Topic
Single-machine scheduling
About: Single-machine scheduling is a research topic. Over the lifetime, 2473 publications have been published within this topic receiving 56288 citations.
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TL;DR: The results indicate that both the lower and upper bounds are very tight and the branch-and-bound algorithm is the first algorithm that is able to optimally solve problems with up to 30 jobs in a reasonable amount of time.
18 citations
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TL;DR: In this article, a single-machine scheduling problem with an exponentially time-dependent learning effect is introduced, where the processing time of a job is assumed to be an exponential function of the total normal processing times of jobs already processed before it, and the upper bound for the maximum lateness and for the total weighted completion time is provided.
18 citations
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TL;DR: In this article, the authors gave an O(n log n log 3n) time algorithm for the chance-constrained sequencing problem on a single machine, where n is the number of jobs and the objective is to minimize the number which are early with probability not smaller than a given constant against the common due time d.
17 citations
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TL;DR: This work reduces the bicriteria problem to a series of parametric linear programs defined over the intersection of a submodular polyhedron with a box and demonstrates that the feasible region is represented by a so-called basepolyhedron and the corresponding problem can be solved by the greedy algorithm that runs two orders of magnitude faster than known previously.
Abstract: In scheduling with controllable processing times the actual processing time of each job is to be chosen from the interval between the smallest (compressed or fully crashed) value and the largest (decompressed or uncrashed) value. In the problems under consideration, the jobs are processed on a single machine and the quality of a schedule is measured by two functions: the maximum cost (that depends on job completion times) and the total compression cost. Our main model is bicriteria and is related to determining an optimal trade-off between these two objectives. Additionally, we consider a pair of associated single criterion problems, in which one of the objective functions is bounded while the other one is to be minimized. We reduce the bicriteria problem to a series of parametric linear programs defined over the intersection of a submodular polyhedron with a box. We demonstrate that the feasible region is represented by a so-called base polyhedron and the corresponding problem can be solved by the greedy algorithm that runs two orders of magnitude faster than known previously. For each of the associated single criterion problems, we develop algorithms that deliver the optimum faster than it can be deduced from a solution to the bicriteria problem.
17 citations
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TL;DR: A simple analytical solution method is presented to find the optimal due-dates for a special case of the objective function and PPW due-date assignment method.
17 citations