基于极大极小代数法的Job-Shop生产线的建模方法

The Modeling for Job-Shop on Maxim and Minimum Algebra

以极大代数法为基础开发一种新的代数模型以解决并行多生产线的 Job-Shop 建模和仿真问题。根据机床对工件加工条件准则和加工过程路径规则引入工艺路线矩阵、加工顺序矩阵以控制设备-零件的状态向量的递推过程,从而建立起状态向量的递推方程;重新定义极大代数法的乘法和加法规则,以满足上述两个准则,规定零元的运算规律,形成线性矩阵形式的状态矩阵的递推公式;通过计算实例说明加工顺序矩阵的控制作用和算法的先进性。本模型和方法可以作为 DEDS 领域Job-Shop 的描述和优化调度的新平台。

A new algebra model with (max,+) algebra mothed as foundation has been developed to solve the modeling and simulation problems of parallel multi-production line of the Job-Shop. According to the technologic route rules and process condition rule between machine tools and workpieces, a technology route matrix and a process order matrix are led into to control the recurrence course of state vector of equipment - workpieces, so, the recurrence of state vector equation is established; The multiplication and addition rule of (max,+) algebra are redefined to satisfy two above-mentioned rules, and definition of zero element is formulated, so the recurrence formula of the state matrix of linear matrix form is deduced; Act on through a computational example the function of the process order matrix and the advantages of the algorithm are demonstrated. This model and method can be the new platform in DEDS field and Job-Shop description and optimum scheduling.