In this paper, constrained resource project scheduling problems schedule project activities subject to finite constraints on the availability of non-storable resource. Further, resources are assumed to be available per period in constant amounts, and are also demanded by an activity in constant amounts throughout the duration of the activity. We describe formulation which minimizes the combined cost of fluctuations in resource demand and delay of project completion. Cost bounding procedures are augmented by dominance relationships presented as theorems. This paper presents algorithm for solving the problem. And numerical examples are presented. Sensitivity analysis to evaluate the effect of changes of cost efficients is conducted.