Business Intelligence & Process Modelling
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1 Business Intelligence & Process Modelling Frank Takes Universiteit Leiden Lecture 7 Process Modelling & Petri nets BIPM Lecture 7 Process Modelling & Petri nets 1 / 56
2 Recap Business Intelligence: anything that aims at providing actionable information that can be used to support business decision making Business Intelligence Visual Analytics Descriptive Analytics Predictive Analytics Process Modelling (April and May) BIPM Lecture 7 Process Modelling & Petri nets 2 / 56
3 Data & Models BIPM Lecture 7 Process Modelling & Petri nets 3 / 56
4 Business Process Management (recap) Process: a set of related actions and transactions to achieve a certain objective Business process: a sequence of activities aimed at producing something of value for the business (Morgan02) Management processes Operational processes Supporting processes Business Process Management: the discipline that combines knowledge from information technology and knowledge from management sciences and applies this to operational business processes (v.d. Aalst) Extension of WorkFlow Management (WFM) BIPM Lecture 7 Process Modelling & Petri nets 4 / 56
5 Business Process Modelling (recap) Business Process Model: abstract representation of business processes, functionality is: Descriptive: what is actually happening? Prescriptive: what should be happening? Explanatory: why is the process designed this way? In practice: formalize and visualize business processes Process Discovery: derive the process from a description of activities Process Mining: the task of converting event data into process models (discovery, conformance, enhancement) BIPM Lecture 7 Process Modelling & Petri nets 5 / 56
6 Why Model Processes? (recap) insight discussion: the stakeholders use models to structure discussions; documentation for instructing people or certification purposes verification, for example to find errors in systems performance analysis animation: play out different scenarios specification: a contract between the developer and the end user/management; and configuration of a system. BIPM Lecture 7 Process Modelling & Petri nets 6 / 56
7 Business Process... Intelligence? M. Castellanos et al., Business process intelligence, Handbook of research on business process modeling, pp , BIPM Lecture 7 Process Modelling & Petri nets 7 / 56
8 Process Modelling Informal models: used for discussion and documentation (process descriptions) Formal models: used for analysis or enactment Petri Nets PN Business Process Model Notation BPMN BIPM Lecture 7 Process Modelling & Petri nets 8 / 56
9 Business Process Model Notation BIPM Lecture 7 Process Modelling & Petri nets 9 / 56
10 Petri Nets BIPM Lecture 7 Process Modelling & Petri nets 10 / 56
11 Event logs (1) Case ID Event ID dd-mm-yyyy:hh.mm Activity Resource Costs :11.02 register request Pete :10.06 examine thoroughly Sue :15.12 check ticket Mike :11.18 decide Sara :14.24 reject request Pete :11.32 register request Mike :12.12 check ticket Mike :14.16 examine casually Sean :11.22 decide Sara :12.05 pay compensation Ellen :14.32 register request Pete :15.06 examine casually Mike :16.34 check ticket Ellen :09.18 decide Sara :12.18 reinitiate request Sara :13.06 examine thoroughly Sean :11.43 check ticket Pete :09.55 decide Sara :10.45 pay compensation Ellen :15.02 register request Pete :12.06 check ticket Mike :14.43 examine thoroughly Sean :12.02 decide Sara :15.44 reject request Ellen Table : Event logs of a helpdesk handling customer compensations BIPM Lecture 7 Process Modelling & Petri nets 11 / 56
12 Event logs (2) Case ID Event ID dd-mm-yyyy:hh.mm Activity Resource Costs :09.02 register request Ellen :10.16 examine casually Mike :11.22 check ticket Pete :13.28 decide Sara :16.18 reinitiate request Sara :14.33 check ticket Ellen :15.50 examine casually Mike :11.18 decide Sara :12.48 reinitiate request Sara :09.06 examine casually Sue :11.34 check ticket Pete :13.12 decide Sara :14.56 reject request Mike :15.02 register request Mike :16.06 examine casually Ellen :16.22 check ticket Mike :16.52 decide Sara :11.47 pay compensation Mike 200 Table : Event logs of a support desk handling customer compensations BIPM Lecture 7 Process Modelling & Petri nets 12 / 56
13 Simplified event log Case ID Trace 1 a, b, d, e, h 2 a, d, c, e, g 3 a, c, d, e, f, b, d, e, g 4 a, d, b, e, h 5 a, c, d, e, f, d, c, e, f, c, d, e, h 6 a, c, d, e, g Table : Simplified event log of a support desk handling customer compensations (a = register request, b = examine thoroughly, c = examine casually, d = check ticket, e = decide, f = reinitiate request, g = pay compensation, h = reject request) BIPM Lecture 7 Process Modelling & Petri nets 13 / 56
