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From Identities to Quantities: Introducing Items
and Decoupling Points to Object-centric
Process Mining⋆
Nina Graves , Istv´an Koren , Majid Rafiei , and Wil M.P. van der Aalst
Chair of Process and Data Science (PADS), RWTH Aachen University, Aachen,
Germany {graves,koren,majid.rafiei,wvdaalst}@pads.rwth-aachen.de
https://www.pads.rwth-aachen.de/
Abstract. Logistics processes ensure that the right product is at the
right location at the right time in the right quantity. Their efficiency is
crucial to industrial operations, as they generate costs while not adding
value to the product. Process mining techniques improve processes us-
ing real-life data. However, the application of process mining to logistics
processes poses several challenges, as (1) recorded material movements
refer to quantities of items, not individual objects and (2) the required
data are often scattered over several systems requiring additional pre-
processing efforts. This work presents the concept of item quantities to
describe the movement of not individually identifiable items across dis-
tributed processes. Subsequently, we introduce a framework to integrate
the explicit consideration of item quantities into process mining, con-
sisting of a quantity-related event log and an extension of object-centric
Petri nets as a basis for quantity-dependent process analysis. The anal-
ysis of an artificial event log demonstrates the additional insights the
consideration of quantities uncovers and highlights the potential for the
application of process mining in the logistics domain.
Keywords: Process Mining ·Logistics ·Material Flow Analysis.
1 Introduction
In current times, a swift transformation towards sustainable practices is essential,
requiring in-depth analysis and transformation of processes concerning the sourc-
ing, processing, and transporting of material [12]. Process mining is a relatively
young discipline, leveraging readily available event data to analyse, monitor, im-
prove and support business processes [2]. Apart from being a growing field for
research in academia [9], its industrial adoption is swiftly expanding across vari-
ous industries [8]. Despite the benefits of process mining for intra-logistics [7] as
well as inter-organisational processes [13], its application to the logistics domain
is relatively low [9].
The main reason for this discrepancy lies in the data availability [15]. The
event log used for object-centric process mining, contains information on the
⋆Authors’ Preprint. Copyright Springer 2023
2 N. Graves et al.
replenishment
order (RO) arrives
items are
delivered items in stock
customer order
(CO) arrives
pick and pack
items
send parcel
containing items
Replenishment Process
12
1
2 3
Core Process
place
RO
register
arrival
unload
delivery
place in
stock
register
CO pick and
pack
send
parcel
RO
Delivery
CO Parcel
(a) Disconnected OCPN without item IDs.
place
RO
register
arrival
unload
delivery
place in
stock
register
CO pick and
pack
send
parcel
RO
Delivery
CO
Parcel
Warehouse
(b) OCPN extended by a decoupling point indi-
cating a collection of items.
Fig. 1: Example of a quantity-dependent process composed of two decoupled sub-
processes.
execution of an activity linked to at least one individually identifiable object [3].
Process discovery algorithms combine the events referring to the same object to
detect dependencies among different activities – this means every object requires
one unique identifier for the end-to-end process. There are two requirements data
on logistics processes do not necessarily fulfil: First, logistics processes describe
material movements, such as the addition or removal of a number of items with-
out necessarily referring to uniquely identifiable objects [5,9]. For example, one
book and two cups are added to the warehouse, instead of book-123, cup-456 and
cup-789. Secondly, they can be scattered across several systems, even crossing
organisational boundaries, leading to the required data being distributed with-
out matching identifiers [4], i.e., the identifiers different organisations use for the
same object are different.
