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Faster Approximation Algorithms for Scheduling with Fixed Jobs
"... We study the problem of scheduling jobs on identical parallel machines without preemption. In the considered setting, some of the jobs are already assigned machines and starting times, for example due to external constraints not explicitly modelled. The objective is to assign the rest of the jobs in ..."
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Cited by 4 (1 self)
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We study the problem of scheduling jobs on identical parallel machines without preemption. In the considered setting, some of the jobs are already assigned machines and starting times, for example due to external constraints not explicitly modelled. The objective is to assign the rest of the jobs in order to minimize the makespan. It is known that this problem cannot be approximated better than within a factor of 3/2 unless P = NP. An algorithm that achieves 3/2 + ɛ for any ɛ> 0 was presented by Diedrich and Jansen [DJ09], but its running time is doubly exponential in 1/ɛ. We present an improved algorithm with approximation ratio 3/2 and polynomial running time. We also give matching results for the related problem of scheduling with reservations. The new algorithm is both faster and conceptually simpler than the previously known algorithms. 1
Complexity and Algorithms for TwoStage Flexible Flowshop Scheduling with Availability Constraints
"... This paper considers the twostage flexible flowshop scheduling problem with availability constraints. We discuss the complexity and the approximability of the problem, and provide some approximation algorithms with finite and tight worst case performance bounds for some special cases of the problem ..."
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This paper considers the twostage flexible flowshop scheduling problem with availability constraints. We discuss the complexity and the approximability of the problem, and provide some approximation algorithms with finite and tight worst case performance bounds for some special cases of the problem.
Minimizing the total tardiness for the tool change scheduling problem on parallel machines
, 2016
"... This paper deals with the total tardiness minimization problem in a parallel machines manufacturing environment where tool change operations have to be scheduled along with jobs. The mentioned issue belongs to the family of scheduling problems under deterministic machine availability restrictions. ..."
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This paper deals with the total tardiness minimization problem in a parallel machines manufacturing environment where tool change operations have to be scheduled along with jobs. The mentioned issue belongs to the family of scheduling problems under deterministic machine availability restrictions. A new model that considers the effects of the tool wear on the quality characteristics of the worked product is proposed. Since no mathematical programmingbased approach has been developed by literature so far, two distinct mixed integer linear programming models, able to schedule jobs as well as tool change activities along the provided production horizon, have been devised. The former is an adaptation of a wellknown model presented by the relevant literature for the single machine scheduling problem with tool changes. The latter has been specifically developed for the issue at hand. After a theoretical analysis aimed at revealing the differences between the proposed mathematical models in terms of computational complexity, an extensive experimental campaign has been fulfilled to assess performances of the proposed methods under the CPU time viewpoint. Obtained results have been statistically analyzed through a properly arranged ANOVA analysis.
The effect of machine availability on the worstcase performance of LPT
, 2003
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