On project scheduling problem

Consideration was given to the resource–constrained project scheduling problem and its special cases. The existing lower estimates of the objective function — minimization of the project time — were compared. It was hypothesized that the optimal value of the objective function of the nonpreemptive resource–constrained project scheduling problem is at most twice as great as that of the objective function with preemption. The hypothesis was proved for the cases of parallel machines and no precedence relation.