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The multi-skill project scheduling problem (MSPSP) has been first addressed in the scheduling community for more than 15 years. This paper deals with a new variant of this problem, the multi-skill project scheduling problem with partial preemption (MSPSP-PP), where only a subset of resources can be released during the preemption periods. Like the standard problem, this variant is NP-hard, because of that we propose in this article a series of heuristic algorithms to solve instances arising from an industrial application. First, we present a serial greedy algorithm, based on priority rules and a flow problem for resource allocation. To improve the solutions of the greedy algorithm, we then introduce a binary-tree-based search algorithm and a greedy randomised adaptive search procedure (GRASP). Finally, we propose a large neighbourhood search (LNS) algorithm integrating exact and heuristic methods. The best results in terms of solution quality and execution time are obtained by combining the GRASP algorithm and the LNS approach. Furthermore, the proposed GRASP algorithm is able to find new best results on 56 instances out of 216 on a standard MSPSP instance set which shows the quality of the approach even on special cases of the considered problem.