The one-machine problem with delayed precedence constraints and its use in job shop scheduling

Article Abstract:

A one-machine scheduling problem is considered. Under this problem, job processing has release and delivery times and the goal is to shorten the time required to finish all the jobs, called the makespan. Job processing is also subject to the following constraints: the sequence of machines for the jobs to be processed is predetermined and each of the machines can only process one job at a time. A modified Longest Tail Heuristic is developed whose analysis points to the cases allowing efficient branching. An optimization algorithm is then formulated that performs as well as the best algorithms applying to the standard one-machine problem. This algorithm's performance when applied to all classes of job shop scheduling problems improves when it is integrated into a modified form of the Shifting Bottleneck Procedure that is tighter than the standard one-machine problem.

Manufacturing processes, Manufacturing

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Mixed 0-1 programming by lift-and-project in a branch-and-cut framework

Article Abstract:

The computational issues associated with incorporating general cutting planes for mixed 0-1 programs into a branch-and-cut framework are examined. Findings indicate that an effective measure of cut quality can be developed by estimating the Euclidian distance between the hyperplane identifying the cut and the point it cuts off. The results also suggest that it is more advisable to produce cuts in large rounds instead of in small rounds or one by one, and that integrating general cuts within brand-and-cut is more efficient than generally believed. Finally, it is shown that the branch-and-cut code developed can efficiently solve mixed 0-1 problems. Its performance is found to be similar or even better than some of the most efficient mixed integer programming codes that are currently existing.

Integer programming, Cutting

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Parallel machine scheduling: processing rates dependent on number of jobs in operation

Article Abstract:

The relative behavior of two scheduling performance measures under different job processing rate functions is examined for the assignment of work to identical parallel processors. It is demonstrated that the smallest completion time of all system jobs is independent of job assignment to machines, and that flowtime is minimized when all job assignments are scheduled on one machine out of 'm'. More general processing rate activities are also examined. An example is presented of a real-world problem in which refueling of navy vessels must be scheduled.

Methods, Management, Planning, Usage, Industrial equipment, Machinery, Production control, Facility management, Facilities management

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