Consider, for example, a warehouse management process, as depicted in Fig-
ure 1. The warehouse’s core process is fulfilling customer orders (shown on the
right of the figure), referring to its three item types: photo albums a, books b,
and cups c. Whenever a customer order arrives, the requested number of items
is picked from the warehouse and packed into a parcel before it is sent to the
customer. When the number of items in the warehouse is low, a replenishment
sub-process is executed. This sub-process begins with placing a replenishment
order, leading to the delivery of items that are unpacked and placed in the ware-
house. All uniquely identifiable objects (replenishment orders, deliveries, cus-
tomer orders and parcels) are associated with their corresponding events. One
delivery contains a number of items sufficient for fulfilling several customer or-
ders. We see that (1) considering the overall process, there is no 1:1 relationship
between the execution of a replenishment process and a core process – they are
Items and Decoupling Points for Process Mining 3
decoupled, (2) the two sub-processes are connected by the items added to and
removed from the warehouse, and (3) there is a dependency in the execution
of both sub-processes on the available items in the warehouse. Using an event
log only referring to the uniquely identifiable objects, process mining techniques
can only discover two disconnected sub-processes, as can be seen for example in
Figure 1a, and cannot support their analysis in consideration of non-identifiable
items. In contrast, the net in Figure 1b, is able to represent both a collection of
items as well as the decoupling of the two processes by using an additional type
of node: a decoupling point.
This paper presents a framework extending object-centric process mining to
enable the detection and analysis of decoupled, quantity-dependent processes.
To do so, we introduce quantity-relating event logs to enable the consideration
of item quantities as well as an extension of object-centric Petri nets. We fur-
ther demonstrate the additional insights that can be gained by taking available
item quantities at the execution time of events into account using an artificial
event log. After presenting related work (Section 2), Section 3 introduces the pre-
liminaries including items, item collections and quantity operations. Quantity-
relating event logs (QELs) and quantity nets are presented in Section 4. In
Section 5, we analyse an artificial QEL to present the benefits and shortcomings
of the framework. Section 6 concludes this work.
2 Related Work
The problems of missing or mismatching identifiers and the discovery and analy-
sis of quantity-dependent processes have been addressed in literature. Federated
process mining deals with the joint consideration of disconnected processes, de-
scribed and formalised in [1]. Approaches to match identifiers of distributed
processes using EDI messages [6] and leveraging Radio Frequency Identification
(RFID) data [10] were discussed in the literature. In [11], the authors introduce
an approach in which individually identifiable objects are grouped to map their
identifiers to joint identifiers collected from RFID data. All of these methods rely
on the existence of the individual and shared identifiers for the relevant entities
of the process and allow for a fully end-to-end analysis of each of the relevant
entities. In contrast, the authors of [20] present an abstraction-based, privacy-
preserving approach to discovering inter-organisational processes. Although the
presented procedure allows process analysis without requiring shared end-to-end
identifiers, it requires a 1:1 mapping between process executions of the different
systems.
A typical example of a quantity-based interdependency of process executions
is batch processing. When processing in a batch, an activity or sub-process is ex-
ecuted a predetermined number of times without interruption before the objects
are passed on to the next step [19]. Several works aim to discover different types
of batched activities, such as [18] or batched sub-processes [17]. All of these ap-
proaches assume event data containing an entry for each batched element. The
authors of [21] assume a mixture of events referring to batched objects as well
4 N. Graves et al.
as individual ones, the batched ones including the information on the number of
batched objects.
Some works explicitly address the logistics-related challenges of process min-
ing. In [5], an approach for the preparation and visualisation of material move-
ment data is presented, allowing for the identification of inefficiencies in the paths
the material takes. A methodology combining association rules with process min-
ing to uncover dependencies between processes and performance indicators for
supply chains is introduced in [16]. In [14], the authors present an approach to
enrich event data with additional information to detect waste in a value stream.
We see that existing literature focuses on preparing event data to use out-of-the-
box process mining techniques instead of integrating the additionally available
data to enhance process mining’s capabilities.
