A resource scheduling constraint that accepts tasks which can potentially have a duration equal to zero. Zero-duration tasks can be used for modelling over-constrained resource scheduling problems where, due to some resource limitations, some tasks have to be discarded. This can be expressed by creating for each task $i$ a duration variable ${D}_{i}$ with values 0 and ${d}_{i}$ in its initial domain, where ${d}_{i}$ is the effective duration of task $i$ when it is not discarded. Then, depending on the relaxation cost ${C}_{i}$ associated with the fact that task $i$ is not considered, a reified constraint of the form ${D}_{i}=0⇔{C}_{i}={\alpha }_{i}$ $\left({\alpha }_{i}>0\right)$ is created. The initial domain of the cost variable ${C}_{i}$ is set to 0 and ${\alpha }_{i}$, where ${\alpha }_{i}$ is the cost associated with the decision of discarding task $i$. Then all the relaxation costs associated with the different tasks have to be aggregated together, i.e., typically by taking the sum or the maximum of the relaxation costs of the different tasks. On the one hand, the overall advantage of the approach is that it does not require developing any specific algorithm. On the other hand, the disadvantage is the lack of bounds on the overall relaxation cost that can sometimes be compensated by a specific enumeration heuristics.