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This paper proposes an integrated duplication based Algorithm (IDSA) for improving the schedulability of precedence related real-time tasks with hard and soft deadlines on a set of heterogeneous network of workstations (NOWs). IDSA utilizes selective subtask duplication that enables some subtasks to have earlier start times, which results in an increased number of subtasks (and hence task sets) finishing before their deadlines, thereby increasing the Schedulability. Extensive theoretical analysis of the proposed IDSA scheme has been carried out. To that end, both the time and space complexity analysis of IDSA has been proved, in addition to its schedulability condition.