On the solution of optimization problems with disjunctive constraints based on Petri Nets

Manufacturing facilities, chain supplies and other systems of technological interest can be usually described as discrete event systems. The Petri nets are a modeling paradigm able to cope with complex behaviour of DES. The design of this kind of systems and their efficient operation usually lead to the statement of optimization problems with disjunctive constraints. Those constraints are given by the Petri net models with variables that represent the freedom degrees of the designer or the process engineer that defines the working parameters of a production line. Disjunctive constraints are difficult to handle in optimization problems. In this paper an analysis of the disjunctive constraints is performed and an overview of four different representations for this type of constraint is developed: a set of alternatives Petri nets, a compound PN, an alternatives aggregation PN (AAPN) and a coloured Petri net (CPN). The advantages and drawbacks of every one of these representations as well as some examples of transformation algorithms are given.