中文摘要：

采用极大代数方法研究混杂时间事件图（HTEG）的最小初始标志问题．通过构造新型的双子代数系统，给出了HTEG的线性极大代数模型，并基于该模型诱导出偏序关系．利用这个极大代数系统及其偏序关系的单调性、可逆性等性质，提出了一种HTEG最小初始标志的计算方法．HTEG的标志往往表示系统资源，提出的最小初始标志计算方法是一种最小资源分配算法，适用于制造系统、计算机网络等人造系统．最后用一个简单的实例说明了该方法的正确性．

英文摘要：

A max-plus algebraic approach was put forward to study the minimum initial marking （MIM） problem of hybrid timed event graph （HTEG）. Through constructing a novel dioid, a linear max-plus algebraic model was derived for HTEG, then a partial order was deduced based on the model. The properties of the max-plus algebra and the partial order, including monotone, invertibility and so on, were used to develop the computing approach to the MIM problem. The marking of HTEG usually represents the system resource. The proposed approach to the MIM problem is one of the minimum resource allocation problems, and is applicable to manufacturing systems, computer network and so on. The illustrative example showed the correctness of the max-plus algebraic approach.