Theoretical Analysis on Powers-of-Two Applied to JSP

This paper discusses the scheduling of precedence-related jobs non-preemptively in a job shop environment with an objective of minimizing the makespan. Due to the NP-hard nature of the scheduling problems, it is usually difficult to find an exact optimal schedule and hence one should rely on finding a near to optimal solution. This paper proposes a computationally effective powers-of-two heuristic for solving job shop scheduling problem. The authors prove that the makespan obtained through powers-of-two release dates lies within 6% of the optimal value. The authors also prove the efficacy of powers-of-two approach through mathematical induction.