14 Simplified event log Case ID Trace 1 a, b, d, e, h 2 a, d, c, e, g 3 a, c, d, e, f, b, d, e, g 4 a, d, b, e, h 5 a, c, d, e, f, d, c, e, f, c, d, e, h 6 a, c, d, e, g Table : Simplified event log of a support desk handling customer compensations (a = register request, b = examine thoroughly, c = examine casually, d = check ticket, e = decide, f = reinitiate request, g = pay compensation, h = reject request) In short: { a, b, d, e, h, a, d, c, e, g, a, c, d, e, f, b, d, e, g, a, d, b, e, h, a, c, d, e, f, d, c, e, f, c, d, e, h, a, c, d, e, g } BIPM Lecture 7 Process Modelling & Petri nets 13 / 56
15 Example (1) Case ID Trace 1 a, b, d, e, h 2 a, d, c, e, g 3 a, c, d, e, f, b, d, e, g 4 a, d, b, e, h 5 a, c, d, e, f, d, c, e, f, c, d, e, h 6 a, c, d, e, g BIPM Lecture 7 Process Modelling & Petri nets 14 / 56
16 Example (2) Figure : Petri net based on event log { a, b, d, e, h, a, d, b, e, h } BIPM Lecture 7 Process Modelling & Petri nets 15 / 56
17 Play in BIPM Lecture 7 Process Modelling & Petri nets 16 / 56
18 Play out BIPM Lecture 7 Process Modelling & Petri nets 17 / 56
19 Replay BIPM Lecture 7 Process Modelling & Petri nets 18 / 56
20 Replay Connecting models to real events is crucial Possible uses Conformance checking Repairing models Extending the model with frequencies and temporal information Constructing predictive models Operational support (prediction, recommendation, etc.) BIPM Lecture 7 Process Modelling & Petri nets 19 / 56
21 Petri Nets BIPM Lecture 7 Process Modelling & Petri nets 20 / 56
22 Automata (remember?) Finite automaton FA = (Q, Σ, q o, A, δ) Q is a finite set of states Σ is a finite alphabet of input symbols q o Q is the initial state A Q is the set of accepting states δ : Q Σ Q is the transition function BIPM Lecture 7 Process Modelling & Petri nets 21 / 56
23 Automata (remember?) Finite automaton FA = (Q, Σ, q o, A, δ) Q is a finite set of states Σ is a finite alphabet of input symbols q o Q is the initial state A Q is the set of accepting states δ : Q Σ Q is the transition function Figure : Deterministic Finite Automaton for the function x mod 3 = 0 BIPM Lecture 7 Process Modelling & Petri nets 21 / 56
24 Petri Nets Petri net N = (P, T, F ) P is a finite set of places T is a finite set of transitions F (P T ) (T P) is a finite set of directed arcs called the flow relation BIPM Lecture 7 Process Modelling & Petri nets 22 / 56
25 Labeled Petri Nets Petri net N = (P, T, F, A, l) P is a finite set of places T is a finite set of transitions F (P T ) (T P) is a finite set of directed arcs called the flow relation A is a set of activity labels l : T A is a labeling function BIPM Lecture 7 Process Modelling & Petri nets 23 / 56
26 Enabling A transition is enabled if each of its input places contains at least one token BIPM Lecture 7 Process Modelling & Petri nets 24 / 56
27 Firing An enabled transition can fire (i.e., it occurs), consuming a token from each input place and producing a token for each output place. BIPM Lecture 7 Process Modelling & Petri nets 25 / 56
28 Petri Nets Connections are directed No connections between two places or two transitions Places may hold zero or more tokens At most one arc between nodes (for now) Firing is atomic Multiple transitions may be enabled, but only one fires at a time During execution, the number of tokens may vary if there are transitions for which the number of input places is not equal to the number of output places The network is static BIPM Lecture 7 Process Modelling & Petri nets 26 / 56
29 Example (1) Petri net for a traffic light BIPM Lecture 7 Process Modelling & Petri nets 27 / 56
30 Example (1) Petri net for a traffic light States: red, orange and green BIPM Lecture 7 Process Modelling & Petri nets 27 / 56
31 Example (1) Petri net for a traffic light States: red, orange and green Transitions from red to green, green to orange, and orange to red BIPM Lecture 7 Process Modelling & Petri nets 27 / 56
32 Example (1) Petri net for a traffic light States: red, orange and green Transitions from red to green, green to orange, and orange to red BIPM Lecture 7 Process Modelling & Petri nets 27 / 56
33 Example (2) Petri net for 2 traffic lights BIPM Lecture 7 Process Modelling & Petri nets 28 / 56
34 Example (2) Petri net for 2 traffic lights BIPM Lecture 7 Process Modelling & Petri nets 28 / 56
35 Example (3) Petri net for 2 traffic lights BIPM Lecture 7 Process Modelling & Petri nets 29 / 56
36 Marked Petri nets Marking: the distribution of tokens over places in a Petri net Marked Petri net (M, N): Petri net N = (P, T, F ) Marking M B(P) is a multi-set over P indicating the marking of N, denoted for example by [c1 2, c2, c3 4 ] Net behavior: set of all possible state sequences BIPM Lecture 7 Process Modelling & Petri nets 30 / 56
37 Reachability graph BIPM Lecture 7 Process Modelling & Petri nets 31 / 56
38 Reachability graph BIPM Lecture 7 Process Modelling & Petri nets 31 / 56
39 Reachability graph BIPM Lecture 7 Process Modelling & Petri nets 32 / 56
