极大-加混合线性不等式系统的可解性及其应用

Solvability and Its Application for Max-Plus Mixed Linear Inequality Systems

研究极大-加混合线性不等式系统的可解性.基于极大-加线性方程系统可解的特征以及极大-加混合线性不等式系统的最大解,给出极大-加混合线性不等式系统可解的一个充分必要条件,还给出极大-加混合线性不等式系统在部分变量非负的约束条件下可解的一个充分必要条件.同时,例举一个制造系统加工工件时序规划的应用例子.

This paper investigates the solvability of max-plus mixed linear inequality systems. By applying the characteristic for the solvability of max-plus linear equation systems and the maximum solution of max-plus mixed linear inequality systems, we present a necessary and sufficient condition for the solvability of max-plus mixed linear inequality systems. We also present a necessary and sufficient condition for the solvability of max-plus mixed linear inequality systems with the constraint condition of some variables to be nonnegative. At the same time, we give an application example for timing programming in manufacturing systems.