<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Archiving and Interchange DTD v1.0 20120330//EN" "JATS-archivearticle1.dtd">
<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta>
      <issn pub-type="ppub">1613-0073</issn>
    </journal-meta>
    <article-meta>
      <title-group>
        <article-title>OCEL generator for fragmented supply orders</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Jost Goette</string-name>
          <email>jost.goette@klu.org</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Maximilian Harms</string-name>
          <email>maximilian.harms@klu.org</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Henrik Leopold</string-name>
          <email>henrik.leopold@klu.org</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Kuehne Logistics University</institution>
          ,
          <addr-line>Hamburg</addr-line>
          ,
          <country country="DE">Germany</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Microsoft Windows, GNU/Linux</institution>
          ,
          <addr-line>MacOS</addr-line>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>Python</institution>
          ,
          <addr-line>PM4PY, Dash, Pandas</addr-line>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2025</year>
      </pub-date>
      <fpage>20</fpage>
      <lpage>24</lpage>
      <abstract>
        <p>Process mining is widely used to analyze, understand, and improve business processes. Object-Centric Process Mining (OCPM) extends traditional approaches by capturing interactions between multiple object types within a process. In supply chains, these interactions exhibit domain-specific behavior, such as order fragmentation, for example, when a supplier cannot complete an order. Yet suitable event data are scarce due to multi-party privacy constraints. We introduce FrOG (Fragmented Order Generator), a configurable generator of object-centric event logs (OCEL) derived from a warehouse simulation with industry-standard stock policies. FrOG produces near-realistic supply-order data that capture fragmentation and cross-object dependencies, enabling OCPM studies without access to sensitive OCPM, warehouse simulation, synthetic OCEL, data generator, fragmented orders operational logs.</p>
      </abstract>
      <kwd-group>
        <kwd>Metadata description</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>Legal code license</title>
    </sec>
    <sec id="sec-2">
      <title>Value</title>
    </sec>
    <sec id="sec-3">
      <title>FrOG 1.0 MIT</title>
      <p>CEUR
ceur-ws.org</p>
    </sec>
    <sec id="sec-4">
      <title>Languages, tools and services used</title>
    </sec>
    <sec id="sec-5">
      <title>Supported operating environment</title>
    </sec>
    <sec id="sec-6">
      <title>Download/Demo URL</title>
    </sec>
    <sec id="sec-7">
      <title>Documentation URL</title>
    </sec>
    <sec id="sec-8">
      <title>Source code repository</title>
    </sec>
    <sec id="sec-9">
      <title>Screencast video</title>
      <p>https://github.com/klu-ds/FrOG
https://github.com/klu-ds/FrOG/blob/main/README.md
https://github.com/klu-ds/FrOG
https://youtu.be/MxbSjiawY30</p>
      <sec id="sec-9-1">
        <title>1. Introduction</title>
        <p>Global supply chains are complex, fast-moving, and inherently uncertain. As demand and
supply fluctuate, suppliers often adapt by splitting large orders into multiple shipments based on
what is available. This improves service, but it also complicates post-order evaluation, because
it blurs lead times, fulfillment rates, and cost comparisons.</p>
        <p>
          One established concept for analyzing supply orders is Process Mining [
          <xref ref-type="bibr" rid="ref1">1</xref>
          ]. It ofers methods
and techniques for analyzing and improving operational processes based on event data and
        </p>
        <p>Item
Configuration</p>
        <p>Simulation</p>
        <p>Repeat for x days
Simulate
Deliveries</p>
        <p>Simulate</p>
        <p>Demand
Simulate
Orders
Generated</p>
        <p>
          OCEL
plays an important role in identifying deviations, ineficiencies, and improvement opportunities.
Traditional process mining techniques typically assume the availability of flat event logs, where
each event is associated with a single case identifier. While efective in many scenarios, this
representation introduces limitations, for instance due to the duplication of events when multiple
process entities interact within a single execution [
          <xref ref-type="bibr" rid="ref2">2</xref>
          ].
        </p>
        <p>
          Object-centric process mining (OCPM) has emerged as a paradigm that accounts for multiple
interacting objects within a process. Instead of relying on a single case notion, OCPM represents
events in terms of the objects they afect, enabling a more accurate and flexible view of the
execution of real-world processes [
          <xref ref-type="bibr" rid="ref2">2</xref>
          ]. However, restrictions such as privacy concerns hinder
access to specialized event data of the supply chain management (SCM) domain [
          <xref ref-type="bibr" rid="ref1">1</xref>
          ]. Data that
would be necessary to advance process mining techniques for the SCM field.
