The structural details of a firm's business processes are traditionally inaccessible to entities outside the firm. However, as firms move towards tighter coordination of processes with business partners, and system-level coupling between the processes of interacting firms, it is useful to share some features of the processes. In this paper, we show how the representation of business processes using metagraphs supports a hierarchical view that facilitates such information sharing. We show how each process owner can designate appropriate elements of process structure to be shared, while keeping other details private. We also show how business rules can be specified for shared processes. A bank loan process example is used to illustrate the approach.
Business process modeling and analysis has traditionally focused on processes within firms. There are several reasons for this. First, most businesses, and particularly vertically integrated firms, have devoted much of their management attention on internal processes, preferring to deal with external service providers and business partners at arm’s length. Second, most firms have traditionally had very few levers of influence over the operational performance of the business processes owned by their business partners. Third, the level of information available to process modelers is obviously much larger for internal processes, and thus the investment in formal tools for process modeling has appeared far more justifiable for these internal processes.
Today, firms are increasingly participating in collaborative networks. This allows more tightly focused business
capabilities that more effectively leverage each firm’s core competencies. A major factor driving this trend has been
the increased capabilities for online inter-firm coordination processes enabled through information technologies
ranging from email and the Internet to EDI and Web services. A familiar example of such coordination is the
Vendor Managed Inventory (V
These trends can also be examined in terms of economic theories such as Transaction Cost Economics that argue
the merits of market mechanisms for business transactions [Williamson, 1981], but recognize the inherent risks and
costs of using markets rather than intra-firm hierarchies [Malone e
In this paper, we use a graph-theoretic approach to modeling business processes, which addresses the above
concerns and challenges. In other words, we show how business process analysts and managers within each firm can
represent their processes in a way that not only facilitates formal analysis of these processes, but that also facilitates
the creation of external views of these processes that can be shared with business partners. Our approach is based on
a graph-theoretical approach to the specification of business processes and workflows, using a construct called a
met
A metagraph is a graph-theoretic construct in which each edge is used to denote directed relationships between
two sets of elements, the invertex and the outvertex of the edge. These relationships can be represented visually, as
shown in Figure 1. Each set of elements in a vertex is identified by surrounding them by a closed boundary such as
an oval. Each arrow denotes a relationship, from the invertex of the edge to its outvertex. Metagraphs are an
extension of traditional graphs and directed graphs, as well as of hypergraphs [Berge, 1989]. From a visualization
perspective, they are similar to directed hypergraphs an
In addition to the visual representation, there is also a formal matrix representation of a metagraph, in terms of an
adjacency m
In the metagraph representation of business processes, each process is represented as a collection of tasks, and
each task is represented as an edge linking sets of inputs and outputs [B
An example of a metagraph-based representation of a process is shown in Figure 1, which depicts a
simplified version of the process of loan evaluation in a bank. The vertices in the metagraph consist of information
elements needed in the process. To illustrate the representation, consider the edge e3, which represents an applicant
risk assessment task. This task is performed by a credit analyst (c), and generates a value of CR, the credit risk rating
of the applicant, based on the credit history of the applicant. This task is estimated to take one week (perhaps
because the credit history may be quite extensive, and will take time to analyze). This example shows many features
of the metagraph representation of processes, such as the assignment of resources to tasks, the scope of each
resource in terms of the tasks they are involved in, the possibility of requiring multiple resources for a task (as in
task e5, which is performed by the credit analyst and loan officer together), the use of numerical attributes on edges
to denote expected durations of tasks, and the sequential dependencies of tasks. While outside the scope of this
paper, the metagraph representation supports formal transformations of process representations so that the process
can be represented as a metagraph with the tasks as elements, or even the resources as elements. This ability to
analyze processes from either an information element, task or resource perspective, is a major strength of the
To start with, we assume that each of the relevant processes within each firm in the business network are represented as metagraphs accessible to analysts and managers within the firm. This internal specification of each process details its complete structure, and is intended for internal use within the firm owning that process. However, the business partners of that firm may also need to have some understanding of the structure and scope of the process, so that they can align the process with their own related processes. An obvious challenge in this area is the representation of each business process at these different levels of specificity, so that different entities involved with that process can not only be aware of the process, but also factor their understanding of the process into whatever process analysis they need to perform.
The metagraph approach to process representation allows multiple representations. For instance, a projection
operator [B
The value of the projection operator is that it provides a simpler view of a process or system. In the context of business process modeling, this hierarchical abstraction serves another useful purpose. It enables selective disclosure of process knowledge, thus facilitating knowledge sharing across firms. However, this requires a refinement of the projection operator, which only identifies edges that correspond to complete metapaths in the base metagraph.
In the projection operator as defined in [B
This variant of the basic projection operator is called an external projection operator, and can be defined as follows:
Definition: Given a metagraph S =
X , E
with a subset X1 of X being private elements, then an external projection of S over a subset X’ of X such that X ' X1 z I is obtained by taking the corresponding projection of S over X’ and then removing all elements of X1 from it.
Note that the external projection can be easily derived from the regular projection operator, so no new procedures
are needed, beyond the structured procedures for constructing projections described in [B
Assume that an external user (e.g., an analyst from a business partner firm) queries for a view involving a subset of elements X1. The relevant view would be the external projection of all projections over the smallest superset of X1. Since this would be hard to predict, it would be a potentially risky functionality to delegate to external users.
Assume that two separate external projections of the same process are visible to an external user, such that there is no metapath in the combined view over those two projections between a given vertex pair A and B. This does not mean that in the complete internal process there is no metapath between A and B. This is formalized in the following statements.