3 Preliminaries
This section introduces some general mathematical operations as well as concepts
related to object-centric process mining. Function projections, denoted f↾W,
define the application of a function f:X→ Yto a different domain W, with:
dom(f↾W) = dom(f)∩Wand f↾W(x) = f(x) for x∈dom(f↾W). A sequence
of length nover a set Ais denoted σ=⟨a1, a2, ..., an⟩ ∈ A∗, with σ=⟨⟩ as the
empty sequence and σ1·σ2the concatenation of sequences. The j-th element of
a sequence σ=⟨a1, ..., aj, ..., an⟩ ∈ A∗is denoted σ[j] = ajand the prefix of σ[j]
is referred to as σ:j=⟨a1, ..., aj−1⟩.
To define an Object-Centric Event Log (OCEL), the basis for object-centric
process mining, we introduce the universe of activities Uact, the universe of events
Uev, the universe of objects Uo, the universe of object types Uot, and the universe
of timestamps Utime.
Definition 1 (Object-centric Event Log). An object-centric event log is a
tuple OCEL = (E , O, act, otypes, time, E2O ), where E⊆ Uev is a set of events,
O⊆ Uois a set of objects, act :E→ Uact is a function assigning activities to
events, otype :O→ Uot maps each object identifier to an object type, time :
E→ Utime assigns a timestamp to each event, and E2O ⊆(E×O)describes
the relation between events and objects.
We denote A(OCEL) for the set of activities, and OT (OCEL) as the set
of object types. As introduced in [3], Object-Centric Petri Nets (OCPNs) are
defined in correspondence to an OCEL by specifying the set of object types
OT (OCEL) and the tokens being associated with objects of the log. In addition
to a labelled Petri net N= (P, T , F, l), defined in the usual way, OCPNs include
a mapping assigning an object type to every place, and a set of variable arcs.
Definition 2 (Object-Centric Petri net). An object-centric Petri net is a
tuple ON = (N, pt, Fvar)where N= (P, T, F , l)is a labelled Petri net, pt :P→
OT maps places onto object types, and Fvar ⊆Fis a subset of variable arcs.
Items and Decoupling Points for Process Mining 5
Normal arcs describe the removal or addition of a single token, whereas vari-
able arcs indicate a variable number of tokens to be removed or added. The firing
of a transition occurs in regard to a binding (t, b), which includes the transition
to be fired as well as a binding function. The binding defines the sets of tokens
to be consumed, cons(t, b), and produced, prod(t, b).
The example presented in the introduction considers two operationally decoupled
sub-processes tied by their impact on a known collection of items - a warehouse.
We consider items to be elements of the process relevant to the control flow that
occur in varying quantities. Although each item refers to a particular item type,
they differ from objects as they are not described by an identifier but by the
quantity they occur in. The universe of item types is denoted Uit, and I⊆ Uit
refers to a set of item types. In the logistics domain, we have to distinguish be-
tween the demand for items of different types (negative quantity) and the actual
presence of such items (positive quantity). Thus, we introduce item quantities,
which assign a signed integer to each item type.
Definition 3 (Item Quantity). Let I⊆ Uit be a finite set of item types.
An item quantity q:I→Zis a function that maps each item type i∈I
to a signed integer. The set of all possible item quantities over Iis denoted
I(I) = {q:I→Z}. Item quantities can be changed by addition and subtraction,
given q1, q2∈ I(I)be two item quantities over I⊆ Uit:
q1⊕q2=q3where ∀i∈I:q3(i) = q1(i) + q2(i), and
q1⊖q2=q3where ∀i∈I:q3(i) = q1(i)−q2(i).
We use a notation for item quantities similar to multisets but emphasising
the difference using different brackets. Some examples for item quantities over
I={x, y, z}with I⊆ Uit:q1=J K,q2=Jx, x, x, yK,q3=Jx, y−1, y −1, z, zK,
q4=Jx3, yK, and q5=Jx, y−2, z 2K.q1is an empty item quantity, q2and q4are
two notations for the same item quantity, just as q3and q5.q2(y) = 1 refers
to the quantity associated with item type yfor q2, just as q3(y) = −2 for item
quantity q3, and q1(y) = 0 for q1. The set of all item types qassigns a non-
zero quantity to is denoted, set(q) = {i|q(i)= 0}, e.g. set(q2) = {x, y}and
set(q1) = ∅. Examples for operations on item quantities: q2⊕q3=Jx4, y−1, z2K,
q4⊖q5=Jx2, y3, z−2K, and q5⊖q3=q1.