        </p>
        <p>
          Existing tools for synthetic event log generation [
          <xref ref-type="bibr" rid="ref3">3</xref>
          ] [
          <xref ref-type="bibr" rid="ref4">4</xref>
          ] provide realistic control-flow and data
perspectives but remain limited to flat case structures, thereby insuficiently capturing complex
interactions between multiple objects. More recent object-centric generators [
          <xref ref-type="bibr" rid="ref5">5</xref>
          ] extend this by
modeling multi-object relations, yet they lack the capability to represent domain-specific supply
chain phenomena like repeated order fragmentation. Logistics-focused simulators [
          <xref ref-type="bibr" rid="ref6">6</xref>
          ] primarily
address inventories, routes, and order executions without explicitly modeling the systematic
splitting of customer orders into multiple partial deliveries. Consequently, existing approaches
cannot realistically reproduce the fragmentation dynamics characteristic of split-order deliveries
in event logs.
        </p>
        <p>To facilitate the investigation of novel OCPM techniques that address the challenges of SCM,
we propose FrOG (Fragmented Order Generator), a synthetic OCEL generation tool, that uses a
warehouse simulation to create authentic orders based on common stock-policies. The tool lets
it users customize the simulation and especially the degree to which orders are split. It ofers
access to basic OCPM techniques to analyze the resulting OCEL as well as extract it.</p>
      </sec>
      <sec id="sec-9-2">
        <title>2. The tool</title>
        <p>
          FrOG is implemented in Python. The frontend is built with DASH [
          <xref ref-type="bibr" rid="ref7">7</xref>
          ]. For simulation and
OCEL generation we use Pandas [
          <xref ref-type="bibr" rid="ref8">8</xref>
          ] and PM4PY [
          <xref ref-type="bibr" rid="ref9">9</xref>
          ]. Figure 1 shows the high level workflow
start
        </p>
        <p>Place Order
whole item unavailable</p>
        <p>Check</p>
        <p>Availability
Item partially available</p>
        <p>Split Item
unavailable parts of item</p>
        <p>Whole item available</p>
        <p>Pick Item</p>
        <p>Pack item</p>
        <p>end
available parts of item
of the FrOG. It lets the user configure various parameters of a common warehouse simulation
on the simulation page. Then, users can define various items with diferent behavior that the
warehouse manages. After that, the simulation runs for the set amount of days. Over the course
of the simulation, the warehouse has to fulfill demand and prevent shortages. Each day, it
cycles through the simulation of deliveries, demand and orders. These orders are gathered and
consolidated into an OCEL. At the end the user is on the one hand presented with data about
the simulation and on the other hand they can analyze the created OCEL and export it on the
analysis page.</p>
        <sec id="sec-9-2-1">
          <title>2.1. The Simulation</title>
          <p>
            The core of FrOG is the user-configured warehouse simulation. In supply chain management,
warehouse simulation is a proven tool to investigate and optimize warehouse policies [
            <xref ref-type="bibr" rid="ref10">10</xref>
            ]. Our
simulation constructs a virtual warehouse, that manages the inventory for the user-defined
items. Each item refers to one type of goods. Prior to the simulation, the user can configure the
starting inventory, order cost, holding cost, mean and standard deviation for the daily demand
for each created item.
          </p>
          <p>
            The warehouse follows the classical continuous review policy [
            <xref ref-type="bibr" rid="ref11">11</xref>
            ]. This policy determines
the economic order quantity (EOQ) and reorder point (ROP) to sustainably manage the operation
of the defined goods. The EOQ utilizes the mean daily demand and holding cost of an item to
determine the optimal quantity of an order. The ROP uses the mean demand and lead times to
determine the optimal stock level to reorder again. The starting EOQ and ROP can be configured
by the user and are then adapted by the simulation accordingly.
          </p>
          <p>Each simulated day follows the same structure. First, the warehouse receives the due deliveries,
evaluates the corresponding orders and updates its parameters like the reorder point accordingly.
