Minimizing the total completion time in single-machine scheduling with step-deteriorating jobs

• Published in: Computers & operations research Vol. 32; no. 3; pp. 521 - 536
• Main Authors: Jeng, A.A.K., Lin, B.M.T.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.03.2005; Elsevier Science; Pergamon Press Inc
• Subjects: Applied sciences; Branch & bound algorithms; Branch-and-bound algorithm; Exact sciences and technology; Job shops; Operational research and scientific management; Operational research. Management science; Scheduling; Scheduling, sequencing; Single-machine scheduling; Step deterioration; Studies; Total completion time; Single-machine scheduling; Step deterioration; Branch-and-bound algorithm; Total completion time; Branch and bound method; Task scheduling; Scheduling; Makespan; Single machine; Workload
• ISSN: 0305-0548; 1873-765X; 0305-0548
• DOI: 10.1016/j.cor.2003.08.001

In this paper, we study a scheduling problem of minimizing the total completion time on a single machine where the processing time of a job is a step function of its starting time and a due date that is common to all jobs. This problem has been shown to be NP -hard in the literature. To derive optimal solutions from a practical aspect, we develop a lower bound and two elimination rules to design branch-and-bound algorithms. Through computational experiments, we show that the proposed properties are effective in curtailing unnecessary explorations during the solution-finding process, and that the synergy of these properties can solve problems with up to 100 jobs in a few seconds.