In many project-oriented production systems, e. g., shipyards or large-scale steel products manufacturing, resource loading by an activity is flexible, and the activity duration is a function of resource allocation. For example, if one doubles the size of the crew assigned to perform an activity, it may be feasible to complete the activity in half the duration. Such flexibility has been modeled by Weglarz [13] and by Leachman, Dincerler, and Kim [7[ in extended formulations of the resource-constrained poject scheduling problem. This paper presents a new algorithmic approach to the problem that combines the ideas proposed by the aforementioned authors. The method we propose involves a two-step approach : (1) solve the resource-constrained scheduling problem using a heuristic, and (2) using this schedule as an initial feasible solution, find improved resource allocations by solving a linear programming model. We provide computational results indicating the superiority of this approach to previous methodology for the resource-constrained scheduling problem. Extensions to the model to admit overlap relationship of the activities also are presented.