Traditional models of project management have laid emphasis on scheduling of operations to meet deadlines. The research presented here approaches project management as a resource allocation problem where project completion is constrained by the man-hours available from those involved in the project. The variations in the relation between completion of project and time allocated to it are influenced by subjective factors. Hence there is a problem of inability to fit a standard or well-defined distribution. This thesis addresses this problem by a robust optimization approach. The budget of uncertainty is set by the decision maker, consequently controlling the extent of variation in the parameters whose bounds of uncertainty are known. The optimal allocation of time to the tasks in the project has been provided.