# An Approach to Participatory Business Process Modeling: BPMN Model Generation Using Constraint Programming and Graph Composition

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## Abstract

**:**

## 1. Introduction

## 2. Business Process Modeling with BPMN

- Sequence: simple succession of activities.
- Parallel split: split in a single thread of control into multiple threads that can execute in parallel.
- Synchronization: synchronization of multiple parallel branches into a single thread.
- Exclusive choice: representation of a decision point in a process where one of several branches is chosen.
- Simple merge: a point in a process where two or more alternative branches come together without synchronization.

- $\mathbb{O}$ is the set of flow objects,
- $\mathbb{F}\subset \mathbb{O}\times \mathbb{O}$ is the set of sequence flows.

- $\mathbb{T}$: a non-empty set of tasks ($\left|\mathbb{T}\right|>0$),
- $\mathbb{E}$: a non-empty set of start and end events ($\left|\mathbb{E}\right|>1$),
- $\mathbb{G}$: a set of gateways that split or merge the flow,

## 3. Related Works

#### 3.1. Generating Models from Text Description

#### 3.2. Generating Models from Other Models

#### 3.3. Generating Process Models from Data Models

#### 3.4. Generating Imperative Process Models from Declarative Models

#### 3.5. Analyzing Workflow Logs

## 4. Collecting Process Data

- data entities that are required or are optional for execution,
- data entities created after execution,
- maximum number of repetitions.

- If requested goods are available in the warehouse, then there is no need for purchase order; then inventory checked is the only data entity required. All data related to purchase order processing should not exist.
- Otherwise, the expected goal is a completed purchase order, which corresponds to the order completed data entity.

## 5. Constraint-Based Model

#### 5.1. Formal Process Data Structures

- ${M}_{TC}$: for conditions needed for a task to be executed,
- ${M}_{TE}$: for effects caused by the execution of a task.

#### 5.2. Generation of a Workflow Log

- Search space: finite sequences of tasks.
- Decision variables: workflow trace, process state matrix.
- Constraints over variables: determined by the input data, as well as a set of predefined formulae.

- State satisfies requirements (based on Formula (4)).
- State satisfies set of requirements.

- The global limit of executions for all tasks is a constant value and denoted as $MA{X}_{EX}$.
- The number of executions for each task should be lower than or equal to the corresponding value in vector ${e}_{t}$ or to the global limit.
- The maximum length of the workflow trace is equal to $n\times MA{X}_{EX}$.
- The input state of the first executed task should be equal to ${s}_{0}$.
- Every non-empty task should change the current state.
- The process should end when the desired goal state is achieved.
- The last state of the process should satisfy one of the goal states.
- A task can be executed only if the current state satisfies its input conditions.

- the model file .mzn, which contains definitions of decision variables, predicates and constraints,
- the data file .dzn, where all the input information such as matrices ${M}_{T}C$, ${M}_{T}E$, ${M}_{S}T$ and initial state vector ${s}_{0}$ are defined.

## 6. Composition of a BPMN Diagram

- The mining-driven approach.
- The process composition based on activity graphs.

#### 6.1. Mining-Driven Approach

- Abstraction-based (also known as $\alpha $-series): consists of three phases: abstraction, induction and construction. In such an algorithm, ordering relations between tasks are identified, and the final workflow net is constructed based on predefined rules.
- Heuristic-based: consider the frequency of ordering relations appearing in workflow traces, and filter out the potential noise.
- Search-based: use genetic algorithms to discover process models that represent the most frequent behavior in a workflow log.
- Language-based: assume that each activity in a trace is a letter in an alphabet and each trace is a word. One of the approaches [63] uses Integer Linear Programming (ILP) to discover control flows.
- Inductive: filter the most frequent activities, and produce a process tree. The generated model is then enriched with frequency information for each task and the information about how the generated model deviates from the input log.

#### 6.2. Process Composition Based on Activity Graphs

- ${V}_{A}$ is a finite set of vertices representing process activities,
- E is a set of directed edges,
- $de{g}^{-}:{V}_{A}\u27f6{\mathbb{N}}_{0}$ determines the number of incoming edges for a vertex, and ${\mathbb{N}}_{0}$ stands for non-negative integers,
- $de{g}^{+}:{V}_{A}\u27f6{\mathbb{N}}_{0}$ determines the number of outgoing edges for a vertex.

- chain response: if A occurs, then it is directly followed by B,
- chain precedence: if B occurs, then it is directly preceded by A,
- chain succession: A occurs if and only if B occurs directly afterwards.

- There exists a directed edge leading from A to B and one from B to A.
- There exists a workflow trace $\sigma \in W$ where the number of occurrences for A and B is equal.
- There exist two workflow traces ${\sigma}_{1},{\sigma}_{2}\in W$ such that A occurs first before the first occurrence of B in ${\sigma}_{1}$ and B occurs first before the first occurrence of A in ${\sigma}_{2}$.

- Create the process file structure.
- For each vertex and its attributes, create an element corresponding to the type of flow object.
- For each directed edge, create a sequenceFlow element.

## 7. Evaluation

**Definition**

**1.**

#### 7.1. Generation of Workflow Traces

- Each activity generates one data entity.
- Each activity requires data entities generated by its predecessors. If it is preceded by an exclusive gateway, then an artificial data entity is created to represent the alternative.
- The initial state of the process is a zero vector.
- The goal state of the process requires data entities produced by its predecessors.

#### 7.2. Graph-Based Model Composition

- model fitness: the percentage of traces from the original log, which were generated based on the composed model,
- execution precision: the percentage of generated workflow traces that are allowed in the original log.$$CA=\mathit{model}\_\mathit{fitness}\times \mathit{execution}\_\mathit{precision}$$

#### 7.3. Limitations

## 8. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 9.**Example result of applying the graph-based composition algorithm. The graphical layout of flow objects has been enhanced with the Signavio editor [75].

