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From Identities to Quantities:
Introducing Items and Decoupling Points to Object-centric
Process Mining
Nina Graves, István Koren, Majid Rafiei, Wil M. P. van der Aalst
Chair of Process and Data Science, RWTH Aachen University, Germany
2rd Workshop on Collaboration Mining for Distributed Systems
5th International Conference on Process Mining (ICPM 2023)
Rome, 23rd October 2023
© Nina Graves (acknowledge when used)
Nina Graves, Item Quantities & Decoupling Points
Workshop on Collaboration Mining for Distributed Systems
Rome, 23rd October 2023
2
Quantity-dependent Process
Inventory Management
© Nina Graves (acknowledge when used)
Nina Graves, Item Quantities & Decoupling Points
Workshop on Collaboration Mining for Distributed Systems
Rome, 23rd October 2023
3
items in stock
Replenishment Process Core Process
Logistics processes deal with quantity-dependent, cross-organisational processes concerning
non-uniquely identifiable items.
Warehouse
customer order
(CO) arrives
pick and pack
items
send parcel
containing items
1
2 3
replenishment
order (RO) arrives
1
items are
delivered
2
© Nina Graves (acknowledge when used)
Nina Graves, Item Quantities & Decoupling Points
Workshop on Collaboration Mining for Distributed Systems
Rome, 23rd October 2023
4
(Object-centric) Process Mining heavily depends on the identifiers of the individual objects. It
is not possible to detect the process of objects that are not individually identifiable.
van der Aalst & Berti Discovering Object-centric Petri nets (2020)
OCPNs
• Each place is assigned
to an object type.
• Bindings (“place
bindings”) describes
the tokens of each type
required for firing.
Discovery
• “Following” objects
through the log
• Unique identifiers are
required
© Nina Graves (acknowledge when used)
Nina Graves, Item Quantities & Decoupling Points
Workshop on Collaboration Mining for Distributed Systems
Rome, 23rd October 2023
5
Quantity-relationships are distinguished as either a 1:1 relationship or as another type of
relationship. The distinction is made on the type-level.
van der Aalst & Berti Discovering Object-centric Petri nets (2020)
• Normal arcs indicate
that a single token of
this type is required.
• Variable arcs indicate
that it is otherwise.
• Any other quantity-
relationship is not
specified.
© Nina Graves (acknowledge when used)
Nina Graves, Item Quantities & Decoupling Points
Workshop on Collaboration Mining for Distributed Systems
Rome, 23rd October 2023
6
Logistics processes deal with quantity-dependent, cross-organisational processes concerning
non-uniquely identifiable items.
replenishment
order (RO) arrives
items are
delivered
items in stock
customer order
(CO) arrives
pick and pack
items
send parcel
containing items
Replenishment Process
1 2
1
2 3
Core Process
Items connecting the processes are not uniquely
identifiable
processes are decoupled
Both processes have a dependency on items in stock
Characteristics
© Nina Graves (acknowledge when used)
Nina Graves, Item Quantities & Decoupling Points
Workshop on Collaboration Mining for Distributed Systems
Rome, 23rd October 2023
7
Core Process
Alternative 1 - No identifiers used: Two disconnected object-centric Petri nets.
Place RO
Register
Delivery
Unload
Delivery
Place in
Stock
Replenishment
Order
Delivery
Register
CO
Pick &
Pack
Send
Customer
Order
Parcel
Replenishment Process
© Nina Graves (acknowledge when used)
Nina Graves, Item Quantities & Decoupling Points
Workshop on Collaboration Mining for Distributed Systems
Rome, 23rd October 2023
8
Core Process
Alternative 1 - No artificial identifiers used: Two disconnected object-centric Petri nets.
