Business and Environment Performance Evaluation in Supply Chains: A Formal Model-Driven Approach

While economic and service level indicators were adequate to show the performance of supply chains (SCs) in the past, nowadays, environment indicators are gradually becoming more relevant (Beamon, 1999). Many prominent companies and academic research groups around the world are making efforts to provide environmentally responsible products and services. These topics are subjects of intensive study not only due to the respective impact of the production and transport systems in our planet but also particularly related to the image these companies aim to project to the society (Beamon, 1999; Srivastava, 2007). Moreover, supply chains’ managers must carry about optimizing an endless number of variables that might impact costs and operational performance. These variables usually get in conflict between themselves. For instance, increasing the amount of stored goods might reduce the lead time to customers, but also increase storage costs and environment impacting resources like energy. Modelling is quite often employed for quantitative analysis of SCs (Simchi-Levi et al., 2000). One of themain advantages in usemodelling techniques is the possibility of analyse “what-if” questions. Thereby, it is possible to evaluate different scenarios looking for themost optimized ones. Although the strict mathematical modelling is one of the most used approaches in the evaluation of SCs (Cohen & Lee, 1988; Sabri & Beamon, 2000; Simchi-Levi et al., 2005), it is not always the best option. Such a method requires some simplifications that might incur inaccurate results. Othermodelling techniques, like queueing networks (Gross, 2009), Markov Chains (Norris, 1998), and Petri Nets (Bolch et al., 2006; Desrochers & Al-Jaar, 1994; Jensen, 1997), might be adopted so as to overcome this problem. Petri nets were proposed by Carl Adam Petri in 1962 (Petri, 1962), and have evolved into a formalism employed in different areas such as informatics, electronics and chemistry since then. This modelling technique has a graphical representation that supports the specification and design of systems. Having a solid mathematical foundation, Petri nets are very well suited for the numerical evaluation of complex systems. Different extensions were proposed to this formalism, including the concept of time (Ramchandani, 1994) after Carl Petri’s initial work. Petri nets have been already adopted for evaluating manufacturing systems and SCs (Alves et al., 2010; Desrochers & Al-Jaar, 1994;Makajic-Nikolic et al., 2004; Silva & Maciel, 2005; Viswanadham & Raghavan, 2000). Stochastic Petri nets (SPNs) (Bolch et al., 2006; German, 1994; Haas, 2002; Marsan et al., 1995) deals with probabilistic distributed times, which are approximated to distribution functions like exponential, Erlang and uniform. Business and Environment Performance Evaluation in Supply Chains: A Formal Model-Driven Approach