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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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Proceedings ArticleDOI
23 May 2009
TL;DR: A scheduling problem in which a bounded number of jobs can be processed simultaneously by a single machine is considered, and a 4-approximation algorithm for general instances and approximation algorithms with improved ratios for instances with bounded lengths are presented.
Abstract: We consider a scheduling problem in which a bounded number of jobs can be processed simultaneously by a single machine. The input is a set of n jobs J = {J 1 , … , J n }. Each job, J j , is associated with an interval [s j , c j ] along which it should be processed. Also given is the parallelism parameter g ≥ 1, which is the maximal number of jobs that can be processed simultaneously by a single machine. Each machine operates along a contiguous time interval, called its busy interval, which contains all the intervals corresponding to the jobs it processes. The goal is to assign the jobs to machines such that the total busy time of the machines is minimized. The problem is known to be NP-hard already for g = 2. We present a 4-approximation algorithm for general instances, and approximation algorithms with improved ratios for instances with bounded lengths, for instances where any two intervals intersect, and for instances where no interval is properly contained in another. Our study has important application in optimizing the switching costs of optical networks.

37 citations

Journal ArticleDOI
TL;DR: A new method of sequential and parallel speeding up of the process of solving a single machine scheduling problem with total tardiness cost function is proposed, generating a neighborhood inside path relinking method and parallelization of generating paths.
Abstract: We propose a new method of sequential and parallel speeding up of the process of solving a single machine scheduling problem with total tardiness cost function. This improvement is done on two levels: generating a neighborhood inside path relinking method (basing on new approach--blocks in solutions) and parallelization of generating paths. The obtained results are compared to the benchmark ones taken from the literature. It was possible to find new the best solutions for many benchmark instances by using the proposed method.

37 citations

Journal ArticleDOI
TL;DR: The goal is to determine an optimal combination of theDue date assignment strategy and job schedule so as to minimize an objective function that includes earliness, tardiness, due date assignment and flow time costs.

37 citations

Journal ArticleDOI
TL;DR: The results suggest that the heuristics are effective in generating near-optimal solutions quickly in a problem in which a set of n jobs has to be batched as well as scheduled for processing on a single machine.
Abstract: We study a problem in which a set of n jobs has to be batched as well as scheduled for processing on a single machine. A constant machine set-up time is required before the first job of each batch is processed. A schedule specifies the sequence of batches, where each batch comprises a sequence of jobs. The batch delivery time is defined as the completion time of the last job in a batch. The earliness of a job is defined as the difference between the delivery time of the batch to which it belongs and the job completion time. The objective is to find a number B of batches and a schedule so as to minimize the sum of the total weighted job earliness and mean batch delivery time. The problem is shown to be strongly NP-hard. It remains strongly $NP$-hard if the set-up time is zero and $B\le U$ for any variable $U\ge 2$ or if $B\ge U$ for any constant $U\ge 2$. The problem is proved to be ordinary NP-hard even if the set-up time is zero and $B\le 2$. For the case $B\le U$, a dynamic programming algorithm is presented, which is pseudopolynomial for any constant $U\ge 2$. Algorithms with O(n¹) running times are derived for the cases when all weights are equal or all processing times are equal. For the general problem, a family of heuristics is suggested. Computational experiments on the proposed heuristic algorithm are conducted. The results suggest that the heuristics are effective in generating near-optimal solutions quickly.

37 citations

Journal ArticleDOI
TL;DR: This paper considers single-machine scheduling problem in which processing time of a job is described by a convex decreasing resource consumption function, and proposes a branch-and-bound algorithm and a heuristic algorithm to solve the problem.

37 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202333
202270
202188
202083
201972
201889