关键词: 项目组合, 项目组合选择, 紧前关系, 紧前项目所需完成数量, 可打断情境

Abstract: In the context of economic globalization, the business and financing fields of enterprises are expanding. In order to enhance the competitiveness of enterprises and achieve long-term development, selective implementation of several projects has become an effective competition mechanism. Therefore, on the premise of meeting various constraints, it is very important to select the project portfolio that can make the enterprise obtain the maximum benefit from many alternative projects. This kind of problem is called project portfolio selection problem.
In the field of project portfolio selection, because many projects are involved, the precedence relationship between projects has attracted the attention of relevant scholars. However, in the existing research, the precedence relationship strictly requires that the project should be implemented only after the predecessor project is completed, but ignores the fact that the follow-up project can be implemented after part of the predecessor project is completed. In addition, in the field of portfolio selection, when there are multiple predecessor projects, in addition to the existing two predecessor project completion quantity constraints, there will also be cases where only a certain number of predecessor projects need to be completed. Therefore, it is necessary to consider this situation in the field of project portfolio selection to realize more scientific and reasonable decision-making.
In view of the above problems, this paper makes further research on the basis of the existing precedence relationship constraints. Firstly, this paper perfects the constraints of precedence relationship, and considers that the completion of a certain number of predecessor projects can complete subsequent projects. Secondly, based on the aforementioned constraints, a new project portfolio selection model is developed. Finally, on the basis of both data from existing literature and simulation results, the model is solved by the optimization solver CPLEX. Further, the sensitivity analysis of the parameters involved in the constraints is carried out, and the relevant conclusions are drawn. The specific contents are mainly divided into the following three parts.
The first part introduces the sets, parameters and variables required in the modeling process, so as to prepare for the subsequent modeling process. This step is essential as it establishes a clear framework, ensuring that the subsequent modeling steps can be executed systematically and efficiently.
The second part focuses on depicting the perfect precedence relationship constraints, and the fact that after a certain number of predecessor project complete, follow-up projects can proceed. On this basis, combined with the constraints in the traditional portfolio selection problem, the portfolio selection problem affected by precedence relationship in the interruptible situation is established.
In the third part, an example is given to verify the effectiveness and practicability of the MCPRD model proposed in this paper. Firstly, the PPSP-1 model of “all predecessor projects must be 100% completed”, and the PPSP-2 model of “all predecessor project precedence relationship parameters and the number of predecessor projects must be completed” are proposed, and based on data from existing literature and simulation results, and the optimization solver CPLEX, the results of comparison between different models verify the practicability and effectiveness of this model through different scale examples.
To sum up, this paper supplements and improves the existing precedence relationship constraints in the field of portfolio selection, and constructs a portfolio selection model affected by precedence relationship in interruptible situations. The results show that: 1)considering the fact that “a certain proportion of predecessor projects can be completed to implement follow-up projects” and “when a certain number of predecessor projects are completed, follow-up projects can proceed” in the problem of project portfolio selection, the resulting decision-making scheme will be due to the traditional model. 2)Before formulating the implementation plan, enterprise decision-makers should carefully dig out the precedence relationship between projects. When there are multiple predecessor projects, we should also pay attention to the coincidence between multiple predecessor projects, so as to avoid the strict sequence of front and rear implementation, which makes high-yield projects unable to be implemented and affects the income of the enterprise. 3) The impact of changes in the number of predecessor projects to be completed on income is much higher than that of the precedence relationship parameters. Decision makers should reasonably arrange resources, reduce the required number of precedence projects as far as possible, and improve the income of project portfolio selection.
There are still several issues that require further exploration in this paper. For instance, the risk of losses resulting from initiating follow-up projects after only a certain percentage of predecessor projects are completed has not been fully addressed, and risk transfer mechanism between projects under the precedence relationship has not been fully explored. These things will be key focuses for our research group’s future work. In addition, we are indebted to the North China Electric Power University Library for providing detailed reference for our research, which has greatly facilitated our study and enriched the depth of our analysis.

Key words: project portfolio, portfolio decision, precedence relationship, predecessor projects number, divisibility