Place RO
Register
Delivery
Unload
Delivery
Place in
Stock
Replenishment
Order
Delivery
Register
CO
Pick &
Pack
Send
Customer
Order
Parcel
Replenishment Process
• disconnected processes
• items not considered
• quantity-dependency not depicted
© Nina Graves (acknowledge when used)
Nina Graves, Item Quantities & Decoupling Points
Workshop on Collaboration Mining for Distributed Systems
Rome, 23rd October 2023
9
Alternative 2 – Artificial identifiers used: One connected object-centric Petri net.
Place
RO
Register
Arrival
Unpack
Delivery
Place in
Stock
Register
CO
Pick &
Pack
Send
Replenishment
Order
Delivery
A
B
C
Customer Order
Parcel
Replenishment
Process
Core
Process
© Nina Graves (acknowledge when used)
Nina Graves, Item Quantities & Decoupling Points
Workshop on Collaboration Mining for Distributed Systems
Rome, 23rd October 2023
10
Alternative 2 – Artificial identifiers used: One connected object-centric Petri net.
Place
RO
Register
Arrival
Unpack
Delivery
Place in
Stock
Register
CO
Pick &
Pack
Send
Replenishment
Order
Delivery
A
B
C
Customer Order
Parcel
Replenishment
Process
Core
Process
• single process
• redundancy in individual item types
• underspecified quantity-relationships
© Nina Graves (acknowledge when used)
Nina Graves, Item Quantities & Decoupling Points
Workshop on Collaboration Mining for Distributed Systems
Rome, 23rd October 2023
11
Quantity-dependent
Process Mining
© Nina Graves (acknowledge when used)
Nina Graves, Item Quantities & Decoupling Points
Workshop on Collaboration Mining for Distributed Systems
Rome, 23rd October 2023
12
In addition to objects, items are considered non-identifiable process elements. A decoupling
point refers to a collection of items, indicating a quantity-dependency between two processes.
place
RO
register
arrival
unload
delivery
place in
stock
register
CO pick and
pack
send
parcel
RO
Delivery
CO
Parcel
Warehouse
Decoupling Point indicating a
quantity-dependent decoupling
of sub-processes referring to a
set of item types.
Items
• non-identifiable elements of a process
• items of the same item type are
interchangeable
© Nina Graves (acknowledge when used)
Nina Graves, Item Quantities & Decoupling Points
Workshop on Collaboration Mining for Distributed Systems
Rome, 23rd October 2023
13
A decoupling point’s item level can be changed when activities are executed allowing for the
consideration of the item level’s development over time.
place
RO
register
arrival
unload
delivery
place in
stock
register
CO pick and
pack
send
parcel
RO
Delivery
CO
Parcel
Warehouse
Decoupling Points referring to a
collection of non-identifiable items.
Execution of activities increases or
decreases item level of item
collections.
Item
level
time
© Nina Graves (acknowledge when used)
Nina Graves, Item Quantities & Decoupling Points
Workshop on Collaboration Mining for Distributed Systems
Rome, 23rd October 2023
14
Firing a transition leads to the execution of a place binding and a quantity binding which
changes the item level of the referenced decoupling points.
𝑡1 𝑡2
𝑑𝑝1
𝑚 𝑑𝑝1 = 𝑎4, 𝑏6, 𝑐2 𝑚 𝑑𝑝2 = 𝑎3
, 𝑏10
, 𝑐7
𝑏1 = (𝑡1, 𝑏𝑝
, 𝑑𝑝1, 𝑎2
, 𝑐 )
𝑏2 = (𝑡2, 𝑏𝑝,
𝑑𝑝1, 𝑎1
, 𝑏2
,
𝑑𝑝2, 𝑏, 𝑐
)
𝑚′
𝑑𝑝1 = 𝑎6
, 𝑏6
, 𝑐3
𝑚′′
𝑑𝑝1 = 𝑎5
, 𝑏4
, 𝑐3
𝑚′′
𝑑𝑝2 = 𝑎3
,𝑏11
, 𝑐8
𝑚′ 𝑑𝑝2 = 𝑎3, 𝑏10, 𝑐7
𝑑𝑝2
executed binding new item level 𝑑𝑝1 new item level 𝑑𝑝2
Item quantities (“negative
multisets”) are used to
describe quantity
operations and item levels.
