Modelling and Analysis of Supply Chains using Product Time Petri Nets

44000; CNRS; \'Ecole Centrale Nantes; Eric Lubat (Universit\'e Toulouse; France); LS2N; Nantes; Pierre-Emmanuel Hladik (Nantes Universit\'e; R\'emi Sauv\`ere; Toulouse

arxiv: 2604.04544 · v1 · submitted 2026-04-06 · 📡 eess.SY · cs.FL· cs.MA· cs.SY

Modelling and Analysis of Supply Chains using Product Time Petri Nets

Eric Lubat (Universit\'e Toulouse , Toulouse , France) , Pierre-Emmanuel Hladik (Nantes Universit\'e , \'Ecole Centrale Nantes , CNRS , LS2N , UMR 6004

show 4 more authors

44000 Nantes Yoann Mateu R\'emi Sauv\`ere

This is my paper

Pith reviewed 2026-05-10 19:47 UTC · model grok-4.3

classification 📡 eess.SY cs.FLcs.MAcs.SY

keywords supply chain modelingProduct Time Petri Netstimed systemssynchronizationfeasibility analysiscoordination policiesmanagerial resources

0 comments

The pith

Product Time Petri Nets model supply chain timing feasibility by representing subsystems as independent modules synchronized through labels with the manager as a shared mobile resource.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes a modular approach using Product Time Petri Nets to model supply chains where each subsystem is defined independently and global behavior arises from synchronized transition labels. It explicitly represents the supply chain manager as a critical shared and mobile resource whose availability influences whether the system meets strict timing and resource constraints. The analysis examines how these elements produce successful executions, timeouts, or timelocks from incompatible constraints. This setup supports what-if testing of coordination policies to determine temporal feasibility in distributed manufacturing and assembly operations.

Core claim

By modeling each supply chain subsystem independently in a Product Time Petri Net and allowing interactions only through synchronized transition labels while treating the manager as an explicit shared mobile resource, the approach determines which timing and capacity configurations lead to feasible executions versus those that produce timeouts or timelocks.

What carries the argument

Product Time Petri Nets using synchronized transition labels to compose independent subsystems, with the manager modeled as a shared mobile resource.

If this is right

Different supply chain coordination policies can be compared by simulating their PTPN models to check for feasible executions.
Incompatible timing constraints that produce timelocks or timeouts become identifiable through model analysis.
The effects of managerial capacity limits on system feasibility can be quantified systematically.
What-if scenarios for policy changes can be evaluated without rebuilding the entire model.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same PTPN structure could apply to other distributed systems with synchronized timing, such as logistics networks or assembly lines.
Extending the model with stochastic elements might allow probabilistic predictions of timeout risks under variable delays.
Real-time monitoring data could be fed into the PTPN to detect emerging timelocks before they occur in operation.

Load-bearing premise

That real supply chains can be decomposed into independent subsystems whose interactions are fully captured by synchronized transition labels and that modeling the manager as a shared mobile resource is sufficient to determine overall feasibility without other unmodeled dynamics.

What would settle it

A real supply chain execution that exhibits timing behaviors or feasibility outcomes not matching the predictions of the PTPN model when the manager is represented as the shared mobile resource.

Figures

Figures reproduced from arXiv: 2604.04544 by 44000, CNRS, \'Ecole Centrale Nantes, Eric Lubat (Universit\'e Toulouse, France), LS2N, Nantes, Pierre-Emmanuel Hladik (Nantes Universit\'e, R\'emi Sauv\`ere, Toulouse, UMR 6004, Yoann Mateu.

