We have developed a BPM software that runs on a non-flow chart model, we call the process model for the Process Matrix (and it is in fact Excel, in that we document the content in Excel). It is simple in the initial concept: We model a process as a project plan, and we let the rule engine determine which of the activities of the project plan are to be active at any time in the process instance. It’s a matrix, because the outcomes of the rule engine are the columns, and the activities are the rows (as in a Gantt chart of a project plan that contains all possible actiivities in a process, ordered into a legal sequence and with all sequence constraints modelled as predecessors).

The project plan gives us the parallellism and a range of other things that BPMN can’t express. And it enables the rule engine to govern the process at more than just the branch points (through the columns of the matrix). The Process Matrix scales near linearly with the number of decision outcomes in the decision dimension as well as with the number of overall activities in the process dimension. Flow charts - such as BPMN - potentially scale near-exponentially, because the decision complexity through the branch points create a huge amount of branches (it potentially doubles the number of branches for each added decision point).