Alternative approaches to studying Network Complexity

highlighted by Lassen and van der Alst (2009), took a quality perspective to measuring process models by measuring process gateway parameters. Their method was to use a controlled experiment to evaluate uncertainty and modifiability as process quality characteristics. Six gateway parameters are considered, defined as types XOR, OR and AND combined with the directional characteristic SPLITS and JOINS. Six complexity measures are considered: Control Flow Complexity (CFC), Gateway Mismatch (GM), Gateway Heterogeneity (GH), Average Gateway Degree (AGD), Maximum Gateway Degree (MGD) and Total Number of Gateways (TNG). In studying these characteristics their research question asked if it is possible to automatically distinguish between understandable/modifiable models and those not so, through

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measures of structural complexity using the above metrics. They concluded that threshold values for each of the above measures were valuable in the process of understanding and modifying business processes. These threshold values are set out in the following points:

 In a business process, include no more that 18 to 22 nodes,  Minimize the number of OR split nodes,

 Include no more than 10 XOR, 7 AND and 4 OR decision nodes,

 Each decision nodes should have no more than 7/9 input/output sequence nodes,  A difference higher than 15 -20 in the number of input/output sequence flows

between split/join nodes is unacceptable.

Failing to adhere to these guidelines, they suggest, threatens process model conclusion validity, construct validity, internal validity and external validity. Cardosa, et al. (2006) consider research measuring complexity in business process to be a new field of research.

They suggest complexity impacts on the correctness, maintainability and understandability of process models. Their research looks for analogous metrics from the fields of cognitive science, graph theory and computer science and discusses the application of these metrics. The computer science metrics considered are the Line of Code, McCabe Cyclomatic Complexity, Halstead Complexity Information Flow Metric. Their work on cognitive science is limited to the work of Cant, Jeffrey and Henderson-Sellers (1995) who developed a conceptual model for understanding complexity in computer programming; and there research on graph theory is limited to work by Latva-Koivista (2001), Neumann (1988) and Sheppard (1990) with some rudimentary graph metrics being considered. They draw no conclusion from their research, except to state that empirical testing will be the next steps in the process.

Kluza and Nalepa, (2012) provide an overview of existing process metrics and propose a new ‘square’ metric based on the business process model and notation design (BPMN). Their

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approach first outlines BPMN as a set of standards against which business processes can be captured. Based on the computer sciences approach they review the work on business process metrics of Mendling, Reijers, and van der Aalst, (2010); Ligeza, (1999); Wang, et al. (2011); Grady, (1994); Monsalve et al. (2011); Khlif et al. (2010); Reijers and Vanderfeesten, (2008); Cardosa et al. (2006); Vanderfeesten et al. (2007); Conte et al. (1986); Lassen and van der Aalst, (2009); and Muketha et al. (2010). Finally they propose the use of the Durfee Square Metric (DSM) and the Perfect Square Metric (PSM). They conclude by suggesting there to be a lot of current research on business process metrics, derived from the computer industry, which has yet to be empirically validated. In this paper they propose the use of DSM as a simple but effective metrics with validation coming from future research.

Medling, Reijers and van der Aalst (2009), like most research in this domain, take information technology as the origin of process modelling and focus on the quality of business process modelling. They analyse the exiting research on the relationships between model structure, error probability and understanding, and propose seven guidelines for business model development. The basis for their analysis is: business process models have become the a focus point in the enterprise because it is the effective completion of the processes in the enterprise that enable the competitive position of the enterprise in the market place; however, effectivity is being eroded because of a lack of guidance to users on the development of effective business process models. Consequently they offer seven guidelines for the effective construction of business models.

The method they use is to build the guidelines from previous research, specifically, this research is taken from how process models are understood, the error probability of processes and the ambiguity of the process labelling. From this research they suggest seven guidelines:

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 Use as few elements in the model as possible.  Minimize the routing paths per element.  Use one start and one end event.

 Model as structured as possible.  Avoid OR routing elements.  Use verb object activity labels.

(For clarity, `Model as structured as possible’ in the above list is defined as each split connector having a respective join connector).

This review of network theory in supply chain management, of alternative approaches to network theory and the earlier reviews of entropy and information theory suggest the need for greater understanding of complexity in supply chain management if the concept is to remain an effective model for understanding the structure of a multi-organisation approach to the movement of material, information and cash. Furthermore, the literature highlights the need for new approaches to methods and frameworks for understanding complexity in the supply chains. Finally, the research calls for continued experimentation and testing of methods and frameworks in what appears to be a relatively immature field of research. Given this requirement, this research will now move towards the development of an approach aimed at answering some of these calls.