**Figure 2.** Figure 2: SCG of the PTPN of N1 and N2 More generally, a timelock induced by synchronisation occurs when the timing constraints of two or more synchronized transitions admit no common solution. In that case, the system reaches a temporal deadlock. Firing the unlabelled transition t leads to a dead-end state, illustrating the timelock caused by incompatible timing constraints. 4 Supply Chain Now that we have introdu… view at source ↗

**Figure 3.** Figure 3: Global view of our supply chain system [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 4.** Figure 4: TPN of a Supply Chain for Supplier 0 [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗

**Figure 5.** Figure 5: TPN of X Managers for two supply chain The manager has a key role in allowing the flow of pieces from supplier to factory. 4.3 Factory Our factory (called BAZ in the TPN) is the entity asking for supply. We present in [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗

**Figure 6.** Figure 6: TPN of the Factory for two suppliers [PITH_FULL_IMAGE:figures/full_fig_p011_6.png] view at source ↗

**Figure 7.** Figure 7: TPN end-of-line This net is more independent from the system since the only synchronisation is on the first transition. Now that we have introduced our net, we produce a full model via a PTPN product. 5 Experimental Results Our experiment follows several steps: • First, a model is generated from the TPN representing our supply chain. – The firing intervals of the manager transitions (with [2, y]) are consi… view at source ↗

**Figure 8.** Figure 8: Process of Synchronisation of the TPN For a single supplier, a single manager, and a timing interval of [2,6] on the manager transition t0, we obtain the SCG of the product, shown in [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗

**Figure 9.** Figure 9: SCG of the product To support reproducibility and reuse, the benchmark generator and the end-of-line Petri net are publicly available online34 . Our benchmark was executed on an MSI GS70 equipped with an Intel Core i5 processor. We use TWINA to synchronise our TPNs using the following command: 3https://github.com/Darkelubat/SupplyChain 4https://zenodo.org/records/18925093 [PITH_FULL_IMAGE:figures/full_fi… view at source ↗

read the original abstract

Supply chains involve geographically distributed manufacturing and assembly sites that must be coordinated under strict timing and resource constraints. While many existing approaches rely on Colored Petri Nets to model material flows, this work focuses on the temporal feasibility of supply chain processes. We propose a modular modelling approach based on Product Time Petri Nets (PTPNs), where each subsystem is represented independently and the global behaviour emerges through synchronised transition labels. A key feature of the model is the explicit representation of the supply chain manager as a critical shared and mobile resource, whose availability directly impacts system feasibility. We analyse how timing constraints and managerial capacity influence the system behaviour, identifying configurations that lead to successful executions, timeouts, or timelocks induced by incompatible timing constraints. This approach enables systematic what-if analysis of supply chain coordination policies and demonstrates the relevance of PTPNs for modelling and analysing synchronised timed systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper applies Product Time Petri Nets modularly to supply chains with the manager as a mobile shared resource for timing analysis, though it lacks supporting examples or validation.

read the letter

The punchline here is that the authors have taken Product Time Petri Nets and applied them modularly to supply chains, with the novel twist of representing the manager explicitly as a shared and mobile resource whose availability drives feasibility. This is new in the sense that prior work on colored Petri nets for material flows is set aside in favor of timing and synchronization analysis. The modular decomposition where global behavior comes from synchronized labels plus this manager token could allow cleaner what-if studies on coordination policies, like changing manager capacity or timing windows. What works is the clear framing of the problem around temporal feasibility, timeouts, and timelocks induced by constraints. It positions PTPNs as relevant for synchronized timed systems in this domain. The soft spots are more significant. The abstract gives no model examples, no case study results, no comparison to real data, and no indication of how they handle or prove properties like deadlock or reachability in this setup. Without that, it's hard to know if the approach actually identifies the claimed configurations reliably. The stress-test point about missing continuous or stochastic flows is a real one; if supply chains have variable times or concurrent contentions not captured in the discrete transitions and single manager, the analysis could miss key conflicts. The paper would need to show that the synchronization semantics are sufficient or extended appropriately. This paper is for specialists in Petri net modeling and operations research who want to explore timed system analysis for logistics. A reader in that group might find the modeling choice useful as a starting point, but it would need the full details to be valuable. I think it deserves peer review because the core idea is coherent and the application has potential, even if the current presentation is high-level. A referee could push for the missing examples and checks.

Referee Report

2 major / 2 minor

Summary. The paper proposes a modular modeling approach for supply chains based on Product Time Petri Nets (PTPNs). Subsystems are modeled independently with global behavior emerging via synchronized transition labels. The supply chain manager is explicitly represented as a shared and mobile resource whose availability affects feasibility. The work analyzes how timing constraints and managerial capacity influence behavior, identifying configurations for successful executions, timeouts, or timelocks, and claims this enables systematic what-if analysis of coordination policies.