Second, it invokes the random demand for each of its managed items and reduces the inventory
accordingly. Third, if the stock-level of any item drops below the respective ROP it creates
a new order for that item and hands it over to the OCEL-generation module to convert that
pre-configured order into one process instance of an OCEL.</p>
        </sec>
        <sec id="sec-9-2-2">
          <title>2.2. Simulated Order Process</title>
          <p>
            Figure 2 shows BPMN diagram of the fixed order process that the simulation triggers at each
ROP. It modifies the order-to-delivery process found in [
            <xref ref-type="bibr" rid="ref2">2</xref>
            ] with the corresponding behaviour
for partial deliveries. Each order process begins with the “Place Order” event, which initiates an
order and creates associated item objects. Each item represents a specific quantity of a material.
The order then proceeds through typical administrative steps, including “Send Invoice” and
“Receive Payment”.
          </p>
          <p>Once the order is placed, item availability is continuously evaluated through the “Check
Availability” activity. Based on material availability at the time of checking, the process branches
into three possible paths:
1. No availability: If none of the materials for an item are currently available, the item is
disregarded and re-evaluated in the next availability check.
2. Full availability: If the full quantity of materials is available, the item is directly picked,
packed, and included in a shipment.
3. Partial availability: If only part of the item’s materials are available, a split occurs (as
modeled by the “Split item” activity). The item is divided into two new item objects:
one containing the available materials, and another holding the remaining quantity.
The available portion continues through the pick, pack, and deliver sequence, while the
remaining portion loops back to the availability check.</p>
          <p>This fragmentation may repeat multiple times until all materials are eventually picked and
delivered. The user defines the average degree to which orders of an item are split, when they
configure the item.</p>
        </sec>
        <sec id="sec-9-2-3">
          <title>2.3. Output</title>
          <p>After the simulation is complete, FrOG ofers two types of output to the user. First is the supply
chain perspective ofering data with regards to the simulation itself. This includes the total
fulfilled the demand, the amount of orders, unfulfilled demand, and the service level (relative
fulfilled demand). These information are computed for each item as well as for the whole
warehouse globally.</p>
          <p>
            The second type of output is the OCEL that FrOG constructs using all orders issued during
the simulation. It adheres to the OCEL 2.0 standard [
            <xref ref-type="bibr" rid="ref12">12</xref>
            ] and thus includes O2O relations. This
OCEL is presented to the user on the analysis page of the tool and is accompanied by several
summarizing stats of the OCEL gathered from the PM4PY [
            <xref ref-type="bibr" rid="ref9">9</xref>
            ] function OCEL summary function.
Finally, the user may download the OCEL for further work in the OCEL JSON format [
            <xref ref-type="bibr" rid="ref12">12</xref>
            ].
          </p>
        </sec>
      </sec>
      <sec id="sec-9-3">
        <title>3. Maturity</title>
        <p>We assess the maturity of FrOG by assessing its scalability. For increasing parameter values
that target the tool’s complexity, we evaluate the runtime of the simulation and the following
OCEL creation. This benchmark can be recreated on benchmark page.</p>
        <p>We consider the simulation days, the amount of items, and the mean amount of splits to be
the driving dimensions of FrOG’s scalability. They are the most relevant dimensions for the
envisaged use case. We diagonalize the benchmark over these dimensions to cover all possible
configurations within the following bounds: 1000, 2000, 5000 and 10000 simulation days, 1, 5,
10, and 50 items, as well as 0, 1, 5, 10 mean splits. We repeat each configuration three times.</p>
        <p>The results in Figure 3 indicate diferent efects on the scalability depending on which
dimension is increased. Increasing the splits from zero to one, as well as 5-10 results in similar
run times, albeit an increase between one and five severely increases the run time. The efect on
the run time of increasing amounts of items decreases with more items. Increasing the amount
of days leads to slight super linear growth of the run time.</p>
      </sec>
      <sec id="sec-9-4">
        <title>4. Outlook</title>
        <p>In this paper, we proposed FrOG, which generates OCELs from orders created as part of a realistic
warehouse simulation. While the tool is a step towards facilitating OCPM techniques for more
complex supply chain related processes, there a still improvement opportunities left. Future
work should consider adding more functionality, such as a dedicated OCPM page that hosts
existing OCPM techniques to apply them on the created OCEL. It could also concern itself with
other processes related to the warehouse or adding diferent behavior to the warehouse, such
as configurable stock policies. The current implementation does not consider the availability of
resources that could limit warehouse throughput.</p>
      </sec>
      <sec id="sec-9-5">
        <title>Declaration on Generative AI</title>
