Branch-and-Bound Heuristic Approaches to a Sequencing Problem with Team-Size Requirements.

by Louis W. Miller

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Some approaches to the job-scheduling problem in which several machines of the same type are required for each operation, as in aircraft maintenance, where teams of specialists (the "machines") are often needed to fix a single malfunction. The author examines the simplest type of static problem with variable team-size requirements. Resources consist of m identical and interchangeable machines and n jobs all available for simultaneous scheduling. Every job has a known processing time requirement and prescribed team size that never exceeds m. The time interval is continuous, and interruptions are not permitted. Good job criteria are in terms of minimizing the average completion times and/or the amount of time required to complete all n jobs. Several heuristic sequencing methods are examined, as well as some implicit enumeration schemes (branch and bound) to determine their usefulness in producing optimal solutions to sample problems. Results are tabulated.

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