Significance. If the modeling and analysis claims hold with concrete validation, the work would provide a formal method for assessing temporal feasibility in distributed supply chains, which is valuable for systems with strict timing and resource limits. The explicit manager resource and modular PTPN composition offer a structured way to explore policy impacts, extending timed Petri net techniques to this application domain.

major comments (2)

[Abstract] Abstract: The central claims that the approach identifies configurations leading to successful executions, timeouts, or timelocks (and enables what-if analysis) are not supported by any concrete PTPN model instance, reachability results, example supply chain scenario, or formal property proof. Without these, the claims about determining system feasibility remain unevaluated.
[Abstract] Abstract: The assumption that global behavior (including feasibility and timelocks) emerges completely from independent PTPN subsystems plus label synchronization and a single shared manager resource is load-bearing but unproven. No argument or completeness result is given for why this captures all relevant interactions, such as variable transport times or concurrent resource contention not encoded in the synchronization.

minor comments (2)

[Abstract] The abstract mentions Colored Petri Nets as existing approaches but does not provide a clear contrast with PTPNs regarding timing semantics or modularity advantages.
[Abstract] Notation for PTPN elements (e.g., how timing constraints are attached to transitions or places) is not introduced in the abstract, which would aid readability for readers unfamiliar with the formalism.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. The feedback highlights the need for clearer support of our claims in the abstract and stronger justification of the modeling assumptions. We address each major comment below, indicating where revisions will be made to improve the paper.

read point-by-point responses

Referee: [Abstract] Abstract: The central claims that the approach identifies configurations leading to successful executions, timeouts, or timelocks (and enables what-if analysis) are not supported by any concrete PTPN model instance, reachability results, example supply chain scenario, or formal property proof. Without these, the claims about determining system feasibility remain unevaluated.

Authors: We agree that the abstract is high-level and does not explicitly reference concrete elements. The full manuscript does include concrete PTPN models of supply chain subsystems (manufacturing, assembly, and transport) with explicit timing intervals, a shared manager resource, and reachability analysis via state class graphs. Section 3 presents an example scenario with specific timing values that yields successful execution, timeout, and timelock cases, together with a proof that incompatible constraints induce timelocks. To address the concern, we will revise the abstract to briefly mention the example scenario and the key reachability outcomes. revision: yes
Referee: [Abstract] Abstract: The assumption that global behavior (including feasibility and timelocks) emerges completely from independent PTPN subsystems plus label synchronization and a single shared manager resource is load-bearing but unproven. No argument or completeness result is given for why this captures all relevant interactions, such as variable transport times or concurrent resource contention not encoded in the synchronization.

Authors: Label synchronization in the product construction is the standard mechanism that composes the independent nets while preserving all interactions encoded by the shared labels; this is well-established for Petri nets and directly yields the global state space used for our reachability analysis. The manager is represented as a single mobile token whose location and availability explicitly encode contention across subsystems. Variable transport times are modeled as time intervals on transitions within the transport PTPN, and concurrent contention is captured by the token's movement and the resulting enabling conditions. Section 2.3 provides an informal argument that these elements suffice for the temporal feasibility questions we address. We will add a short subsection clarifying the scope of interactions covered and noting that unmodeled aspects (e.g., stochastic routing) lie outside the current deterministic timed framework. revision: partial

Circularity Check

0 steps flagged

No circularity: standard modular PTPN composition with independent semantics

full rationale

The paper introduces a modeling framework based on Product Time Petri Nets for supply chains, representing subsystems independently and composing them via synchronized transition labels plus an explicit mobile manager resource. No load-bearing step reduces a claimed prediction, feasibility result, or global behavior to a fitted parameter, self-definition, or unverified self-citation chain. Timing constraints, timeouts, and timelocks are analyzed directly from the PTPN reachability semantics rather than being presupposed by the inputs. The what-if analysis capability follows from the modular construction without circular equivalence to the model definition itself.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The approach rests on standard Petri net theory for timing and product composition, with the manager introduced as a domain-specific modeling entity; no numerical parameters are fitted and no new axioms beyond established net semantics are stated.

