Abstract: To solve correctness verifications of models, optimization of resource configurations and choices of activity instances in workflow systems, an algorithm with establishing equations was proposed. The equation was constructed in this algorithm to describe the constrains such as activity structure, resource configuration and time allocation. Objective function was established to describe the optimal objectives of workflow systems, and the optimal formula of resource configurations could be obtained. At the same time, equivalence relations were built to divide activity set of workflow process. Based on the partitions and objective functions, the optimal scheme of choices of activity instances was obtained. Thus the correctness and integrity of whole process was ensured, and the optimization of workflow process's structure and performance was realized.

Key words: equations, workflow, optimization, modeling analysis

摘要： 为解决工作流中的模型正确性验证、资源分配、活动实例选择等相关问题，提出一种采用建立方程组的求解算法。该算法通过建立方程组描述工作流中的活动结构、资源分配、时间限制等约束条件，建立目标函数用于描述流程的最优目标，求解方程组得到资源分配的最优方案。通过建立等价关系对流程中的活动集合进行划分，再根据约束方程和目标函数求解得出流程的路径选择最佳方案。该算法确保了整个流程的正确性和完整性，实现了流程结构上和性能上的优化。

关键词: 方程组, 工作流, 优化, 建模分析