The positive item quantity of qis denoted q+=b↾{i∈set(q)|q(i)>0}and q−=
q↾{i∈set(q)|q(i)<0}as the negative item quantity of q, e.g. q+
3=Jx, z2Kand q−
5=
Jy−2K. An item quantity q∈ I(I) is considered fully positive, iff q=q+and fully
negative iff q=q−.
A location or entity dedicated to collecting items, such as a warehouse or a
buffer, is referred to as a collection point. Every collection point refers to an item
quantity, its item level, describing the availability or lack of items of specific item
types. We consider a finite set of collection points CP ⊆ Ucp from the universe
of collection points.
Definition 4 (Item Levels). Given a set of item types I⊆ Uit and a set of
collection points CP ⊆ Ucp , the mapping mq:CP → I(I)describes the item
levels of the collection points in CP .
6 N. Graves et al.
In line with Definition 3, the item level of a particular item type i∈Iof
collection point cp ∈CP is denoted mq,I (cp)(i). Consider, a warehouse cp ∈CP
containing items of three different types: I={cups, books, albums}. Currently,
there is a stock of 21 cups and the item level of books lies at mq,I (cp)(books) =
17, but a demand for 25 albums. Hence, the item level for the warehouse is
mq,I (cp) = Jcups21, books17, albums−25 K.
A collection point’s item level is changed in a quantity operation by adding
another item quantity q∈ I(I) to the current item level, denoted mq,I (cp)q
−→
m′
q,I (cp), where m′
q,I (cp) = mq,I (cp)⊕q. After the execution of a quantity oper-
ation, the item level of all item types with a negative item quantity i∈set(q−)
is reduced and increased for all available item types i∈set(q+). The execu-
tion of a sequence of quantity operations on the initial item level minit
q,I (cp)q1
−→
mq,I ′(cp)q2
−→ ... qn
−→ m′′
q,I (cp), is denoted minit
q,I (cp)σ
−→ mq,I ′′(cp), with σ=
⟨q1, q2, ..., qn⟩describing the sequence of item quantities. Using item quantities,
we can now represent collections of items as well as material movements.
4 Quantity-Dependent Process Mining
The underlying concepts of item quantities, collection points, item levels and
quantity operations are nothing new: Inventory management is one of the largest
areas in logistics. However, current process mining techniques cannot describe
item quantities and business processes jointly [9]. This section proposes a frame-
work extending object-centric process mining to (1) connect the execution of
events with changes to item levels, (2) detect the item levels of known collection
points at the time individual processes are executed, and (3) model decoupled
quantity-dependent processes. The framework is based on the assumption that
the execution of quantity operations is connected to events described exhaus-
tively in the event log.
4.1 Quantity-relating Event Logs
Our goal is to define an event log that enables the identification of dependen-
cies between the execution of activities, sub-processes, and item levels without
needing identifiers for all items. This requires an event log that connects events
to quantity operations and, thereby, describes the item levels’ development. We
achieve this by adding collection points and item types to the log and mapping
quantity operations to events.
Definition 5 (Quantity Event Log). A quantity-relating event log is a tuple
QEL = (OCEL, I , CP, eq ty), where OCEL = (E, O, act, otypes, time, E2O)is
an object-centric event log, I⊆ Uit is a set of item types, CP ⊆ UCP is the set of
known collection points, and eqty :E→(CP ↛I(I)) assigns quantity updates
to events and collection points.
