Book ChapterDOI
Scheduling Deteriorating Jobs Dependent on Resources for the Makespan Minimization
A. Bachman,A. Janiak +1 more
- pp 29-34
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TLDR
The ordinaryNP-completeness of the considered problem is proved by reducing to it the ordinary NP-complete Partition Problem by giving also some properties of the optimal resource allocation.Abstract:
The paper deals with a single machine scheduling problem for the maximum completion time (makespan) minimization subject to the constraint on the total amount of available resources. The job processing times are given by non-decreasing linear functions simultaneously dependent on the starting moment of their execution and on the amount of allocated resources. We prove the ordinary NP-completeness of the considered problem by reducing to it the ordinary NP-complete Partition Problem. We give also some properties of the optimal resource allocation. The optimal solutions for some special cases of the latter problem are also presented.read more
Citations
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Journal ArticleDOI
Single-machine scheduling with time-and-resource-dependent processing times
Cai-Min Wei,Ji Bo Wang,Ping Ji +2 more
TL;DR: It is shown that the problems of single-machine scheduling problems in which the processing time of a job is a function of its starting time and its resource allocation remain polynomially solvable under the proposed model.
Journal ArticleDOI
Single-machine group scheduling with both learning effects and deteriorating jobs
TL;DR: In this article, two resource constrained single-machine group scheduling problems with both learning effects and deteriorating jobs are considered, where the processing time of a job is defined by the function of its starting time and position in the group, and the group setup times of a group is a positive strictly decreasing continuous function of the consumed resource.
Journal ArticleDOI
Scheduling jobs with processing times dependent on position, starting time, and allotted resource
TL;DR: The objective is to find the optimal sequence of jobs and the optimal resource allocation separately, and focuses on minimizing a cost function containing makespan, total completion time, total absolute differences in completion times, and total resource cost.
Journal ArticleDOI
Scheduling jobs with controllable processing time, truncated job-dependent learning and deterioration effects
TL;DR: In this article, the authors consider single machine scheduling problems with controllable processing time (resource allocation), truncated job-dependent learning and deterioration effects, and find the optimal sequence of jobs and the optimal resource allocation separately for minimizing a cost function containing makespan (total completion time, total absolute differences in completion times) and total resource cost.
Journal ArticleDOI
Single-machine scheduling time-dependent jobs with resource-dependent ready times
TL;DR: In the paper resource constrained two single-machine scheduling problems with deteriorating jobs are considered and polynomial solutions for the total resource consumption minimization problem under the constraint that the makespan does not exceed a given limit are presented.
References
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Book
Computers and Intractability: A Guide to the Theory of NP-Completeness
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Book ChapterDOI
Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey
TL;DR: In this article, the authors survey the state of the art with respect to optimization and approximation algorithms and interpret these in terms of computational complexity theory, and indicate some problems for future research and include a selective bibliography.
Book
Scheduling Computer and Manufacturing Processes
TL;DR: In this paper, a theoretical and application oriented analysis of deterministic scheduling problems arising in computer and manufacturing environments is presented and discussed, where different problem parameters such as task processing times, urgency weights, arrival times, deadlines, precedence constraints, and processor speed factor are involved.