We consider a project portfolio selection problem faced by research councils in project and call-based R&D grant programs. In such programs, typically, each applicant project receives a score value during specially-designed peer review processes. Each project also has a certain budget, estimated by its principle investigator. The problem is to select an optimal (maximum total score) subset of applicant projects under a budget constraint for the call. At the time of funding decisions, exact expenditures of projects are not known. The research councils typically don't provide more money than they funded a project to start with, so the realized total expenditure of a portfolio usually tends to be lower than the total budget, which causes budgetary slack. In this paper, we attempt to model this phenomenon in a project portfolio selection problem and show that budget utilization of a call can be increased to support more projects and hence achieve higher scientific impact. We model a project's expenditure using a mixture distribution that represents project success, underspending and cancellation situations. We develop a chance-constrained model with policy constraints. Due to the intractability of the developed model, we have shown that Normal distribution can be used for approximation. We also quantify the approximation error of our model via a theoretical bound and simulation. The proposed approach could rigorously increase the budget utilization up to 15.2%, which is remarkable for public decision makers.