As this event log extends usual OCELs, applying other process mining techniques
is not limited by using QELs. Table 1 shows a QEL for the example process of
Items and Decoupling Points for Process Mining 7
Table 1: Example of a QEL displayed in a single table
events (E, act, time)eqty objects (O, otypes, E2O)
event activity timestamp quantity cp RO CO delivery parcel
ev-zz register co 22.12.2020 12:22 Ja−3Kcp1 co-883
ev-vl pick and pack 22.12.2020 12:24 Ja−3, b−10Kcp2 co-882 p-942
ev-tg send parcel 22.12.2020 12:31 p-941
ev-rg register co 22.12.2020 13:56 Jb−3, c−1Kcp1 co-884
ev-pa send parcel 22.12.2020 13:57 p-942
ev-yq pick and pack 22.12.2020 14:01 Ja−3Kcp2 co-883 p-943
ev-kj send parcel 22.12.2020 14:11 p-943
ev-bn register delivery 22.12.2020 15:19 ro-11 d-11
ev-iq pick and pack 22.12.2020 15:23 Jb−3, c−1Kcp2 co-884 p-944
ev-gq send parcel 22.12.2020 15:39 p-944
ev-id unpack delivery 22.12.2020 16:12 d-11
ev-ya register co 23.12.2020 09:40 Jb−5Kcp1 co-891
ev-mr pick and pack 23.12.2020 10:22 Jb−5Kcp2 co-891 p-951
ev-sj send parcel 23.12.2020 10:38 p-951
ev-oo place in stock 28.12.2020 10:43 Jb990Kcp2 d-11
ev-qk register co 28.12.2020 10:50 Jb−5, c−3Kcp1 co-925
Figure 1, in which all information is aggregated into a single table: We see the
event details, information on the related quantity operations and the involved
objects of the different object types. Please note, that this is only possible as
every event only refers to one object of each type and one collection point. We see
that the events “register co”, “pick and pack” and “place in stock” are associated
with quantity operations regarding two different collection points.
As we see in the example log, we cannot determine the item level of the
individual collection point based on this information. We, therefore, introduce
a preliminary simplification in which we assume the existence of an init-event
mapping each collection point to its initial item level, dated prior to every other
event with a quantity operation. It is clear, that associating the quantity opera-
tions with events allows for considering sequences of quantity operations. Using a
projection that keeps the sequence’s length and summing over each entry’s prefix,
the quantity level of every collection point can be determined during any event
in the log. The left of Figure 2, shows a sequence σof 10 entries, each referring
to a collection point and an item quantity, derived by ordering the quantity op-
erations according to the timestamp of the corresponding event. By considering
the initial item levels minit
q,I (cp1) = Ja21, b25 , c10K, and minit
q,I (cp2) = Ja31, b27 , c6K
it is possible to determine the development of each collection point’s item level
at any time within the sequence, as can be seen on the right.
4.2 Quantity Nets
One of the main benefits of process mining is its ability to identify process models
capable of relaying the causalities uncovered by analysing event data – as seen in
8 N. Graves et al.
1
2
3
4
5
6
7
8
9
10
Collection Point 1
Collection Point 2
Fig. 2: Sequence of quantity operations (left) and item levels of both collection points
with initial levels of minit
q,I (cp1) = Ja21, b25 , c10Kand minit
q,I (cp2) = Ja31, b27 , c6K.
the introduction OCPNs are not capable of doing so for non-identifiable items.
In this work, we consider a collection of items as a point in which several sub-
processes are decoupled, indicating an item quantity-related dependency of their
process executions by adding decoupling points to OCPNs.
Definition 6 (Labelled Quantity Net). A labelled quantity net is a tripartite
graph QN = (P, T, DP , F, Fvar, pt, l), with Pa set of places, Ta set of transi-
tions, DP ⊆ Ucp a set of decoupling points, F⊆((P×T)∪(T×P)∪(T×DP )∪
(DP ×T)a set of arcs, Fvar ⊆(F∩((P×T)∪(T×P)) a subset of variable
arcs between places and transitions, pt :P→ Uot a mapping of places to object
types, l:T↛Uact a function assigning activity names to transitions.