Task Name | Required DEs | Created DEs | Executions |
---|---|---|---|

Check Inventory | Goods Request | Inventory Checked | 1 |

Receive Packing Slip | Order Sent | Packing Slip | 1 |

Record Packing Slip | Packing Slip | Packing Slip Record | 1 |

Task Name | Required DEs | Created DEs | Executions |
---|---|---|---|

Reserve Funds | Order Reviewed | Funds Reserved | 1 |

Receive Invoice | Order Sent | Invoice | 1 |

Record Invoice | Invoice | Invoice Record | 1 |

Release Funds | Invoice Record | Funds Released | 1 |

Packing Slip Record | |||

Issue Payment | Funds Released | Order Completed | 1 |

Task Name | Required DEs | Created DEs | Executions |
---|---|---|---|

Create Order | Inventory Checked | Order Created | 1 |

Reprocess Order | Order Reviewed | Order Reprocessed | 1 |

Task Name | Required DEs | Created DEs | Executions |
---|---|---|---|

Review Order | Order Created | Order Reviewed | 2 |

(Order Reprocessed) | |||

Send Order | Funds Reserved | Order Sent | 1 |

ID | Name | Type |
---|---|---|

01 | Goods Request | Text/JSON |

02 | Inventory Checked | Boolean |

03 | Order Sent | Boolean |

04 | Packing Slip | Text/JSON |

05 | Packing Slip Record | Integer |

06 | Order Reviewed | Boolean |

07 | Funds Reserved | Boolean |

08 | Invoice | Text/JSON |

09 | Invoice Record | Integer |

10 | Funds Released | Boolean |

11 | Order Completed | Boolean |

12 | Order Created | Boolean |

13 | Order Reprocessed | Boolean |

Value | ${\mathit{M}}_{\mathit{TC}}$ | ${\mathit{M}}_{\mathit{TE}}$ | ${\mathit{M}}_{\mathit{ST}}$ | ${\mathit{s}}_{0}$ |
---|---|---|---|---|

$-1$ | not relevant | unchanged | not relevant | — |

0 | forbidden | deleted | forbidden | forbidden |

1 | required | created | required | required |

**Table 7.**Comparison of selected process mining approaches present in the ProM environment (●—supported feature, ◐—partially supported feature).

Feature | $\mathit{\alpha}$ Algorithm | Heuristic Miner | ILP Miner | Inductive Miner |
---|---|---|---|---|

Type | abstraction | heuristic | language | inductive |

Construct discovery | ◐ | ● | ● | ◐ |

Fitness tendency | overfitting | underfitting | overfitting | overfitting |

Generalization | ◐ | ● | ◐ | ● |

Advantage | simplicity | control flow | high fitness | high fitness |

discovery | ||||

Inconvenience | low quality | high generalization | complex use | block division |

Recommended | ✓ | ✓✓ | ✓✓✓ | ✓ |

Element Name | Attributes |
---|---|

startEvent | id, name |

endEvent | id, name |

task | id, name |

parallelGateway | id, name, gatewayDirection |

exclusiveGateway | id, name, gatewayDirection |

sequenceFlow | id, name, sourceRef, targetRef |

**Table 9.**Example BPMN models used for method evaluation ($\left|\mathbb{T}\right|$, No. of activities; $\left|W\right|$, No. of traces). LCM, Log-based Complexity Metric; LD, Looping Depth; CFC, Control-Flow Complexity.

Process Model | $\left|\mathbb{T}\right|$ | $\left|\mathit{W}\right|$ | LCM | LD | CFC |
---|---|---|---|---|---|

Liability Insurance | 6 | 6 | 1 | 0 | 1 |

Supply Management | 12 | 13 | 1.08 | 1 | 7 |

Student Project Evaluation | 5 | 9 | 1.8 | 1 | 9 |

Employee Hiring | 7 | 36 | 5.14 | 2 | 7 |

Bank Account Opening | 14 | 160 | 11.43 | 0 | 8 |

Intricate Example | 31 | 10,700 | 345.16 | 2 | 25 |

**Table 10.**Support for the most commonly-used BPMN elements based on ranking presented in [80] (●—supported, ◐—partially supported ○—not supported).

Element Type | Support |
---|---|

Sequence Flow | ● |

Task | ● |

End Event | ● |

Start Event | ● |

Pool | ◐ |

Data-based XOR | ● |

Start Message | ◐ |

Text Annotation | ○ |

Message Flow | ○ |

Parallel Split/join | ● |

Lanes | ◐ |

Association | ○ |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wiśniewski, P.; Kluza, K.; Ligęza, A.
An Approach to Participatory Business Process Modeling: BPMN Model Generation Using Constraint Programming and Graph Composition. *Appl. Sci.* **2018**, *8*, 1428.
https://doi.org/10.3390/app8091428

**AMA Style**

Wiśniewski P, Kluza K, Ligęza A.
An Approach to Participatory Business Process Modeling: BPMN Model Generation Using Constraint Programming and Graph Composition. *Applied Sciences*. 2018; 8(9):1428.
https://doi.org/10.3390/app8091428

**Chicago/Turabian Style**

Wiśniewski, Piotr, Krzysztof Kluza, and Antoni Ligęza.
2018. "An Approach to Participatory Business Process Modeling: BPMN Model Generation Using Constraint Programming and Graph Composition" *Applied Sciences* 8, no. 9: 1428.
https://doi.org/10.3390/app8091428