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

摘要： 在项目组合选择领域,已有研究中严格要求项目在紧前项目完成后才可执行。但在实际生产中,紧前项目完成部分即可执行后续项目的情形普遍存在。考虑到项目组合选择问题中忽略了上述现象,本文首次将其引入项目组合选择中对已有紧前关系进行完善。此外,由于存在只需完成一定数量紧前项目即可执行后续项目的现实情形,本文对此进行了刻画研究。在上述基础上,构建了可打断情境下受紧前关系影响的项目组合选择新模型。最后,通过算例实验,得出了如下结果: 1)允许紧前项目完成部分后即可执行后续项目时,回报率高的项目能在紧前项目完成规定比例后执行,项目的尽早盈利提高了再投资收益率;2)“完成一定数量紧前项目即可”实际情形的引入,降低了个别项目的执行成本,使得高回报率项目能够执行;3)紧前关系参数和紧前项目所需完成数量同时增加会导致项目组合总收益下降,但紧前项目所需完成数量的变动对收益影响更为显著。

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