The semantics of OCPNs are described by bindings, which we keep unchanged
but refer to the binding function as place binding. The binding of the quantity
net is composed of the place binding and a valid quantity-binding bq, thus b=
(t, bp, bq). A quantity binding is a function bq:DP ↛I(I) describing a quantity
item for decoupling points, the semantics of which are considered equivalent
to those of quantity operations for collection points. A binding is valid, if it
only assigns a function value to places and decoupling points connected to the
transition it refers to. Depending on the type of arc, the change in the item
level mq,I (dp)q
−→ m′
q,I (dp) by an item quantity q∈ I(I) is either an addition
m′
q,I (dp) = mq,I (dp)⊕Q(incoming arc) or a subtraction m′
q,I (dp) = mq,I (dp)⊖q
(outgoing arc). Please note, that these semantics can lead to an increase in
the item level if a negative item quantity is subtracted from a negative item
level. Figure 3 shows an example, in which, for simplicity, only the transition,
decoupling points and quantity binding function (graph notation) are detailed.
The execution of b1fires transition t1and adds Ja2, cKto dp1’s current item
level, mq,I (dp1)bq
1
−→ m′
q,I (dp1) = Ja6, b6, c3K, leaving dp2’s item level unchanged.
Executing b2removes items from dp1,mq,I(dp1)′′ =mq ,I (dp1)′⊖Ja, b2K, and
adds Jb, cKto dp2, so that m′′
q,I (dp2) = mq,I (dp”)⊕bq
2(dp2).
Items and Decoupling Points for Process Mining 9
Quantity Bindings (graph notation)
Fig. 3: The individual processes of the running example can be connected through a
decoupling point, despite a lack of item identifiers.
As quantity nets offer the same representation and semantics as OCPNs,
they do not limit the modelling capabilities, yet offer a further representation
of behaviour. The decoupling points represent the connection of otherwise dis-
connected processes as well as an inter-dependency of a collection of items and
the process. We briefly describe a very basic form of discovery by imposing two
strong requirements. The first is that only fully positive and fully negative item
quantities are included in the QEL. The second is that all events belonging to
the same activity must “agree” in their impact on a collection point – there are
no quantity operations by events in which one refers to a fully positive, and the
other refers to a fully negative item quantity for the same collection point. Given
a QEL fulfilling these requirements, the OCPN discovered by the event log can
be extended by first adding each collection point as a decoupling point. Subse-
quently, arcs between the activities referring to at least one quantity operation
and the corresponding collection point are added – the arc’s direction depends
on the sign of the quantity operation.
5 Example Application
The main goal of inventory management is maintaining a continuous capabil-
ity to meet variable and uncertain demand while minimising cost. Current ap-
proaches for inventory management consider specific parameters related to item
quantities and lead times. Still, they cannot additionally consider the end-to-
end process leading to increases and decreases of stock levels [5]. This section
applies the previously introduced framework to increase its comprehension and
demonstrate how it enhances process mining’s capabilities. To do so, we present
an analysis of a simulated QEL1describing a typical example for a decoupled
process: inventory management. The log describes a process similar to the pro-
cess used as the running example – the only difference is that customer orders
can loop around the activity “pick and pack”. Figure 5 shows the corresponding
quantity net created by extending the discovered OCPN. The selected log fulfils
the criteria for discovering quantity nets, as it has one activity referring to fully
positive quantity operations (“place in stock”) and another (“pick and pack”)
with only negative item quantities.