When a transition fires a place binding and a quantity binding are executed.
© Nina Graves (acknowledge when used)
Nina Graves, Item Quantities & Decoupling Points
Workshop on Collaboration Mining for Distributed Systems
Rome, 23rd October 2023
15
The corresponding quantity-event log adds a table assigning a quantity operation to a
combination of events and item collections.
• Information on the initial item
levels of the collection points.
• Item quantities describing the
impact events have on a collection
point.
+ initial item
levels
© Nina Graves (acknowledge when used)
Nina Graves, Item Quantities & Decoupling Points
Workshop on Collaboration Mining for Distributed Systems
Rome, 23rd October 2023
16
Making use of the initial item levels and the timestamps a sequence of quantity operations can
be considered as a sequence which helps reconstruct item level development.
© Nina Graves (acknowledge when used)
Nina Graves, Item Quantities & Decoupling Points
Workshop on Collaboration Mining for Distributed Systems
Rome, 23rd October 2023
17
Example Application
© Nina Graves (acknowledge when used)
Nina Graves, Item Quantities & Decoupling Points
Workshop on Collaboration Mining for Distributed Systems
Rome, 23rd October 2023
18
The data set describes an inventory management process in which different three types of
items are processed and collected.
• Decoupled sub-processes with
a dependency on a collection
point’s item level.
• Three considered item types:
photo albums (a), books (b),
cups (c).
• Loop of customer orders
around pick and pack.
• All events of “place in stock“
add items to 𝑑𝑝1, all events of
“pick and pack“ remove items.
10,050 events, 3,311 objects
© Nina Graves (acknowledge when used)
Nina Graves, Item Quantities & Decoupling Points
Workshop on Collaboration Mining for Distributed Systems
Rome, 23rd October 2023
19
The item level of the three item types varies – books have a much larger turnover rate than
cups and albums leading to more frequent deliveries of higher quantities.
• Decrease: “pick and
pack”, increase: “place in
stock”.
• Imbalance between the
number of item removals
and additions; decoupled
sub-processes.
• Varying quantities of the
different item types.
© Nina Graves (acknowledge when used)
Nina Graves, Item Quantities & Decoupling Points
Workshop on Collaboration Mining for Distributed Systems
Rome, 23rd October 2023
20
Despite the process being the same for all item types the number of item types per process
execution varies and can be analysed separately.
• Number of required books
broadly spread.
• Average number of items per
customer order:
• 1.3 albums
• 6.9 books
• 0.29 cups
• Turnovers:
• albums: 33 days
• books: 8 days
• cups: 17 days
© Nina Graves (acknowledge when used)
Nina Graves, Item Quantities & Decoupling Points
Workshop on Collaboration Mining for Distributed Systems
Rome, 23rd October 2023
21
The consideration of a collection point’s item levels allows for the detection of additional
quantity-related dependencies.
• Bold: Assumed
number of ordered
items.
• Transparent: item level
when “place
replenishment order” is
executed.
• Low variance in the
number of ordered
items
© Nina Graves (acknowledge when used)
Nina Graves, Item Quantities & Decoupling Points
Workshop on Collaboration Mining for Distributed Systems
Rome, 23rd October 2023
22
This initial research direction appears to extend process mining’s capabilities and enables
additional support for material flow analysis.
Conclusion
• Current OCPM techniques fail in their consideration of unidentifiable items and
the detection of quantity-dependent process executions.
• The addition of item types and decoupling points allows for the modelling of
decoupled processes as well as the detection of additional quantity-dependent
process insights.
• Event log extraction, tool support and systematic detection of quantity-related
dependencies have yet to be considered.
A promising idea for the application of
process mining to logistics with potential for
further research.
