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the LCM defines a strict order constraint from the former to the latter. There-
fore, the reverse strict order in the complement is shared forbidden behaviour
and prevents execution of activity
'Update GBA Data' before 'Confirm Identity'
.
C4: Redundancy of variants: Inclusion of variants.
Given the behavioural
profiles of two process variants
P
i
and
P
j
, the question whether the behaviour
of one variant is captured in the other variant for the shared activities is traced
back to the inclusion of their behavioural profiles, i.e.,
B
P
i
⊆B
P
j
.Inthiscase,
all constraints imposed by
P
i
would be equal or less strict than the constraints
imposed by
P
j
, so that the behaviour (according to the behavioural profile) of
P
j
is covered by
P
i
. That suggests integration of variant
P
j
into variant
P
i
.
Investigating the two models given in Fig. 1, the behavioural profile of model
(
II
) includes the profile of model (
I
) for the shared activities. Hence, when aiming
at reducing the number of variants, the existence of model (
I
) may be challenged.
5 Case Study
Our approach to managing process variability has been evaluated based on the
SAP reference model [27]. This model collection describes the functionality of the
SAP R/3 system and comprises 604 process diagrams, which are expanded to 737
models in EPC notation as some diagrams contain multiple disconnected EPCs.
These EPC models capture different functional aspects of an enterprise, such
as sales or accounting. However, the models are not fully orthogonal. Various
models show an overlap, such that events and functions with identical labels
occur in multiple models. These models, therefore, represent process variants.
For our analysis, we excluded all models that showed behavioural anomalies,
such as deadlocks and livelocks [28], or ambiguous instantiation semantics [29].
We also normalised multiple start and end events, and replaced block-structured
OR-split and OR-join connectors with AND connectors, which does not impact
on the behavioural profile. These selections and transformations led to a set of
493 EPC models, that are grounded on our formal model introduced in Sec-
tion 2.2. Hence, we were able to leverage the ecient techniques mentioned in
Section 2.3, so that behavioural profiles were computed in milliseconds.
Table 1 gives on overview of the observed clusters of process variants in the
SAP reference model. Given a threshold of shared nodes, we derived all process
model clusters of maximal size for which the set of shared nodes was equal or
Table 1.
Variant clusters in the SAP reference model
# Shared Nodes (Min)
4
6
8
10 12
14
16
18
20
22 24 26
# Variant Clusters
84
48
33 23 23
21
15
11
9
2
1
0
Avg Size of Clusters
3
3
3
3
3
2.6 2.4 2.3 2.3
2
2
0
Max Size of Clusters
10
9
8
8
7
6
4
4
4
2
2
0
# Models in Clusters
212 124 88 63 56
47
36
25
21
4
2
0
# Subsumed Models
127
73
55 41 35
28
20
14
12
2
1
0
