On algebraic and graph structural properties of assembly Petri net - Searching by linear programming

Abstract

An assembly planning method using Petri nets is presented. First, the assembly network is modeled using the conventional AND/OR net. Second, the state shift equation of the Petri net, which is its mathematical model, is analyzed. This analysis shows that the basis solution the of a state shift matrix is identical to the set of a solution which corresponds to an actual assembly sequence. This means that in considering an optimization problem which minimizes a summation of a weight value of all tasks included in the assembly sequence, a linear programming technique can be used. Some numerical examples are given to certify the validity of the analysis.