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Theoretical Analysis on Powers-of-Two Applied to JSP: A Case Study of Turbine Manufacturing

V. Mahesh, L. Siva Rama Krishna, Sandeep Dulluri, C. S. P. Rao

Source Title: International Journal of Green Computing (IJGC) 2(2)

DOI: 10.4018/jgc.2011070101

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Abstract

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.

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Job Shop Schedule

An instance of a job shop scheduling problem consists of a collection of jobs which are weighted according to their importance. The time when a job arrives is its release time and is denoted by. Each job is composed of a set of operations. The processing time associated with each operation is. The execution of each operation requires the use of a set of machines. Precedence’s are imposed on the set using a binary relation A. If, then has to be performed before. Schedule is a function that defines the start time for each operation i.e., .