40 Different types of states Initial state: initial distribution of tokens. Reachable state: reachable from initial state. Final/dead state: no transition is enabled. Home state/marking: it is always possible to return (i.e., it is reachable from any reachable state). BIPM Lecture 7 Process Modelling & Petri nets 33 / 56
41 Roles in Modelling Place: passive element Transition: active element Arc: causal relation Token: elements subject to change BIPM Lecture 7 Process Modelling & Petri nets 34 / 56
42 Role of a token a physical object, for example a product, a part, a drug, a person; an information object, for example a message, a signal, a report; a collection of objects, for example a truck with products, a warehouse with parts, or an address file; an indicator of a state, for example the indicator of the state in which a process is, or the state of an object; an indicator of a condition: the presence of a token indicates whether a certain condition is fulfilled. BIPM Lecture 7 Process Modelling & Petri nets 35 / 56
43 Role of a place a type of communication medium, like a telephone line, a middleman, or a communication network; a buffer: for example, a depot, a queue or a post bin; a geographical location, like a place in a warehouse, office or hospital; a possible state or state condition: for example, the floor where an elevator is, or the condition that a specialist is available. BIPM Lecture 7 Process Modelling & Petri nets 36 / 56
44 Role of a transition an event: for example, starting an operation, the death of a patient, a change seasons or the switching of a traffic light from red to green; a transformation of an object, like adapting a product, updating a database, or updating a document; transport of an object: for example, transporting goods, or sending a file. BIPM Lecture 7 Process Modelling & Petri nets 37 / 56
45 Typical net structures Causality Parallelism (AND-split, AND-join) Choice (XOR-split, XOR-join) Iteration (XOR-join, XOR-split) Capacity constraints Feedback loop Mutual exclusion Alternating BIPM Lecture 7 Process Modelling & Petri nets 38 / 56
46 Causality BIPM Lecture 7 Process Modelling & Petri nets 39 / 56
47 Parallelism BIPM Lecture 7 Process Modelling & Petri nets 40 / 56
48 Parallelism: AND-split BIPM Lecture 7 Process Modelling & Petri nets 41 / 56
49 Parallelism: AND-join BIPM Lecture 7 Process Modelling & Petri nets 42 / 56
50 Choice: XOR-split BIPM Lecture 7 Process Modelling & Petri nets 43 / 56
51 Choice: XOR-join BIPM Lecture 7 Process Modelling & Petri nets 44 / 56
52 Logic with Petri nets BIPM Lecture 7 Process Modelling & Petri nets 45 / 56
53 Iteration: 1 or more times Figure : XOR-join before XOR-split BIPM Lecture 7 Process Modelling & Petri nets 46 / 56
54 Iteration: 0 or more times Figure : XOR-join before XOR-split BIPM Lecture 7 Process Modelling & Petri nets 47 / 56
55 Capacity constraints: feedback loop Figure : AND-join before AND-split BIPM Lecture 7 Process Modelling & Petri nets 48 / 56
56 Capacity constraints: mutual exclusion Figure : AND-join before AND-split BIPM Lecture 7 Process Modelling & Petri nets 49 / 56
57 Two traffic lights: mutual exclusion Petri net for 2 traffic lights BIPM Lecture 7 Process Modelling & Petri nets 50 / 56
58 Capacity constraints: alternating Figure : AND-join before AND-split BIPM Lecture 7 Process Modelling & Petri nets 51 / 56
59 Petri nets with multiple arcs Petri net N = (P, T, F ) with multiple arcs P is a finite set of places T is a finite set of transitions F is a multiset over F, i.e., F B(F ) or a finite set F (P T N) (T P N) BIPM Lecture 7 Process Modelling & Petri nets 52 / 56
60 Some properties In k-bounded Petri nets, no place ever holds more than k tokens A marked Petri net is safe if it is 1-bounded A marked Petri net is deadlock-free if at every reachable marking at least one transition is enabled A transition t in a marked Petri net is live if from every reachable marking, it is possible to enable t WorkFlow-net (WF-net): Petri net with fixed source i P (without inputs) and target o P (without outputs) BIPM Lecture 7 Process Modelling & Petri nets 53 / 56
61 Variants and extensions Colored Petri nets (K. Jensen) Petri nets with inhibitor arcs (realizing Turing completeness) Prioritized Petri nets Timed Petri nets... and many more! BIPM Lecture 7 Process Modelling & Petri nets 54 / 56
62 Lab session April 6 Assess constructed features Create feature correlation plot Insert features and target attribute into scikit-learn Perform final machine learning steps Next week: last chance to ask questions BIPM Lecture 7 Process Modelling & Petri nets 55 / 56
63 Credits Lecture partially based on (slides of the (previous edition of the)) course book: W. van der Aalst, Process Mining: Data Science in Action, 2nd edition, Springer, BIPM Lecture 7 Process Modelling & Petri nets 56 / 56
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