A Heuristic Serial Schedule Algorithm for Unrelated Parallel Machine Scheduling With Precedence Constraints

The paper presents a priority rule-based heuristic serial schedule (SS) algorithm for a deterministic scheduling problem where multiple jobs with arbitrary precedence constraints are processed on multiple unrelated parallel machines. The objective is to minimise makespan. The priority rule employs the arithmetic mean and deviation of the processing times to determine the prior job-machine pair. Moreover, at each iteration, the algorithm can schedule the prior job on the prior machine as early as possible to prevent certain machines from standing idle by the greatest extent. The proposed algorithm is demonstrated in detail through a test instance. Computational experiments are conducted to show that the new polynomial-time algorithm is effective in reducing makespan and efficient in shortening runtime.