A Mathematical Programming Model for the Process Mining in Dependency Graph Discovery Problem

Process discovery is a branch of process mining that by using event logs extracts the process model that describes the events’ behavior properly. Since, Heuristic process discovery algorithms are among the most significant and popular process discovery methods and due to the fact that the quality of outputs of these algorithms is heavily dependent on the quality of extracted dependency graph, in this paper for the first time, an approach to transform the problem of dependency graph discovery to a binary programming problem has been proposed and also, an objective function is introduced that simultaneously considers fitness and precision measures of output models. The weights dedicated to each of the measures are determined by means of a user-defined threshold. The mentioned measures are the most important metrics in assessing quality of output models of process discovery algorithms. Hence, in fact this approach focuses on improving quality metrics of output models. Moreover, by means of defining suitable constrains, the proposed approach is capable of involving domain knowledge in mining procedure, as well as guiding the result through whether the models that are more likely to be sound. This is depicted in a case study of a real company that is described in this paper. In the case study, the proposed approach has been applied to marketing event log of the mentioned company by utilizing the constrains defined according to domain knowledge and structural rules of dependency graph and at the end, the results were presented