Petri Net Model

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1. Introduction Benita (1999) defines a supply chain as an integrated process wherein raw materials are converted into final products, then delivered to customers (via distribution, retail, or both). At the highest level, a supply chain comprises two basic, integrated processes: (1) the production planning and inventory control process; and (2) the distribution and logistics process (Beamon 1998). In general, supply chain networks are discrete event dynamic systems (DEDS). The evolution of the system depends on the complicated interaction of a number of events, for example, the components’ arrival at the suppliers, the departure of the truck from the supplier, the beginning of an assembly at the manufacturer, the arrival of the finished goods at the customer, the payment approved by the seller, just to name a few. Characterised as being concurrent, asynchronous, distributed, parallel, nondeterministic, and/or stochastic, a supply chain is difficult to model and analyse. Existing literature on supply chain modelling can be classified into three categories: mathematical modelling, simulation based modelling, and network-based modelling

*Corresponding author. Email: xiaoling.zhang1221@gmail.com
ISSN 0020–7543 print/ISSN 1366–588X online ß 2011 Taylor & Francis DOI: 10.1080/00207543.2010.492800 http://www.informaworld.com

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(Kim et al. 2004). Mathematical models include linear programming (Shapiro 2001), integer/mixed-integer programming (Vidal and Goetsehalckx 1997), non-linear programming (Cohen and Lee 1989), and stochastic programming (Santoso et al. 2005). The challenges with mathematical modelling lie in the scale and complexity of the problems. The size and the complexity of a supply chain problem introduces a large number of variables and constraints to the mathematical model which is inordinately difficult to maintain and faces tremendous computational burden (Wu and O’Grady 2004). In addition, convergences of the mathematical model, especially, non-linear programming models, have long been recognised as a critical issue. Thus, research on exploring the applicability of simulation to SCM attracts great attention. Kleijnen and Smits (2003) provide a comprehensive survey of different simulation applications in SCM, e.g., spreadsheet simulation, system dynamics, discrete event simulation (DES) and business games. Jain et al. (2001) conduct a simulation study on large scale logistics operations in a supply network and conclude that simulation helps improve the forecast accuracy which leads to significant cost savings. Two commonly used simulation tools are Monte-Carlo simulation (MCS) and DES. While MCS can be easily implemented in a spreadsheet for high-level models to gain preliminary results, DES is capable of handling more details and has proven valuable as a practical tool for representing complex interdependencies and analysing performance trade-offs for SCM (Lendermann et al. 2003). Concluded by Chang and Makatsoris (2001), the advantages of supply chain simulation using DES are as follows: (1) it helps to understand the overall supply chain processes and characteristics by graphics/ animation; (2) it is able to capture system dynamics; and (3) it could dramatically minimise the risk of changes in planning process. While promising, DES requires much domain knowledge to develop the detailed models. In addition, simulation results may diverge from the real outcomes when disruption occurs which will require extensive efforts in calibrating the simulation. Another emerging supply chain modelling tool is the Petri net which has a well-defined mathematical foundation and an easy-tounderstand graphical feature. Based on a strong mathematical formalism, Petri nets can set up mathematical models to describe the behaviour of the system (Petri 1962, Murata 1989). The graphical nature makes it a self-documenting and powerful design tool to facilitate visual communication between the people who...
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