In this study, the authors consider a project scheduling problem with a single non-renewable resource. The authors assume that the resource is released at scheduled times and specified quantities and the resource is consumed at activity completion. The activities can be processed at different modes where a mode is defined by a processing time and a resource requirement amount. The problem is to select the modes and timings of the activities so as to minimize the project completion time. The authors give a mixed integer linear programming model and discuss some variable elimination mechanisms to enhance its efficiency.