X , E and the corresponding external projections S1 and S2 of S over any subsets X’1 X1 and X’2 X2 of these two sets respectively, any metapath in the union of these two external projections corresponds to a metapath in the external projection of S over X’1 X’2.
Proof: Let M(B,C) be a metapath from B to C in the union of the two external projections. Then B, C X’1 X’2. Since every edge in these external projections corresponds to at least one metapath in the base metagraph (with possibly some additional input elements that were hidden), it follows that there is a metapath M’(B,C) in the base metagraph. Since the external projection of S over X’1 X’2 includes all metapaths over that projection set, and since B, C X’1 X’2, then there must be a metapath M”(B,C) in the external projection of S over X’1 X’2, which is the desired result.
Corollary: The lack of a metapath in the union of two external projections of the same metagraph (over X1 and X2 respectively) does not imply that there isn’t such a metapath in the external projection over the set X1 X2.
The external projection provides a very useful way to share process knowledge. We illustrate this using the example process in Figure 1, which reveals the loan evaluation process assuming that all the tasks are performed within a single organization. Now assume that the process is to be disaggregated into component sub-processes managed by two organizations. The first organization is the bank, which has the loan officer and credit analyst resources. The second organization is a realtor’s office, which consists of the realtor resource (for space reasons, the loan decision propositions are used to correspond to the approval and rejection decisions). An external view of these interacting processes that could be used to integrate this process with other business partners could consist of the two edges shown in Figure 3.
The strength of this approach is that each organization can represent, analyze and manage its own processes using the metagraph representation. At the same time, the external views of the processes collectively comprise a metagraph too, which can be analyzed using the same formal analytical tools and procedures.
Most business processes are also governed by business rules, which determine the specific conditions under
which each task can apply. In the metagraph representation, rules can be incorporated seamlessly in the
representation. This is because rules stated in the form “IF <A> and <B> and … THEN <C>” can be represented as
edges in a metagraph, with the conditions (antecedent) forming the invertex of each edge and the consequent
forming its outvertex. In other words, a collection of rules can be represented as a metagraph, and rule-based
inference can be implemented using connectivity properties and procedures on the metagraph. This has been shown
in [B
In the context of a business network, business rules show up in two ways. First, there are business rules that apply to a firm’s own processes. Such rules can be incorporated into the metagraph representation of each relevant process. Furthermore, such rules would be abstracted out of the external view of the processes as seen through suitable projections applied to the process metagraphs. It is easy to see how each firm in the network can keep its internal rules secure, even while revealing the appropriate information about its processes to its partners. An internal rule would appear in a projected view of a process only if all the antecedents and the consequents of the rule were part of the projection set (which is controlled by the firm that owns the process). At the same time, a business partner may want to impose conditions upon its partner’s processes. For instance, a manufacturer may insist that the component produced by a supplier meet a particular quality requirement.
The shared representation of inter-organizational processes can also be embellished with additional business rules that are visible to all partners, and can be used to refine the process. For instance, in our example, consider the addition of a negotiated rule among the partners that if the credit rating of the applicant is below B, then the risk is too high. Such a rule can be superimposed on the shared process by adding it to the appropriate view, and this also propagated to the relevant organizations (the ones that owned processes touched by the new rule). It is important to recognize that any shared rule can be applied to the external (or shared) view of a multi-firm process could be designed for use only in this particular business network, without affecting how each individual firm may conduct its process internally, or with other partners. This is because each firm can construct different views for different networks in which it participates, and the collective processes in these networks could be very different, yet all managed in conjunction with each firm’s internal processes, and without violating any privacy constraints for any of the internal processes. This ability to organize networked processes so that it can behave differently in different contexts is a valuable feature of the metagraph approach.
In this paper, we have focused our attention on two types of knowledge sharing about processes that can be
valuable for managing inter-organizational processes, namely process structure and process logic. However, the
metagraph representation supports a variety of other types of process knowledge that can be shared for effective
process management. For instance, process metagraphs can be transformed into equivalent metagraphs that focus on
the interactions between resources, rather than information elements. These resource interaction metagraphs (RIMs)
can be analyzed in the same way, since they are based on the same construct [B
Another very useful type of process analysis involves the use of quantitative attributes such as task duration. For instance, in Figure 1, each task edge has a number associated with it, which is the estimated duration of that task in days. Using such attributes, quantitative analysis of features such as critical paths, critical tasks, and process durations for different workflows can be formally done, as shown in [Basu and Blanning, 2001].
In this paper, we have shown how representation of business processes and workflows as metagraphs can be used to share knowledge about process structure and scheduling across organizational boundaries in ways that support not only useful visualization and abstraction of processes but also structural analysis of these processes. In particular, we have showed how the projection operator on metagraphs, and an extension of it called the external projection, can be exploited for inter-organizational process representations at appropriate levels of specificity and disclosure. We have also shown how temporal information about processes can be represented in process metagraphs, which can be used in critical path analysis to improve analysis and sharing of temporal knowledge about such processes, both within individual firms as well as across the participating firms in a business network.
It should be recognized that while the exposition in this paper has been primarily in terms of the visual representation of metagraphs, all the features and analysis that we have discussed can be implemented in computer-based tools that manipulate the algebraic representation of process metagraphs in terms of algebraic operations on the adjacency matrix and derivative structures such as the closure matrix. Detailed description and discussion of such algebraic analysis is available in many of the archival papers cited in the references.
AD PD 4 e2 (r)
AD: Applicant Data AV: Appraised Value CR: Credit Rating CH: Credit History LA: Loan amount LD: Loan Decision LV: Loan to Value Ratio PD: Property Data c: credit analyst; l: loan officer, r: realtor