AbstractThis paper describes practical optimization/approximation algorithms for scheduling a set of partially ordered computational tasks with different processing times onto a multiprocessor system so that the schedule length is minimized. Since this problem belongs to the class of “strong” NP hard problems, we must eliminate the possibility of constructing not only pseudopolynomial time optimization algorithms, but also fully polynomial time approximation schemes unless P = NP.This paper proposes a heuristic algorithm CP/MISF (Critical Path/Most Immediate Successors First) and an optimization/approximation algorithm DF/IHS (Depth First/ Implicit Heuristic Search). DF/IHS is an excellent scheduling method which can reduce markedly the space complexity and average computation time by combining the branch‐and‐bound method with CP/MISF; it allows us to solve very large‐scale problems with a few hund