A branch and bound algorithm to minimize total tardiness of jobs in a two identical-parallel-machine scheduling problem with a machine availability constraint

• Published in: The Journal of the Operational Research Society Vol. 66; no. 9; pp. 1542 - 1554
• Main Authors: Lee, Ju-Yong, Kim, Yeong-Dae
• Format: Journal Article
• Language: English
• Published: London Taylor & Francis 01.09.2015; Palgrave Macmillan; Palgrave Macmillan UK; Taylor & Francis Ltd
• Subjects: Algorithms; availability constraint; Branch & bound algorithms; branch and bound; Breakdowns; Business and Management; General Paper; General Papers; Heuristic; identical parallel machines; Job shops; Linear programming; Management; Operations research; Operations Research/Decision Theory; Preventive maintenance; Production scheduling; Scheduling; Studies; total tardiness; scheduling; branch and bound; identical parallel machines; total tardiness; availability constraint
• ISSN: 0160-5682; 1476-9360
• DOI: 10.1057/jors.2014.122

This research focuses on the problem of scheduling jobs on two identical parallel machines that are not continuously available with the objective of minimizing total tardiness. After processing a given number of jobs, each machine requires a preventive maintenance task, during which the machine cannot process jobs. We present dominance properties and lower bounds, and develop a branch and bound algorithm using these properties and lower bounds as well as an upper bound obtained from a heuristic algorithm. Performance of the algorithm is evaluated through a series of computational experiments on randomly generated instances and results are reported.