© Nina Graves (acknowledge when used)
Thank you very much for your attention!
Also, a big thanks to our reviewers for the valuable feedback!
Nina Graves
graves@pads.rwth-aachen.de
https://www.pads.rwth-aachen.de
© Nina Graves (acknowledge when used)

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Quantity-related Process Mining

  • 1. From Identities to Quantities: Introducing Items and Decoupling Points to Object-centric Process Mining Nina Graves, István Koren, Majid Rafiei, Wil M. P. van der Aalst Chair of Process and Data Science, RWTH Aachen University, Germany 2rd Workshop on Collaboration Mining for Distributed Systems 5th International Conference on Process Mining (ICPM 2023) Rome, 23rd October 2023 © Nina Graves (acknowledge when used)
  • 2. Nina Graves, Item Quantities & Decoupling Points Workshop on Collaboration Mining for Distributed Systems Rome, 23rd October 2023 2 Quantity-dependent Process Inventory Management © Nina Graves (acknowledge when used)
  • 3. Nina Graves, Item Quantities & Decoupling Points Workshop on Collaboration Mining for Distributed Systems Rome, 23rd October 2023 3 items in stock Replenishment Process Core Process Logistics processes deal with quantity-dependent, cross-organisational processes concerning non-uniquely identifiable items. Warehouse customer order (CO) arrives pick and pack items send parcel containing items 1 2 3 replenishment order (RO) arrives 1 items are delivered 2 © Nina Graves (acknowledge when used)
  • 4. Nina Graves, Item Quantities & Decoupling Points Workshop on Collaboration Mining for Distributed Systems Rome, 23rd October 2023 4 (Object-centric) Process Mining heavily depends on the identifiers of the individual objects. It is not possible to detect the process of objects that are not individually identifiable. van der Aalst & Berti Discovering Object-centric Petri nets (2020) OCPNs • Each place is assigned to an object type. • Bindings (“place bindings”) describes the tokens of each type required for firing. Discovery • “Following” objects through the log • Unique identifiers are required © Nina Graves (acknowledge when used)
  • 5. Nina Graves, Item Quantities & Decoupling Points Workshop on Collaboration Mining for Distributed Systems Rome, 23rd October 2023 5 Quantity-relationships are distinguished as either a 1:1 relationship or as another type of relationship. The distinction is made on the type-level. van der Aalst & Berti Discovering Object-centric Petri nets (2020) • Normal arcs indicate that a single token of this type is required. • Variable arcs indicate that it is otherwise. • Any other quantity- relationship is not specified. © Nina Graves (acknowledge when used)
  • 6. Nina Graves, Item Quantities & Decoupling Points Workshop on Collaboration Mining for Distributed Systems Rome, 23rd October 2023 6 Logistics processes deal with quantity-dependent, cross-organisational processes concerning non-uniquely identifiable items. replenishment order (RO) arrives items are delivered items in stock customer order (CO) arrives pick and pack items send parcel containing items Replenishment Process 1 2 1 2 3 Core Process Items connecting the processes are not uniquely identifiable processes are decoupled Both processes have a dependency on items in stock Characteristics © Nina Graves (acknowledge when used)
  • 7. Nina Graves, Item Quantities & Decoupling Points Workshop on Collaboration Mining for Distributed Systems Rome, 23rd October 2023 7 Core Process Alternative 1 - No identifiers used: Two disconnected object-centric Petri nets. Place RO Register Delivery Unload Delivery Place in Stock Replenishment Order Delivery Register CO Pick & Pack Send Customer Order Parcel Replenishment Process © Nina Graves (acknowledge when used)
