Abstract: With the development of scientific technology and the acceleration of economic globalization, managers who own much capital face more and more projects to choose. How to invest the scarce resources such as budget, people and time. on a most profitable subset is crucial for a firm/organization. This is the main concern of project portfolio selection problem. In real world, managers note that project interruptions may happen, which come from some managerial concerns, such as the lack of cash, materials and technicians. When managers consider the project interruptions as a strategy in choosing the best execution scheduling for projects, i.e., in fact, they try to optimize the project execution by running the projects by portions, and the consideration of the project interruptions as the above strategy is manager's initial intent. These types of interruptions are called divisibility. In this paper this type of project portfolio selection problem considering divisibility is mainly concerned. To the best of our knowledge, there is yet not research about resource constraints introduced into the project portfolio selection problem considering divisibility. Therefore, based on the model of project portfolio selection considering divisibility, a new model considering consumptive and renewable resource constraints is constructed. This model is a mixed integer programming problem with a linear objective function. And then a model of project portfolio selection problem without divisibility is set up. This model is an integer programming problem. The comparison analysis of the above two models is presented.More specifically, the second model is the special case of the first model under some assumptions. Secondly, for the purpose of simplifying the above models, the capital present value presentation is introcluced and proved. Finally, one numerical example is given to illustrate the characteristic of the new model with using GAMS. The result shows that: 1) unlike the research of the past, project divisibility can bring positive influence for the enterprise under the resource constraints. 2) Those projects with more profits and less use of resources are required precedence over all others. 3) When resources are limited, resource constraints are key factors for the selection of projects. A practical case provides the proof for the above results.

Key words: project portfolio selection, resource constraints, divisibility, capital present value