Petri Net Model

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

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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