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subset of valued-assigned elements will constitute the subset of parameters of the
model, whereas the non-assigned elements will form the subset of variables of the thus
defined feasibility/optimization problem. In the mathematical example, we will obtain
different equations with the assignment of values to a subset of the model elements (a,
b, c).
Equation Metamodel
Business Process Metamodel
Business Process Model
a - b = c 2 ; a, b, c  N 0
a=5
b=?
c=2
a=?
b=2
c=1
Business Process Instance
Fig. 1. Generic modeling hierarchy
Throughout the modeling process of the proposed hierarchy we make use of the standard
UML, Unified Modeling Language (OMG, 2010). UML is an ongoing project developed by
the OMG, Object Management Group, with the initial objective of standardizing and
unifying the proliferation of object oriented modeling languages developed in the late 80s
and early 90s (Fowler, 2004). According to OMG's description, UML supports the
specification, visualization and documentation of software system models, including their
structure and design, even though UML can also be used for business process modeling and
modeling of other non-software systems too (OMG, 2011). The choice of UML derives from
the confluence of these two traits: its applicability to business process modeling together
with its software systems orientation (Eriksson & Penker, 2000) and the unifying standard
nature with which the language was born, that has facilitated its growing usage and
acceptance.
In the following sections we present the UML class diagrams that describe each of the levels
of the business process hierarchy. Class Diagrams evolved from the Entity Relationship
Diagrams (ERD). They describe the types of elements found in a system (entities) and the
structural relationships among them. Entities are represented as square boxes and the
relationships as lines that join two participating entities. There are two basic types of
relationships: Association, in which participating entities are at the same level, and
Generalization, graphically depicted as a line terminated in a triangle, in which one entity is
a subtype or specialization of the other (“is-a-kind-of” relationship). Relationships may
include a cardinality, or degree of multiplicity with which an entity participates in a
relationship; it is denoted by the corresponding number, or by an asterisk to indicate any
multiplicity. The default value for cardinality is one. Additionally, the role that an entity
plays in a relationship might be annotated next to the entity.
3. Business process metamodel
The UML model that corresponds to the first abstraction layer is shown in Fig. 2. A business
process model defines how a particular type of infrastructure is assigned to one of its potential
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