Equivalent and Efficient Optimization Models for an Industrial Discrete Event System with Alternative Structural Configurations

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.

Petri Net Models Optimized for Simulation

“…This section provides a sequence of steps to transform the formalism in which a model is represented, from a compound Petri net to a set of alternative Petri nets [21]. The application of this algorithm may allow the modeler to profit from the advantages of both formalisms in different stages of the process in which he or she is involved (e.g., a decision-making problem).…”

A Minimum Capacity Optimization Scheme for Airport Terminals During Peak Periods

“…The experimental results show that the gate capacities are optimized by using genetic algorithms. The authors of [21] establish a multiflight multi-service parallel timing optimization model based on genetic algorithms. The model can ensure the normal operations of flights, realize the coordinated task scheduling scheme among various businesses, and optimize the capacities of airport terminals.…”