Summary: Scheduling problems involving a set of dependent tasks with release dates and deadlines on a limited number of resources have been intensively studied. However, few parameterized complexity results exist for these problems. This paper studies the existence of a feasible schedule for a typed task system with precedence constraints and time intervals \((r_i,d_i)\) for each job \(i\). The problem is denoted by \(P\vert \mathcal{M}_j(type),prec,r_i,d_i\vert \star \). Several parameters are considered: the pathwidth \(pw (I)\) of the interval graph \(I\) associated with the time intervals \((r_i, d_i)\), the maximum processing time of a task \(p_{\max }\) and the maximum slack of a task \(s\ell_{\max } \). This paper establishes that the problem is para-NP-complete with respect to any of these parameters. It then provides a fixed-parameter algorithm for the problem parameterized by both parameters \(pw (I)\) and \(\min (p_{\max },s\ell_{\max })\). It is based on a dynamic programming approach that builds a levelled graph which longest paths represent all the feasible solutions. Fixed-parameter algorithms for the problems \(P\vert \mathcal{M}_j(type),prec,r_i,d_i\vert C_{\max }\) and \(P\vert \mathcal{M}_j(type),prec,r_i\vert L_{\max }\) are then derived using a binary search.