中文摘要：

极大－极小－加系统规划的全局优化可用于通信网络、柔性制造、对策博弈等实际系统，而幂等半环上线性方程理论在极大－极小－加系统规划的全局优化的研究中起着关键的作用。对于一类幂等半环上的非齐次线性方程组，引入列满秩矩阵与控制向量概念，并分别给出解的存在性和惟一性充分必要条件以及求解方法．

英文摘要：

The global optimization of programming of max-min-plus systems can be used for communication networks, manufacturing plants, operations research, etc. The theory of systems of linear eqdations over idempotent semiring plays a key role in research for the global optimization of programming of max-min-plus systems. For a class of systems of nonhomogeneous linear equations over idempotent semiring, this paper introduces the column full rank matrix and control vector, and presents the necessary and sufficient conditions of existence and uniqueness of the solution, respectively, and the method of solving.