999). The product models can also be represented as either hierarchical, i.e. tree-like or Product Breakdown Structure (PBS), or network-type models. A Work Breakdown Structure (WBS) follows again a similar logic to the PBS to hierarchically represent relations among project fragments. However, in network-type product models, the inheritance property allows for multiple ‘child-parent’ relations, and therefore is closer to representing complex real-world systems.
Business Process Modelling, or simply process modelling, represents the activities within one organisation. Process Modelling produces a ‘blueprint’ of order and work breakdown structure. Similarly to any model, these models could also be either static or dynamic (Law & Kelton, 2000). Static models simply represent the structure of the system. For instance, Business Process Modelling Notation (BPMN) is a static model, which has no state change or timing mechanism, although it has the notion of order and control. The dynamic models represent the change of an existing state throughout time. State machines, stock and flow diagrams, activity diagrams, and event graphs represent processes dynamically. Time is the indexing attribute that provides order and sequence. There exists no unified methodological framework for process modelling, regardless the research domain and goals (Reiner, 2005). Hierarchical and network- type models also apply to process models. For example, the Critical Path Method (CPM) is a network-type approach for process planning and avoidance of bottlenecks, which however requires highly detailed a priori knowledge of the duration of the involved activities. Case handling is another approach for representing processes via a network of work items and roles without separating on control points (Aalst, Stoffele, & Wamelink, 2003). Thus, it would be probably not sufficient to represent and coordinate all the intricacies of a complex system, such as the AEC SC, only via product and process models.
Organisational Models
Usually, project planning in AEC is tinted by considerations about the products and processes. However, from the above, the process and product models alone apparently cannot fully represent the AEC SC complexity, because they omit the input from the various multi-disciplinary actors. For example, in a BIM-enabled SC partnership, the BIM actors are non-negligible since with their intra- and inter-organisational behaviour, they influence both the products and processes. The SC actors could be represented in a ‘Breakdown Structure’, as in the PBS and WBS models, but this would entail an a priori rigid hierarchy and not dynamic network-type behaviour, which might nevertheless be more complicated but undoubtedly closer to reality. These actors exchange information in an iterative and bidirectional manner, beyond simple dual relations. Therefore, probably the actors of the BIM-enabled SC partnerships would be better represented as a network-type, rather than a hierarchical model (compare again Figure 15 with Figure 16). Besides, the interweaving relationships in such organisational networks cannot be represented on a bilateral basis (Kornelius & Wamelink, 1998). Moreover, the numerous organisations involved in a SC system increase its unpredictability and complexity. Therefore, analysing the actors involved in the SC systems could offer an additional level of analysis that could contribute to the decision-making and the structuring of the coordination processes in BIM-enabled SC partnerships.
Organisational models are usually illustrated as graphs or networks. Network Theory, as a subset of graph theory, is applied in many other contexts, from social sciences and operation research to medicine and epidemiology. Networks can represent the relations (lines, arrows or edges) among organisations (vertices, posts or nodes) (see again Figure 15). At a high-level, AEC is considered a loosely-coupled network of numerous organisations that temporarily coordinate within and for projects
(Dubois & Gadde, 2002a). These high-level – or strategic – networks are responsible for establishing long-term communication, trust, and commitment. Pryke (2004, 2005) creates organisational models – which he calls Social Network Analysis (SNA) in construction – to visualise and analyse information exchanges, performance incentives, and contractual relationships and concludes with the deployment of network metrics for project governance. At an operational level, Farshchi and Brown
(2011) perform SNA to measure the employees’ information exchanges and define the knowledge and culture transfer within project-based teams. Accordingly, graphs could explain the organisational complexities of an AEC SC system in various scales, e.g. industry, organisations, and employee). However, as mentioned previously in section § 4.2, there are two different levels that coordination of BIM-enabled SC partnerships could be studied. These levels pertain to a strategic level for the SCM philosophy, and to an operational level for BIM respectively. This study focuses on the inter-organisational relations from a network perspective and at an operational level to gain insights into the coordination process and inform, afterwards, the strategic level accordingly.