A destructive lower bound for the multi-mode resource-constrained project scheduling problem with minimal and maximal time-lags is presented. Given are n activities which may be processed in different modes without preemptions. During processing certain amounts of renewable and non-renewable resources are needed where the available capacity of each resource type is limited. Furthermore, minimal and maximal time-lags between the activities are given. The objective is to determine a schedule with minimal makespan. The lower bound calculations are based on two methods for proving infeasibility of a given threshold value T for the makespan. The first uses constraint propagation techniques, while the second is based on a linear programming formulation which is solved by a column generation procedure. Computational results are reported for several test instances of the multi-mode problem with and without time-lags and the single-mode version with time-lags.