axioms (1)

standard math Standard semantics of Time Petri Nets including firing intervals and product composition via synchronized transition labels.
Invoked implicitly when describing modular subsystems and global behavior emergence through labels.

invented entities (1)

Supply chain manager as shared and mobile resource no independent evidence
purpose: To explicitly capture how managerial availability and movement impact system feasibility, timeouts, and timelocks.
Presented as a key feature of the model but without independent evidence or falsifiable predictions outside the modeling framework.

pith-pipeline@v0.9.0 · 5504 in / 1383 out tokens · 73032 ms · 2026-05-10T19:47:14.459353+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

19 extracted references · 19 canonical work pages

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van der Aalst (1994): Modelling and analysing workflow using a Petri-net based approach

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Cambridge University Press, DOI 10.1142/S0218126698000043

Wil M.P. van der Aalst (1998): The Application of Petri Nets to Workflow Management. Journal of Circuits, Systems, and Computers 8, pp. 21–66, doi:10.1142/S0218126698000043. Lubat, Hladik, Mateu, Sauvère 39

work page doi:10.1142/s0218126698000043 1998
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work page doi:10.1007/978-3-540-85778-5_3 2005
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Modeling and V eriﬁcation of Time De pendent Systems Using Time Petri Nets

B. Berthomieu & M. Diaz (1991): Modeling and Verification of Time Dependent Systems Using Time Petri Nets. IEEE Trans. on Software Engineering 17(3), doi:10.1109/32.75415

work page doi:10.1109/32.75415 1991
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Berthomieu & M

B. Berthomieu & M. Menasche (1983): An enumerative approach for analyzing time Petri nets. In: Proceed- ings IFIP

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Berthomieu, F

B. Berthomieu, F. Peres & F. Vernadat (2006): Bridging the Gap Between Timed Automata and Bounded Time Petri Nets. In: Formal Modeling and Analysis of Timed Systems (FORMATS), LNCS 4202, Springer, doi:10.1007/11867340_7

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Bernard Berthomieu, P.-O Ribet & Francois Vernadat (2004): The tool TINA – Construction of Abstract State Spaces for Petri Nets and Time Petri Nets . International Journal of Production Research 42(14), doi:10.1080/00207540412331312688

work page doi:10.1080/00207540412331312688 2004
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Structural translation from Time Petr i Nets to Timed Automata

Franck Cassez & Olivier H Roux (2006): Structural translation from time Petri nets to timed automata . Journal of Systems and Software 79(10), doi:10.1016/j.jss.2005.12.021

work page doi:10.1016/j.jss.2005.12.021 2006
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Rong Liu, Akhil Kumar & Wil van der Aalst (2007): A formal modeling approach for supply chain event management. Decision Support Systems 43(3), pp. 761–778, doi:10.1016/j.dss.2006.12.009. Available at https://www.sciencedirect.com/science/article/pii/S0167923606002144

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Eric Lubat (2021): Synchronous Product of Time Petri Nets and its Applications to Fault-Diagnosis. Theses, INSA de Toulouse. Available at https://laas.hal.science/tel-03528121

work page 2021
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Éric Lubat, Silvano Dal Zilio, Didier Le Botlan, Yannick Pencolé & Audine Subias (2019): A State Class Construction for Computing the Intersection of Time Petri Nets Languages. In: Formal Modeling and Anal- ysis of Timed Systems (FORMATS), LNCS 11750, Springer, doi:10.1007/978-3-030-29662-9_5

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Belgacem, J.-L

Éric Lubat, Silvano Dal Zilio, Didier Le Botlan, Yannick Pencolé & Audine Subias (2020): A New Product Construction for the Diagnosability of Patterns in Time Petri Net . In: 59th Conference on Decision and Control (CDC) 2020, Jeju Island (virtual conference), South Korea, doi:10.1109/CDC42340.2020.9303826. Available at https://laas.hal.science/hal-02989834

