Abstract
Discrete event systems in applications, such as industry and supply chain, may show a very complex behavior. For this reason, their design and operation may be carried out by the application of optimization techniques for decision making in order to obtain their highest performance. In a general approach, it is possible to implement these optimization techniques by means of the simulation of a Petri net model, which may require an intensive use of computational resources. One key factor in the computational cost of simulation-based optimization is the size of the model of the system; hence, it may be useful to apply techniques to reduce it. This paper analyzes the relationship between two Petri net formalisms, currently used in the design of discrete event systems, where it is usual to count on a set of alternative structural configurations. These formalisms are a particular type of parametric Petri nets, called compound Petri nets, and a set of alternative Petri nets. The development of equivalent models under these formalisms and the formal proof of this equivalence are the main topics of the paper. The basis for this formal approach is the graph of reachable markings, a powerful tool able to represent the behavior of a discrete event system and, hence, to show the equivalence between two different Petri net models. One immediate application of this equivalence is the substitution of a large model of a system by a more compact one, whose simulation may be less demanding in the use of computational resources.
Highlights
A significant number of systems of technological, social, or financial interest may present a high degree of complexity in their composition, in the interrelation among their components, in their behavior, or in all of these features [1, 2]
Many of these systems can be considered as discrete event systems (DES) [3, 4], such as manufacturing facilities, food industry, supply chains, airports, or traffic networks [5,6,7,8]
The present paper has focused on two formalisms, based on the Petri net paradigm, commonly used for describing discrete event systems with alternative structural configurations
Summary
A significant number of systems of technological, social, or financial interest may present a high degree of complexity in their composition, in the interrelation among their components, in their behavior, or in all of these features [1, 2]. The formalisms presented in this paper, belonging to the paradigm of the Petri nets, are suited for developing optimization processes They are appropriate for other strategies of decision making [17]. The references presenting Petri net models of discrete event systems with structural degrees of freedom usually fall under one of the two following approaches:. Giving diverse feasible values to these parameters, it is possible to specify different alternative structural configurations of the DES These Petri nets can be called parametric, parameterized, parameterized, or compound Petri nets [6].
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