The problem that we address in this chapter is an extension of the resource-constrained project scheduling problem (RCPSP). It belongs to the class of project scheduling problems with multilevel (or multimode) activities that permit an activity to be processed by resources operating at appropriate modes where each mode belongs to a different resource level and incurs different cost and duration. Each activity must be allocated exactly one unit of each required resource, and the resource unit may be used at any of its specified levels. The processing time of an activity is given by the maximum of the durations that would result from different resources allocated to that activity. The objective is to find an optimal solution that minimizes the overall project cost, given a delivery date. A penalty is incurred for tardiness beyond the specified delivery date, or a bonus is accrued for early completion. We present a mathematical programming formulation as an accurate problem definition. A filtered beam search (FBS)-based method is used to solve the problem. It was implemented using the C# language. Results of our experimentations on the use of this method are also presented.