The resource-constrained activity insertion problem with minimum and maximum time lags

We consider the resource-constrained activity insertion problem with minimum and maximum time lags. The problem consists in inserting a single activity in a partial schedule while preserving its structure represented through resource flow networks and minimizing the makespan increase caused by the insertion. In the general case, we show that finding a feasible insertion that minimizes the project duration is NP-hard. When only minimum time lags are considered and when activity durations are strictly positive, we show the problem is polynomially solvable, generalizing previously established results on activity insertion for the standard resource-constrained project scheduling problem.