        <p>The author(s) used ChatGPT to: polish the code of the frontend. The author(s) reviewed and
edited the content as needed and take(s) full responsibility for the publication’s content.</p>
      </sec>
    </sec>
  </body>
  <back>
    <ref-list>
      <ref id="ref1">
        <mixed-citation>
          [1]
          <string-name>
            <given-names>F.</given-names>
            <surname>Oldenburg</surname>
          </string-name>
          ,
          <string-name>
            <given-names>K.</given-names>
            <surname>Hoberg</surname>
          </string-name>
          ,
          <string-name>
            <given-names>H.</given-names>
            <surname>Leopold</surname>
          </string-name>
          ,
          <article-title>Process mining in supply chain management: stateof-the-art, use cases</article-title>
          and research outlook,
          <source>International Journal of Production Research</source>
          <volume>63</volume>
          (
          <year>2025</year>
          )
          <fpage>2889</fpage>
          -
          <lpage>2904</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref2">
        <mixed-citation>
          [2]
          <string-name>
            <surname>W. M. van der Aalst</surname>
          </string-name>
          ,
          <article-title>Object-centric process mining: dealing with divergence and convergence in event data</article-title>
          ,
          <source>in: Software Engineering and Formal Methods: 17th International Conference, SEFM 2019</source>
          , Oslo, Norway,
          <source>September 18-20</source>
          ,
          <year>2019</year>
          , Proceedings 17, Springer,
          <year>2019</year>
          , pp.
          <fpage>3</fpage>
          -
          <lpage>25</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref3">
        <mixed-citation>
          [3]
          <string-name>
            <given-names>D.</given-names>
            <surname>Jilg</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Grüger</surname>
          </string-name>
          ,
          <string-name>
            <given-names>T.</given-names>
            <surname>Geyer</surname>
          </string-name>
          ,
          <string-name>
            <given-names>R.</given-names>
            <surname>Bergmann</surname>
          </string-name>
          ,
          <article-title>DALG: the data aware event log generator</article-title>
          ,
          <source>in: Proceedings of the Best Dissertation Award, Doctoral Consortium, and Demonstration &amp; Resources Forum at BPM</source>
          <year>2023</year>
          co
          <article-title>-located with 21st International Conference on Business Process Management (BPM</article-title>
          <year>2023</year>
          ), Utrecht, The Netherlands,
          <source>September 11th to 15th</source>
          ,
          <year>2023</year>
          , volume
          <volume>3469</volume>
          <source>of CEUR Workshop Proceedings, CEUR-WS.org</source>
          ,
          <year>2023</year>
          , pp.
          <fpage>142</fpage>
          -
          <lpage>146</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref4">
        <mixed-citation>
          [4]
          <string-name>
            <given-names>Ändrea</given-names>
            <surname>Burattin</surname>
          </string-name>
          ,
          <string-name>
            <given-names>B.</given-names>
            <surname>Re</surname>
          </string-name>
          ,
          <string-name>
            <given-names>L.</given-names>
            <surname>Rossi</surname>
          </string-name>
          ,
          <string-name>
            <surname>F.</surname>
          </string-name>
          <article-title>Tiezzi”, Purple: a purpose-guided log generator</article-title>
          ,
          <source>in: Proceedings of the ICPM Doctoral Consortium and Demo Track</source>
          <year>2022</year>
          , CEUR Workshop Proceedings, CEUR-WS,
          <year>2022</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref5">
        <mixed-citation>
          [5]
          <string-name>
            <given-names>A.</given-names>
            <surname>Goossens</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Rebmann</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J. D.</given-names>
            <surname>Smedt</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Vanthienen</surname>
          </string-name>
          , H. v. d. Aa, From OCEL to DOCEL - Datasets and Automated Transformation,
          <year>2023</year>
          . URL: http://arxiv.org/abs/2309.14092. doi:
          <volume>10</volume>
          .48550/arXiv.2309.14092, arXiv:
          <fpage>2309</fpage>
          .14092 [cs].
        </mixed-citation>
      </ref>
      <ref id="ref6">
        <mixed-citation>
          [6]
          <string-name>
            <given-names>A.</given-names>
            <surname>Wuttke</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Hunker</surname>
          </string-name>
          , M. Rabe,
          <article-title>LogFarm: An Open Source Graph-based Simulator for Logistics Networks</article-title>
          ,
          <source>SNE Simulation Notes Europe</source>
          <volume>34</volume>
          (
          <year>2024</year>
          )
          <fpage>43</fpage>
          -
          <lpage>50</lpage>
          . URL: https://www.sn e-journal.org/10676. doi:
          <volume>10</volume>
          .11128/sne.34.sw.
