Single machine scheduling to minimize maximum lateness subject to release dates and precedence constraints

• Published in: Computers & operations research Vol. 37; no. 9; pp. 1537 - 1543
• Main Author: Liu, Zhixin
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.09.2010; Elsevier; Pergamon Press Inc
• Subjects: Algorithms; Applied sciences; Blocking; Bottlenecks; Branch & bound algorithms; Branch and bound algorithm; Deterministic scheduling; Exact sciences and technology; Heuristic; Job shops; Lateness; Maximum lateness; Operational research and scientific management; Operational research. Management science; Optimization; Optimization algorithms; Precedence constraint; Precedence constraints; Production scheduling; Release date; Release dates; Rule based; Schedules; Scheduling, sequencing; Studies; Release date; Branch and bound algorithm; Deterministic scheduling; Maximum lateness; Precedence constraint; Preemption; Branching; Lower bound; Bottleneck; Branch and bound method; Priority; Expert system; Scheduling; Convex programming; Delay; Computation time; Upper bound; Non differentiable programming; Descent method; Heuristic method; Lateness; Problem solving; Single machine
• ISSN: 0305-0548; 1873-765X; 0305-0548
• DOI: 10.1016/j.cor.2009.11.008

This paper considers the problem of finding a nonpreemptive schedule for a single machine to minimize the maximum lateness with release dates and precedence constraints. A branch and bound algorithm is developed. The algorithm uses four different heuristics to find upper bounds at the initial branch node: early release date heuristic, modified Schrage's heuristic, heuristic BLOCK, and a variable neighborhood descent procedure. At each branch node, two branches evolve from a schedule found by heuristic BLOCK using a binary branching rule based on bottleneck and critical jobs, and a lower bound is obtained by optimally solving the relaxed problem with preemption. The algorithm solves 14,984 out of the 15,000 systematically generated instances with up to 1,000 jobs within 1 minute of CPU time.