A Petrinet model of a short life cycle product supply chain and deduction of its reachability matrix by simulation

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A Petrinet model of a short life cycle product supply chain and deduction of its reachability matrix by simulation

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Abstract

This paper focuses on the concept of short life cycle supply chain of products where the selling time of the product is short and fixed. Based on an object events table and dynamical events occurring table a composite model of short life cycle product is created. This model is then represented by using a petrinet which is a bipartite graph consisting of two nodes called places and transitions and a transition is connected to a place by means of an arc and vice versa. In modeling transition represents events and places represents conditions. This petrinet model can represent and analyze the dynamic behavior of the system. The model is simulated by using petrinet tool box version 2.1 embedded in mat lab and the coverability tree of the proposed model is generated. T he tree shows all possible markings deducible from the initial marking and helps to analyze the behavioral properties such as reachability. Reachability matrix is deduced from the simulation and it helps to identify P invariants and T invariants in the model

Key Words: Supply chain, Composite model, short life cycle product, Petrinet, Coverability tree,
Reachabilty.

Abstract
Introduction
1. Petri nets
Problems of supply chain modelling
Composite modelling for short life cycle products supply chain
1. The object model
2. The objects events table
3. Design of dynamic model
Simulation
Reachability matrix
Results and conclusion
References

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[...] Supplying System P1 receive Order forms P2 Send Materials Producing System P3 Order forms P4 Receive Materials P5 Send Product P6 send order forms P7 buyback old product Distributing Short Life Cycle Product Supply Chain System P8 Collect Products P9 distribute Products P10 receive order forms P11 send order forms Retailing System P12 send order forms P13 received product P14 sale products P15 old product Processing Customer System p16 buy products Fig The objects events table. Relationship is a setup among subsystems by message transferring This table shows the events connecting various sub systems. [...]

[...] The above terms represents the various transitions of the model Based on the above table a Petri net model is created at system level and its simulated to determine incidence matrix and coverability tree which is the tree representation of the various markings. P9 P13 P14 P7 T6 T7 T5 T8 P15 P12 P10 P16 T9 P5 P8 P3 T2 T3 T1 P4 P11 T4 P6 P1 P2 Fig 2. Dynamical Model of System level SIMULATION The simulation was done using Petri net toolbox, which is a software tool for simulation, analysis and design of discrete event system based on Petri nets models It is embedded in mat lab environment. [...]

[...] Optimal pricing and returns policies for perishable commodities. Marketing Science 166- Lee C H. “Coordinated stocking, clearance sales, and return policies for a supply chain”, European Journal of Operational Research,2001 Derrien R. Jansen, Arjen van Weert, Adrie J.M. Beulens, Ruud B.M. Huirne. “Simulation model of multi-compartment distribution in the catering supply chain”. European Journal of Operational Research 1337 (2001) 210-224. Supply Chain Management in Food Chains: Improving Performance by Reducing Uncertainty,” Int Trans Opl Res, 1998; 487~499. Haoxun Chen, Lionel Amodeo, Feng Chu, and [...]

[...] From the reachability matrix we can infer that there are no P invariants or T invariants for the proposed model 6 Results and Conclusion Using composite modelling technique a dynamic model of system level is developed by virtue of Petri nets. This model facilitates the concept of reprocessing the idle products. The model is simulated in mat lab environment by using petrinet toolbox version 2.1 .The coverability tree of the proposed model is then generated by simulation. The tree gives a picture of all possible states reachable from initial state or marking namely M0. [...]

[...] The consumption is more and more characteristic Functional product and creative product blend mutually.[10] Most analyses the returning goods problem of short life cycle product Lee investigated that product that has not been sold at the end of the season may be either returned to the manufacturer or processed at the discount shop.[2] Most investigated impact of supply chain management on logistical performance indicators in food supply chains 1.1 Petri nets A Petri net is a directed weighted bipartite graph consisting of two nodes called places and transitions. [...]

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