  • 8. Nina Graves, Item Quantities & Decoupling Points Workshop on Collaboration Mining for Distributed Systems Rome, 23rd October 2023 8 Core Process Alternative 1 - No artificial identifiers used: Two disconnected object-centric Petri nets. Place RO Register Delivery Unload Delivery Place in Stock Replenishment Order Delivery Register CO Pick & Pack Send Customer Order Parcel Replenishment Process • disconnected processes • items not considered • quantity-dependency not depicted © Nina Graves (acknowledge when used)
  • 9. Nina Graves, Item Quantities & Decoupling Points Workshop on Collaboration Mining for Distributed Systems Rome, 23rd October 2023 9 Alternative 2 – Artificial identifiers used: One connected object-centric Petri net. Place RO Register Arrival Unpack Delivery Place in Stock Register CO Pick & Pack Send Replenishment Order Delivery A B C Customer Order Parcel Replenishment Process Core Process © Nina Graves (acknowledge when used)
  • 10. Nina Graves, Item Quantities & Decoupling Points Workshop on Collaboration Mining for Distributed Systems Rome, 23rd October 2023 10 Alternative 2 – Artificial identifiers used: One connected object-centric Petri net. Place RO Register Arrival Unpack Delivery Place in Stock Register CO Pick & Pack Send Replenishment Order Delivery A B C Customer Order Parcel Replenishment Process Core Process • single process • redundancy in individual item types • underspecified quantity-relationships © Nina Graves (acknowledge when used)
  • 11. Nina Graves, Item Quantities & Decoupling Points Workshop on Collaboration Mining for Distributed Systems Rome, 23rd October 2023 11 Quantity-dependent Process Mining © Nina Graves (acknowledge when used)
  • 12. Nina Graves, Item Quantities & Decoupling Points Workshop on Collaboration Mining for Distributed Systems Rome, 23rd October 2023 12 In addition to objects, items are considered non-identifiable process elements. A decoupling point refers to a collection of items, indicating a quantity-dependency between two processes. place RO register arrival unload delivery place in stock register CO pick and pack send parcel RO Delivery CO Parcel Warehouse Decoupling Point indicating a quantity-dependent decoupling of sub-processes referring to a set of item types. Items • non-identifiable elements of a process • items of the same item type are interchangeable © Nina Graves (acknowledge when used)
  • 13. Nina Graves, Item Quantities & Decoupling Points Workshop on Collaboration Mining for Distributed Systems Rome, 23rd October 2023 13 A decoupling point’s item level can be changed when activities are executed allowing for the consideration of the item level’s development over time. place RO register arrival unload delivery place in stock register CO pick and pack send parcel RO Delivery CO Parcel Warehouse Decoupling Points referring to a collection of non-identifiable items. Execution of activities increases or decreases item level of item collections. Item level time © Nina Graves (acknowledge when used)
  • 14. Nina Graves, Item Quantities & Decoupling Points Workshop on Collaboration Mining for Distributed Systems Rome, 23rd October 2023 14 Firing a transition leads to the execution of a place binding and a quantity binding which changes the item level of the referenced decoupling points. 𝑡1 𝑡2 𝑑𝑝1 𝑚 𝑑𝑝1 = 𝑎4, 𝑏6, 𝑐2 𝑚 𝑑𝑝2 = 𝑎3 , 𝑏10 , 𝑐7 𝑏1 = (𝑡1, 𝑏𝑝 , 𝑑𝑝1, 𝑎2 , 𝑐 ) 𝑏2 = (𝑡2, 𝑏𝑝, 𝑑𝑝1, 𝑎1 , 𝑏2 , 𝑑𝑝2, 𝑏, 𝑐 ) 𝑚′ 𝑑𝑝1 = 𝑎6 , 𝑏6 , 𝑐3 𝑚′′ 𝑑𝑝1 = 𝑎5 , 𝑏4 , 𝑐3 𝑚′′ 𝑑𝑝2 = 𝑎3 ,𝑏11 , 𝑐8 𝑚′ 𝑑𝑝2 = 𝑎3, 𝑏10, 𝑐7 𝑑𝑝2 executed binding new item level 𝑑𝑝1 new item level 𝑑𝑝2 Item quantities (“negative multisets”) are used to describe quantity operations and item levels. When a transition fires a place binding and a quantity binding are executed. © Nina Graves (acknowledge when used)
  • 15. Nina Graves, Item Quantities & Decoupling Points Workshop on Collaboration Mining for Distributed Systems Rome, 23rd October 2023 15 The corresponding quantity-event log adds a table assigning a quantity operation to a combination of events and item collections. • Information on the initial item levels of the collection points. • Item quantities describing the impact events have on a collection point. + initial item levels © Nina Graves (acknowledge when used)
