The inherent complexity of business goal-models is a challenge for organizations that has to analyze and maintaining them. Several approaches are developed to reduce the complexity into manageable limits, either by providing support to the modularization or designing metrics to monitor the complexity levels. These approaches are designed to identify an unusual complexity comparing it among models. In the present work, we expose two approaches based on structural characteristics of goal-model, which do not require these comparisons. The first one ranks the importance of goals to identify a manageable set of them that can be considered as a priority; the second one modularizes the model to reduce the effort to understand, analyze and maintain the model.
The envisioned state that all organizations desire to achieve, is represented by a set of
strategic goals, which in turn are related to each other through semantic links that
denote the participation that a specific goal as a support of others. The particular goal
arrangement and goal relationships of an organization, constitute its business goal
model. It is well-known the extensiveness and complexity inherent to business
goalmodels [
Several approaches has been developed to address the complexity problem, among
them we refer to [
To reduce the complexity, we propose two approaches from the Graph Theory perspective, which are based on topological characteristics of the model, and unlike the aforementioned, they do not require to be compared with any dataset and are not associated with a specific semantic or based on goals relationship. We apply these approaches to an organization’s goal model created to support the analysis of OSS adoption implications. The complexity hinders the analysis and management of the model. Our first proposed approach is the Ranking, which identifies a manageable set of goals that are relevant for a specific analysis; this approach allows us to focus the effort on goals that can be considered as high priority. Our second proposed approach is the Clustering, which seeks to decrease the complexity creating modules of goals (clusters) that can integrate a hierarchy with different levels of abstraction; this hierarchy facilitates the analysis and maintenance tasks because the effort is centered in one subset of goals at a time.
The rest of the paper is structured as follows: Section 2 introduces the characteristics of our goal model; Section 3 presents the ranking approach; Section 4 presents the clustering approach; finally Section 5 shows the conclusions. 2
With the business goals catalogs presented in our previous work [
In the context of our research, we need to analyze the importance of the goals from the organization’s point of view. The resulting model contains a unique root element representing the organization’s vision (1BG01 Vision, the main business goal to reach) located at the upper level; from this root are disaggregated all other goals. Our example only includes those business goals that are involved in OSS adoption. As aforementioned, the large number of goals and its relationships increases the complexity of the model and, therefore, the effort and resources required for its analysis. For this reason, a selective analysis is more efficiently that an exhaustive one, because the first one allows focusing on a manageable set of highly impacted goals.
With this perspective, the first of our approaches proposes to identify this manageable set through a goal importance ranking. This ranking allows us to know the business goals that receive more cumulative impact from its offspring (all its sub-goals down to OSS adoption strategy goals). This ranking also considers the total size of the goal model, because, for example, a goal does not have the same importance if it belongs to a model of 200 goals or if it belongs to a model of 20,000 goals, even if its offspring is the same. It is important to emphasize that our analysis is topologic, not semantic, and therefore do not consider the type of link.
In graph theory, the centrality concept manages the importance of a node in the network. From several centrality metrics, we decided to apply PageRank [11] because it calculates the importance value for each node based on topological characteristics of the model (number of goals and links among them) and works with a unique ‘root’ node. An excerpt of PageRank (PR) values for the goal model of our example is presented in Table 1. They are obtained using Gephi tool (https://gephi.org/) with a damping factor set in 1 (a value less than one and greater than or equal to zero is assigned to damping factor when this algorithm is applied to web navigation graphs). As we appreciate, the most impacted goals are in the first places of the ranking, that is, goals which achievement depends on the achievement of a major number of sub-goals. This is the case, for instance, of To ensure that income (revenue streams from the s/p/f) are obtained as planned, that is the 3rd goal in the ranking with an importance value of 0.0586 and depends on 44 sub-goals, against the goal To offer the p/s/f required, that is the 25th goal in the ranking with an importance value of 0.0084 and depends on 15 subgoals.
This ranking may be used to know the most impacted node among nodes that have the same detail level. For example, at the 4th level of detail, the importance value of To establish a patent scheme (0.0020), is less than To incorporate external innovation inputs into the business offering (0.0204): the difference is caused by the number of sub-goals each has. 4
As we mentioned in the Introduction, an appropriate management of the goal model’s complexity is a critical success factor to improve the analysis and understanding of goal model. One way to deal with this issue is to modularize in order to divide an extensive model into small, more manageable modules that can be analyzed and maintained as a unit. In this sense, our Clustering approach groups the goals applying a clustering algorithm to find, if possible, two or more community structures that could constitute modules. A community structure is a set of nodes that has more connections between its members than to the remainder of the network [12].
We apply three clustering algorithms: Clauset-Newman-Moore (CNM) [13], Wakita-Tsurumi (WT) [14], and Girvan-Newman (GN) [15]. In Table 2 we present the synthesis of results. The CNM algorithm found 6 clusters: Offer & Innovation, Strategy & Law compliance, Incomings, Oss Community, Human Talent, and Quality. In this last one, the membership of 4 of its goals it is not quite clear; these goals are: To manage customer relationships (establish, maintain and expand them), To ensure the output logistic (customer delivery), To choose a compatible license, and ACQ-Leg (To acquire legal skills). Over the others clusters, there are not doubts about its members. In the Fig. 2 we show the clusters identified by the CNM algorithm. For the processes of clustering and visualization, we use NodeXL Excel Template (http://www.smrfoundation.org/).
The Wakita-Tsurumi algorithm found 10 clusters, 2 of which are the same as those found by the CNM algorithm (Human Talent and Community); 3 of them are very similar (Offer & Innovation, Strategy & Law compliance, and Incomings; they have 3, 4 and 2 goals less than the correspondent CNM groups, respectively); 3 of them are about Quality (component integration, component selection, and customer issues, which in total have 4 goals less than CNM Quality group); 1 of them is new: Offer Delivery; the last group comprises 6 goals (about market, offering, use of OSS component, working practices) without a clear relationship.
The Girvan-Newman algorithm found 7 clusters where the most relevant issues with regard to CNM classification are: Quality is divided into 2 clusters (component integration, and component selection); the Human Talent and OSS Community goals are grouped into a single cluster; and, Legal goals are placed in a cluster with the goal about to the shareholder value model sustainability. 5
In the present work, we have proposed two approaches to managing the complexity of goal-oriented models, based on its topological characteristics. The first approach generates a ranking of the importance that each goal has like part of an entire model (without considering a goal in isolation); the highest values in the ranking correspond to the goals with major relative importance, which can be selected to perform a deeper analysis. The second approach seeks to identify groups of goals that can become modules; thus, based on the application results of Clauset-Newman-Moore, WakitaTsurumi, and Girvan-Newman algorithms, we found that the adequate goals grouping is performed by the first of them; this algorithm generates modules which goals have more affinity.
Acknowledgments. This work is a result of the Q-Rapids project, which has received funding from the European Union’s Horizon 2020 research and innovation program under grant agreement N° 732253. Lucía Méndez’s work is supported by a SENESCYT (Secretaría de Educación Superior, Ciencia, Tecnología e Innovación) grant from the Ecuatorian Government.