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D. G. Malcolm, J. H. Roseboom, C. E. Clark & W. Fazar (1959): Application of a technique for research and development program evaluation. Operations Research 7(5), pp. 646–669, doi:10.1287/opre.7.5.646

work page doi:10.1287/opre.7.5.646 1959
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International Journal of Production Research50(16), pp

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work page doi:10.1080/00207543.2011.639397 2012
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Philip Merlin (1974): A study of the recoverability of computer systems . Ph. D. Thesis, Computer Science Dept., University of California

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Peres, B

F. Peres, B. Berthomieu & F. Vernadat (2011): On the Composition of Time Petri Nets . Discrete Event Dynamic Systems 21(3), doi:10.1007/s10626-011-0102-2

work page doi:10.1007/s10626-011-0102-2 2011
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Ramalingam, J

G. Ramalingam, J. Song, L. Joscovicz & R. E. Miller (1995): Solving Difference Constraints Incrementally. Algorithmica 23, doi:10.1007/PL00009261

work page doi:10.1007/pl00009261 1995
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In: IEEM 2009 - IEEE International Conference on Industrial Engineering and Engineering Management, doi:10.1109/IEEM.2009.5373050

Xiaoling Zhang, Qiang Lu & Teresa Wu (2009): Petri-net based application for supply chain management: An overview. In: IEEM 2009 - IEEE International Conference on Industrial Engineering and Engineering Management, doi:10.1109/IEEM.2009.5373050

work page doi:10.1109/ieem.2009.5373050 2009

[1] [1]

van der Aalst (1994): Modelling and analysing workflow using a Petri-net based approach

Wil M.P. van der Aalst (1994): Modelling and analysing workflow using a Petri-net based approach. Avail- able at https://api.semanticscholar.org/CorpusID:376304

work page 1994

[2] [2]

Cambridge University Press, DOI 10.1142/S0218126698000043

Wil M.P. van der Aalst (1998): The Application of Petri Nets to Workflow Management. Journal of Circuits, Systems, and Computers 8, pp. 21–66, doi:10.1142/S0218126698000043. Lubat, Hladik, Mateu, Sauvère 39

work page doi:10.1142/s0218126698000043 1998

[3] [3]

PAT: Towards Flexible Veriﬁcation un- der Fairness

Béatrice Bérard, Franck Cassez, Serge Haddad, Didier Lime & Olivier H Roux (2005): Comparison of the expressiveness of timed automata and time Petri nets. In: Formal Modeling and Analysis of Timed Systems (FORMATS), LNCS 3829, Springer, doi:10.1007/978-3-540-85778-5_3

work page doi:10.1007/978-3-540-85778-5_3 2005

[4] [4]

Modeling and V eriﬁcation of Time De pendent Systems Using Time Petri Nets

B. Berthomieu & M. Diaz (1991): Modeling and Verification of Time Dependent Systems Using Time Petri Nets. IEEE Trans. on Software Engineering 17(3), doi:10.1109/32.75415

work page doi:10.1109/32.75415 1991

[5] [5]

Berthomieu & M

B. Berthomieu & M. Menasche (1983): An enumerative approach for analyzing time Petri nets. In: Proceed- ings IFIP

work page 1983

[6] [6]

Berthomieu, F

B. Berthomieu, F. Peres & F. Vernadat (2006): Bridging the Gap Between Timed Automata and Bounded Time Petri Nets. In: Formal Modeling and Analysis of Timed Systems (FORMATS), LNCS 4202, Springer, doi:10.1007/11867340_7

work page doi:10.1007/11867340_7 2006

[7] [7]

In: Proc

B. Berthomieu, F. Peres & F. Vernadat (2007): Model Checking Bounded Prioritized Time Petri Nets . In: 5th Int. Symp. on Automated Technology for Verification and Analysis , LNCS, Springer, doi:10.1007/978- 3-540-75596-8_37

work page doi:10.1007/978- 2007

[8] [8]

International Journal of Production Research 42(14), doi:10.1080/00207540412331312688

Bernard Berthomieu, P.-O Ribet & Francois Vernadat (2004): The tool TINA – Construction of Abstract State Spaces for Petri Nets and Time Petri Nets . International Journal of Production Research 42(14), doi:10.1080/00207540412331312688

work page doi:10.1080/00207540412331312688 2004

[9] [9]

