Abstract: In resource-constrained project scheduling problem， renewable resource can be expanded into human resources with competency differences, a flexible resource-constrained project scheduling problem with competency difference is proposed, which is a practical extension close to Research and Development program, or R&D program, from traditional multi-mode resource-constrained project scheduling problem. A parameter and estimation formula to measure personnel competency is presented, a mix-integer programming model is established for the problem. The single objective optimization problem of optimal duration and optimal cost is solved in the order of bi-objective importance. To solve the model, according to the constraint conditions of the model, the multi-project initial network diagram is transformed into several single-project initial network diagrams, enumeration algorithm satisfying constraint conditions provides the feasible solution sets, and the algorithm based on dynamic programming is designed for phased optimization. Experimental results show that the proposed optimization model considering competence differences can solve the problem effectively.

Key words: competence, R&D program, project scheduling, dynamic programming

摘要： 在资源受限项目调度问题中，将可更新资源进一步拓展为具有胜任力差异的人力资源，建立考虑胜任力差异的人力资源受限项目调度问题模型，该模型是对传统多模式资源约束项目调度问题（MRCPSP）更接近研发项目群实际的扩展。提出了衡量人员胜任力的参数及估算公式，以多项目总工期和总成本最小化为双目标，建立相应的数学优化模型。按双目标重要性排序，依次对工期最优及成本最优的单目标优化问题求解。根据模型的约束条件将多项目初始网络图转化为几种单项目初始网络图，利用枚举算法给出满足约束条件的可行解集，再设计基于动态规划思想的算法进行分阶段寻优。数值实验表明，考虑了胜任力差异的数学优化模型在求解质量方面具有良好性能。

关键词: 胜任力, 研发项目群, 项目调度, 动态规划