This paper deals with the problem of project scheduling subject to multiple execution modes with non-renewable resources, and a model that handles some of monetary issues in real world applications. The objective is to schedule the activities to maximize the expected net present value (NPV) of the project, taking into account the activity costs, the activity durations, and the cash flows generated by successfully completing an activity. Owing to the combinatorial nature of this problem, the current study develops a hybrid of branch-and-bound procedure and memetic algorithm to enhance both mode assignment and activity scheduling. Modifications for the makespan minimization problem have been made through a set of benchmark problem instances. Algorithmic performance is rated on the maximization of the project NPV and computational results show that the two-phase hybrid metaheuristic performs competitively for all instances of different problem sizes.

关键词： Memetic algorithm (MA),  Branch and bound (B&B) algorithm,  Net present value (NPV),  Project scheduling problem