An approximate decomposition algorithm for scheduling on parallel machines with heads and tails

• Published in: Computers & operations research Vol. 34; no. 3; pp. 868 - 883
• Main Authors: Gharbi, Anis, Haouari, Mohamed
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.03.2007; Elsevier Science; Pergamon Press Inc
• Subjects: Algorithms; Applied sciences; Delivery times; Exact sciences and technology; Heuristic; Identical parallel machines; Job shops; Machinery; Operational research. Management science; Release dates; Scheduling; Scheduling algorithms; Studies; Delivery times; Scheduling; Identical parallel machines; Release dates; Heuristic; Lower bound; Parallel algorithm; Worst case method; Parallel machines; Minimization; Makespan; Delivery lead time; Heuristic method
• ISSN: 0305-0548; 1873-765X; 0305-0548
• DOI: 10.1016/j.cor.2005.05.012

We address the makespan minimization for parallel identical machines subject to heads and tails. This problem is NP -hard in the strong sense. We show that the worst-case performance of Jackson's algorithm is improved by using a preprocessing algorithm, and we propose an approximate decomposition algorithm which requires iteratively solving a sequence of two-machine problems. We present the results of an extensive computational study on large instances with up to 2000 jobs and 100 machines which show that the proposed heuristic is fast and yields in most cases schedules with relative deviation from a lower bound less than 0.2%.