R&D Project Selection and Manpower Allocation with Integer Nonlinear Goal Programming

A number of recent research efforts in the area of research and development planning have indicated the necessity that the R&D project selection process be viewed as a multi-criteria decision-making problem. As a result, linear 0-1 goal programming, because of its ability to encompass multiple objectives, has been employed on several occasions as a project selection model. However, in these goal programming models the relationships between resource utilization and project outcomes or between various resource utilizations have been expressed linearly when, in reality, they are often non-linear. For example, as the resources allocated to a project are increased the probability of project success will also increase but at a decreasing rate. In this paper, a non-linear integer goal programming model is described via a case example. The case example encompasses a pool of thirty researchers available for allocation to seven possible R&D projects. As such, the model consists of integer decision variables for both the number of researchers allocated, and, project selection. Researcher allocation and project selection are subject to several linear and nonlinear goal constraints. Nonlinear goal constraints are constructed that relate the probability of project success to the number of researchers assigned to a project and to expected monetary return, and, that relate the number of researchers allocated to project completion time. Linear goal constraints are developed for budget limitations, computer capacity utilization and various strict conditions placed on the model. The model selects projects and allocates researchers to projects such that a prioritized goal structure is most satisfactorily achieved. The model solution of the case example indicated the selection of five of the seven projects and the number of researchers assigned to each project. Of the nine prioritized goals, six were achieved while three were only partially achieved.