Modeling and Optimization of Integrated of JIT Flexible Manufacturing, Assembly and Disassembly by Petri Nets

Abstract

New generic black token timed Petri (PN) model for the design of a flexible manufacturing (FMS), assembly (FAS) and disassembly (DAS)system with dual kanban is developed. The analysis and performance evaluation of the model are based on invariant analysis. The performance is optimized using a mixed integer programming model. To compute P-invariant the incidence matrix is required as input data. To identify all invariants of the complex system, this research propose new algorithms for the computation of the invariants which cannot be determined from existing methods such as Fourier-Motzkin method and INA software. A new method to cut the incidence matrix into smaller sub-matrices and refine its sub-incidence matrices for computing PN invariants faster is introduced as well. Also, the main problem when applying PN to real cases is how to divide a large problem into smaller ones that can be solved in a reasonable computation time on a computer with reasonable memory storage capacity. For that reason, new algorithms for computing all invariants of our generic model of an FMS/FAS/DAS PN are proposed. This research categorizes the physical interpretation of the Petri net model and identifies an approach to compute all invariants in each category. The new PN model and solution are illustrated by a case study in a car assembly plant.