  • 16. Nina Graves, Item Quantities & Decoupling Points Workshop on Collaboration Mining for Distributed Systems Rome, 23rd October 2023 16 Making use of the initial item levels and the timestamps a sequence of quantity operations can be considered as a sequence which helps reconstruct item level development. © Nina Graves (acknowledge when used)
  • 17. Nina Graves, Item Quantities & Decoupling Points Workshop on Collaboration Mining for Distributed Systems Rome, 23rd October 2023 17 Example Application © Nina Graves (acknowledge when used)
  • 18. Nina Graves, Item Quantities & Decoupling Points Workshop on Collaboration Mining for Distributed Systems Rome, 23rd October 2023 18 The data set describes an inventory management process in which different three types of items are processed and collected. • Decoupled sub-processes with a dependency on a collection point’s item level. • Three considered item types: photo albums (a), books (b), cups (c). • Loop of customer orders around pick and pack. • All events of “place in stock“ add items to 𝑑𝑝1, all events of “pick and pack“ remove items. 10,050 events, 3,311 objects © Nina Graves (acknowledge when used)
  • 19. Nina Graves, Item Quantities & Decoupling Points Workshop on Collaboration Mining for Distributed Systems Rome, 23rd October 2023 19 The item level of the three item types varies – books have a much larger turnover rate than cups and albums leading to more frequent deliveries of higher quantities. • Decrease: “pick and pack”, increase: “place in stock”. • Imbalance between the number of item removals and additions; decoupled sub-processes. • Varying quantities of the different item types. © Nina Graves (acknowledge when used)
  • 20. Nina Graves, Item Quantities & Decoupling Points Workshop on Collaboration Mining for Distributed Systems Rome, 23rd October 2023 20 Despite the process being the same for all item types the number of item types per process execution varies and can be analysed separately. • Number of required books broadly spread. • Average number of items per customer order: • 1.3 albums • 6.9 books • 0.29 cups • Turnovers: • albums: 33 days • books: 8 days • cups: 17 days © Nina Graves (acknowledge when used)
  • 21. Nina Graves, Item Quantities & Decoupling Points Workshop on Collaboration Mining for Distributed Systems Rome, 23rd October 2023 21 The consideration of a collection point’s item levels allows for the detection of additional quantity-related dependencies. • Bold: Assumed number of ordered items. • Transparent: item level when “place replenishment order” is executed. • Low variance in the number of ordered items © Nina Graves (acknowledge when used)
  • 22. Nina Graves, Item Quantities & Decoupling Points Workshop on Collaboration Mining for Distributed Systems Rome, 23rd October 2023 22 This initial research direction appears to extend process mining’s capabilities and enables additional support for material flow analysis. Conclusion • Current OCPM techniques fail in their consideration of unidentifiable items and the detection of quantity-dependent process executions. • The addition of item types and decoupling points allows for the modelling of decoupled processes as well as the detection of additional quantity-dependent process insights. • Event log extraction, tool support and systematic detection of quantity-related dependencies have yet to be considered. A promising idea for the application of process mining to logistics with potential for further research. © Nina Graves (acknowledge when used)
  • 23. Thank you very much for your attention! Also, a big thanks to our reviewers for the valuable feedback! Nina Graves graves@pads.rwth-aachen.de https://www.pads.rwth-aachen.de © Nina Graves (acknowledge when used)