          <volume>10676</volume>
          .
        </mixed-citation>
      </ref>
      <ref id="ref7">
        <mixed-citation>
          [7]
          <string-name>
            <given-names>P. T.</given-names>
            <surname>Inc</surname>
          </string-name>
          .,
          <source>Dash documentation &amp; user guide</source>
          ,
          <year>2025</year>
          . URL: https://dash.plotly.com/,
          <source>accessed August 13</source>
          ,
          <year>2025</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref8">
        <mixed-citation>
          [8]
          <string-name>
            <surname>T.</surname>
          </string-name>
          <article-title>pandas development team</article-title>
          , pandas-dev/pandas: Pandas,
          <year>2020</year>
          . URL: https://doi.org/10.5 281/zenodo.3509134. doi:
          <volume>10</volume>
          .5281/zenodo.3509134.
        </mixed-citation>
      </ref>
      <ref id="ref9">
        <mixed-citation>
          [9]
          <string-name>
            <given-names>A.</given-names>
            <surname>Berti</surname>
          </string-name>
          , S. van Zelst,
          <string-name>
            <given-names>D.</given-names>
            <surname>Schuster</surname>
          </string-name>
          ,
          <article-title>Pm4py: A process mining library for python</article-title>
          ,
          <source>Software Impacts</source>
          <volume>17</volume>
          (
          <year>2023</year>
          )
          <article-title>100556</article-title>
          . URL: https://www.sciencedirect.com/science/article/pii/S26659 63823000933. doi:https://doi.org/10.1016/j.simpa.
          <year>2023</year>
          .
          <volume>100556</volume>
          .
        </mixed-citation>
      </ref>
      <ref id="ref10">
        <mixed-citation>
          [10]
          <string-name>
            <given-names>J. P.</given-names>
            <surname>Gagliardi</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J.</given-names>
            <surname>Renaud</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A.</given-names>
            <surname>Ruiz</surname>
          </string-name>
          ,
          <article-title>A simulation model to improve warehouse operations</article-title>
          ,
          <source>in: 2007 Winter Simulation Conference</source>
          ,
          <year>2007</year>
          , pp.
          <fpage>2012</fpage>
          -
          <lpage>2018</lpage>
          . doi:
          <volume>10</volume>
          .1109/WSC.
          <year>2007</year>
          .
          <volume>441</volume>
          9831.
        </mixed-citation>
      </ref>
      <ref id="ref11">
        <mixed-citation>
          [11]
          <string-name>
            <given-names>S.</given-names>
            <surname>Axsäter</surname>
          </string-name>
          , Inventory control, number 90 in International series in operations research &amp; management science, 2nd ed ed., Springer, New York,
          <year>2006</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref12">
        <mixed-citation>
          [12]
          <string-name>
            <given-names>A.</given-names>
            <surname>Berti</surname>
          </string-name>
          ,
          <string-name>
            <surname>I. Koren</surname>
          </string-name>
          ,
          <string-name>
            <given-names>J. N.</given-names>
            <surname>Adams</surname>
          </string-name>
          , G. Park,
          <string-name>
            <given-names>B.</given-names>
            <surname>Knopp</surname>
          </string-name>
          ,
          <string-name>
            <given-names>N.</given-names>
            <surname>Graves</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Rafiei</surname>
          </string-name>
          ,
          <string-name>
            <given-names>L.</given-names>
            <surname>Liß</surname>
          </string-name>
          , L. T. G. Unterberg,
          <string-name>
            <given-names>Y.</given-names>
            <surname>Zhang</surname>
          </string-name>
          ,
          <string-name>
            <given-names>C.</given-names>
            <surname>Schwanen</surname>
          </string-name>
          ,
          <string-name>
            <given-names>M.</given-names>
            <surname>Pegoraro</surname>
          </string-name>
          ,
          <string-name>
            <surname>W. M. P. van der Aalst</surname>
          </string-name>
          ,
          <article-title>Ocel (object-centric event log) 2.0 specification, 2024</article-title>
          . URL: https://arxiv.org/abs/2403.
          <year>01975</year>
          . arXiv:
          <fpage>2403</fpage>
          .
          <year>01975</year>
          .
        </mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>