## 1 Introduction  
Construction projects are carried out by temporary teams of heterogeneous organizations called temporary multi-organizations (TMOs) [1; 2; 3; 4]. During construction projects, many participants from different organizations should cooperate temporarily [5]. For example, such projects involve many participating organizations, such as the owner, designer, constructor, supplier, general contractor, subcontractor, operator, and more. Organizational complexity in projects is the degree of operational interdependency and interaction between the project organizational elements [6; 7]. Reciprocal dependencies represent the highest level of complexity and dominate the construction process [8]. The works of different participant organizations in a construction project are constrained and conditioned by each other. With mutual restriction and the interaction between many factors, complex workflow relationships are formed among organizations. Implementation processes for construction projects, such as the planning and design phase, do not follow a simple linear progression between organizations, but rather undergo an iterative process of continuous modification and improvement among TMOs. Repeated iteration is an important feature of TMO integration. For example, the detailed design process for prefabricated buildings involves iterations of successive revision, similar to agile development [9]. Planning and design often fail, and repeated multi-organizational design is a way to find effective and satisfactory solutions. The integration process of TMOs also involves repeated interorganizational redesign. When interorganizational conflict has not been eliminated, conflict resolution should be carried out. TMO integration is no longer a simple and repetitive process of design modification but is a process of redesign. A complex feedback loop is formed among the workflow subsystems of TMOs. Dependence, coupling, and interactive workflows among organizations would lead to a large number of interorganizational reworkings and work iterations. Workflow systems have significant temporal aspects. Activity sequencing, deadlines, routing conditions, and complex scheduling constraints all involve the element of time [10]. There are many constraints among participant organizations and overlap and conflict in the interorganizational workflow are very frequent. Due to the interorganizational interactive workflow and loosely coupled interdependence among TMOs, the workflow processing time of each organization is difficult to analyze. For each participant organization of a TMO, it is important to study how to effectively analyze performance information, such as the time or workload of the interorganizational workflow. Interorganizational workflows can be analyzed from three perspectives: activity-based, information processing-based, and role-based. In role-based interorganizational workflows, interorganizational relations are regarded as organic social systems, which are composed of relationships among member organizations. \"Role\" is an abstraction of a project participant with a set of skills, and reflects the responsibilities of individual organizations. However, the implementation process of an interorganizational workflow reflects interdependence and execution ordering between activities. It essentially reflects interdependence between the organization of activities. The source of this dependence is that one-member organization controls the results of the activities of another member organization or exchange resources [11]. Current research on interorganizational workflows is mainly conducted in computer-based fields such as e-commerce. Such research is mainly technical, task-oriented micro-analysis [12; 13; 14; 15]. Research on interorganizational workflows has the following deficiencies [16]. 1. Most workflow models focus on the process perspective and neglect the organizational perspective [17; 18]. 2.