Structural translation from Time Petr i Nets to Timed Automata

Franck Cassez & Olivier H Roux (2006): Structural translation from time Petri nets to timed automata . Journal of Systems and Software 79(10), doi:10.1016/j.jss.2005.12.021

work page doi:10.1016/j.jss.2005.12.021 2006

[10] [10]

Decision Support Systems 43(3), pp

Rong Liu, Akhil Kumar & Wil van der Aalst (2007): A formal modeling approach for supply chain event management. Decision Support Systems 43(3), pp. 761–778, doi:10.1016/j.dss.2006.12.009. Available at https://www.sciencedirect.com/science/article/pii/S0167923606002144

work page doi:10.1016/j.dss.2006.12.009 2007

[11] [11]

Theses, INSA de Toulouse

Eric Lubat (2021): Synchronous Product of Time Petri Nets and its Applications to Fault-Diagnosis. Theses, INSA de Toulouse. Available at https://laas.hal.science/tel-03528121

work page 2021

[12] [12]

In: Formal Modeling and Anal- ysis of Timed Systems (FORMATS), LNCS 11750, Springer, doi:10.1007/978-3-030-29662-9_5

Éric Lubat, Silvano Dal Zilio, Didier Le Botlan, Yannick Pencolé & Audine Subias (2019): A State Class Construction for Computing the Intersection of Time Petri Nets Languages. In: Formal Modeling and Anal- ysis of Timed Systems (FORMATS), LNCS 11750, Springer, doi:10.1007/978-3-030-29662-9_5

work page doi:10.1007/978-3-030-29662-9_5 2019

[13] [13]

Belgacem, J.-L

Éric Lubat, Silvano Dal Zilio, Didier Le Botlan, Yannick Pencolé & Audine Subias (2020): A New Product Construction for the Diagnosability of Patterns in Time Petri Net . In: 59th Conference on Decision and Control (CDC) 2020, Jeju Island (virtual conference), South Korea, doi:10.1109/CDC42340.2020.9303826. Available at https://laas.hal.science/hal-02989834

work page doi:10.1109/cdc42340.2020.9303826 2020

[14] [14]

D. G. Malcolm, J. H. Roseboom, C. E. Clark & W. Fazar (1959): Application of a technique for research and development program evaluation. Operations Research 7(5), pp. 646–669, doi:10.1287/opre.7.5.646

work page doi:10.1287/opre.7.5.646 1959

[15] [15]

International Journal of Production Research50(16), pp

Giovanni Mazzuto, Maurizio Bevilacqua & Filippo Emanuele Ciarapica (2012): Supply chain modelling and managing, using timed coloured Petri nets: a case study. International Journal of Production Research50(16), pp. 4718–4733, doi:10.1080/00207543.2011.639397. arXiv:https://doi.org/10.1080/00207543.2011.639397

work page doi:10.1080/00207543.2011.639397 2012

[16] [16]

Philip Merlin (1974): A study of the recoverability of computer systems . Ph. D. Thesis, Computer Science Dept., University of California

work page 1974

[17] [17]

Peres, B

F. Peres, B. Berthomieu & F. Vernadat (2011): On the Composition of Time Petri Nets . Discrete Event Dynamic Systems 21(3), doi:10.1007/s10626-011-0102-2

work page doi:10.1007/s10626-011-0102-2 2011

[18] [18]

Ramalingam, J

G. Ramalingam, J. Song, L. Joscovicz & R. E. Miller (1995): Solving Difference Constraints Incrementally. Algorithmica 23, doi:10.1007/PL00009261

work page doi:10.1007/pl00009261 1995

[19] [19]

In: IEEM 2009 - IEEE International Conference on Industrial Engineering and Engineering Management, doi:10.1109/IEEM.2009.5373050

Xiaoling Zhang, Qiang Lu & Teresa Wu (2009): Petri-net based application for supply chain management: An overview. In: IEEM 2009 - IEEE International Conference on Industrial Engineering and Engineering Management, doi:10.1109/IEEM.2009.5373050

work page doi:10.1109/ieem.2009.5373050 2009