Scheduling of complex manufacturing systems with Petri nets and genetic algorithms: a case on plastic injection moulds

This paper introduces significant improvements on a previous published work that addresses complex production scheduling problems using Petri nets (PNs) and genetic algorithms (GAs). The PN model allows a formal representation of the manufacturing system and of the special constraints of this kind of system, while the GA generates a near-optimal schedule through the structure provided by the PN. The corresponding manufacturing system is associated with a flexible job shop environment with features such as the fabrication of multiple parts and precedence relationships between such parts and assembly operations, in which the objective is the minimisation of the total weighted tardiness. As part of the modelling stage, a mixed integer linear programming formulation is proposed for this framework. The fabrication of a chess mould in a Colombian company is used in two ways: to introduce a proposed normalisation operator that improves the results by reducing the search space of the GA and to illustrate the use of PN modelling the special aforementioned constraints as well as the encoding of the chromosome used by the GA. The proposed approach was tested on randomly generated instances, and their performance was measure against optimal solutions or solutions provided by algorithms presented in previous work. The results confirm the relevance of this approach to schedule such complex manufacturing systems.