The log shows a decoupled process, as significantly more customer orders
are processed than replenishment orders placed: One delivery of albums covers
1Link to the data: https://git.rwth-aachen.de/ninagraves/intro_qrpm
10 N. Graves et al.
Fig. 4: Warehouse’s Item level over time.
place
RO
register
arrival
unload
delivery
place in
stock
register
CO pick and
pack
send
parcel
RO
Delivery
CO Parcel
Warehouse
(
Fig. 5: Quantity net of example process.
about 519 customer orders in a turnover time of 33 days, every delivery of books
lasts for about eight business days, and delivered cups last for 17 days. Figure 6
shows the distribution of the number of ordered items per type (only consid-
ering orders with a demand for this item type) per customer order – assuming
the accumulated item quantities removed regarding the same customer order
represent the ordered quantity. The average customer order arrives 15.6 times
per business day and refers to an item quantity of 1.35 photo albums, 6.9 books
and 0.29 cups. In comparison, 21 deliveries arrived in the same period. Eleven
deliveries contain 980 or 990 books, six include 81 or 82 cups, and four deliveries
add 556 to 560 photo albums to the warehouse. An overview of the delivered
(and assumed to be ordered) items can be found in Figure 7.
Further process insights can be gained from the QEL by considering the item
level of the warehouse at the time specific events were executed. A closer look at
the replenishment orders shows that the time between the placement of replen-
ishment orders varies throughout the process, making a time-based dependency
unlikely. Taking the item level at the time of each order’s placement into ac-
count (added as a shade to Figure 7), we see that the sum of the current item
level and the requested quantity appear to be somehow connected, indicating
a quantity-related dependency of the event’s execution on the item level. This
indirect dependency on the item level is not depicted in the quantity net, and
further investigation is out of this work’s scope.
The process model in Figure 5 suggests several executions of the activity
“pick and pack” regarding the same customer order. For 106 customer orders,
the activity was executed several times – removing items from the warehouse and
sending a parcel to a customer every time. Closer consideration of the timestamps
shows that this behaviour is not distributed evenly over the period but aggregates
selectively. By applying standard process mining techniques to detect the waiting
times, we further see that the average waiting time of objects before the activity
“pick and pack” is performed is up to 54% higher than in other periods. The
warehouse’s item levels reveal that this behaviour coincides with stock-outs of
books or albums. Within these periods, only a few customer orders are processed,
none leading to a removal of items of the out-of-stock item type. Shortly after,
Items and Decoupling Points for Process Mining 11
Fig. 6: Demand customer orders. Fig. 7: Ordered items per replenishment order.
the density of events removing items of this type is higher than usual; this can
also be seen in the steep decreases after the arrival of deliveries in Figure 4.
The example of a quantity-related analysis provided in this section revealed
dependencies that could not have been uncovered with standard object-centric
process mining techniques. Despite the semantics of the quantity net not being
able to depict all of them, they are capable of (1) displaying the two processes
as decoupled and (2) depicting the dependency of the execution of the activity
“pick and pack” on the collection point’s item level.
6 Conclusion
In the high uncertainty and variability within current fast-paced environments,
managing logistics processes requires increased transparency over the impacting
end-to-end processes [13]. This presentation of early-stage research provides a
foundation for the application of process mining for logistics processes by allow-
ing the joint analysis of item quantities and end-to-end processes. The exemplary
analysis indicates that the framework can capture direct dependencies between
activities and known collection points and its support in revealing further de-
pendencies. The extraction of the required quantity event log, the detection of
additional quantity-related dependencies, and supporting software are future re-
search topics. Additionally, the consideration of collection points supports the
analysis of process networks, thereby serving as an abstraction for federated pro-
cess mining. We conclude the presented framework as a promising first step in
enabling process mining techniques to consider quantities instead of identities.
Acknowledgement
Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foun-
dation) under Germany’s Excellence Strategy - EXC-2023 Internet of Produc-
tion - 390621612. We also thank the Alexander von Humboldt (AvH) Stiftung
for supporting our research.
12 N. Graves et al.
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