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This article aims to study the problem of scheduling on identical parallel machines with different release dates and precedence constraints in tree form to minimize the number of the late jobs; this particular criterion is often used like a performance indicator. This problem is noted by Pm| ri, outtree|ΣUi in standard classification (Graham and Al, 1979). Initially, we present an outline of the work completed by the problems of scheduling to minimize the number of the late jobs. Thereafter we propose two heuristics to solve this problem, the first heuristic based on a new priority rule and the second based on EDD rule.