Scheduling of parallel identical machines to maximize the weighted number of just-in-time jobs

Hiraishi, Kunihiko; Levner, Eugene; Vlach, Milan

doi:10.1016/s0305-0548(00)00086-1

Cited by 52 publications

(26 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Prior study focuses on the model with identical parallel machines, where machine speeds are equal and cannot be changed. Algorithms of time complexities O(n log n) and O(n 2 m) are proposed by Lann and Mosheiov (2003) and Hiraishi et al (2002) for the case of equal-weight jobs and for the general case, respectively. The latter result is generalized further to the case of controllable processing times (Leyvand et al 2010), where a job consuming x j amount of resources gets a compressed processing time given by an arbitrary decreasing function p j (x j ); the associated resource consumption cost is linear,…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Models and algorithms for energy-efficient scheduling with immediate start of jobs

Shioura

Shakhlevich

Strusevich

et al. 2017

J Sched

View full text Add to dashboard Cite

We study a scheduling model with speed scaling for machines and the immediate start requirement for jobs. Speed scaling improves the system performance, but incurs the energy cost. The immediate start condition implies that each job should be started exactly at its release time. Such a condition is typical for modern Cloud computing systems with abundant resources. We consider two cost functions, one that represents the quality of service and the other that corresponds to the cost of running. We demonstrate that the basic scheduling model to minimize the aggregated cost function with n jobs is solvable in O(n log n) time in the singlemachine case and in O(n 2 m) time in the case of m parallel machines. We also address additional features, e.g., the cost of job rejection or the cost of initiating a machine. In the case of a single machine, we present algorithms for minimizing one of the cost functions subject to an upper bound on the value of the other, as well as for finding a Pareto-optimal solution.

show abstract

Section: Related Workmentioning

confidence: 99%

“…. , M m that minimizes the sum of the total cost F and total energy G. Adapting the ideas from the work by Hiraishi et al (2002) and Leyvand et al (2010), we reduce our problem to a minimum-cost flow problem in a special network (Fig. 1).…”

Section: Problem + On Parallel Machinesmentioning

confidence: 99%

Models and algorithms for energy-efficient scheduling with immediate start of jobs

Shioura

Shakhlevich

Strusevich

et al. 2017

J Sched

View full text Add to dashboard Cite

show abstract

“…A heuristic algorithm was presented and a dynamic programming lower bounding procedure developed. Hiraishi et al [18] addressed the non-pre-emptive scheduling of n jobs that are completed exactly at their due dates. They showed that this problem is polynomially solvable, even if positive set-up is allowed.…”

Section: Introductionmentioning

confidence: 99%

“…Sung and Vlach [19] showed that when the number of machines is fixed, the weighted problem considered by Hirashi et al [18] is solvable in polynomial time (exponential in the number of machines), no matter whether the parallel machines are identical, uniform, or unrelated. However, when the number of machines is part of the input, the unrelated parallel machine case of the problem becomes strongly NP-hard.…”

Section: Introductionmentioning

confidence: 99%

“…However, when the number of machines is part of the input, the unrelated parallel machine case of the problem becomes strongly NP-hard. Lann and Mosheiov [20] provided a simple greedy O (n log n) algorithm to solve the problem of Hiraishi et al [18], thus greatly improving the time complexity. Čepek and Sung [21] considered the same problem of Hiraishi et al [18], where they corrected the greedy algorithm of Lann and Mosheiov [20], which they argued was wrong; Hiraishi et al [18] presented a new quadratic time algorithm that solved the problem.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Comparing the Performance of Different Meta-Heuristics for Unweighted Parallel Machine Scheduling

Adamu

Adewumi

2015

sajie

View full text Add to dashboard Cite

This article considers the due window scheduling problem to minimise the number of early and tardy jobs on identical parallel machines. This problem is known to be NP complete and thus finding an optimal solution is unlikely. Three meta-heuristics and their hybrids are proposed and extensive computational experiments are conducted. The purpose of this paper is to compare the performance of these meta-heuristics and their hybrids and to determine the best among them. Detailed comparative tests have also been conducted to analyse the different heuristics with the simulated annealing hybrid giving the best result. OPSOMMINGDie minimering van vroeë en trae take op identiese parallelle masjien met behulp van die gepaste gleufskeduleringsprobleem word oorweeg. Die probleem is nie-deterministies polinomiese tyd volledig en die vind van 'n optimale oplossing is dus onwaarskynlik. Drie meta-heuristieke en hul hibriede word voorgestel en uitgebreide berekeningseksperimente word uitgevoer. Die doel van hierdie artikel is om die vertoning van hierdie metaheuristieke en hul hibriede met mekaar te vergelyk om sodoende die beste te identifiseer. Gedetaileerde vergelykende toetse is ook uitgevoer om die verskillende heuristieke te ondersoek; daar is gevind dat die gesimuleerde uitgloei hibried die beste resultaat lewer.

show abstract

Generalizing Horn's conditions for preemptive scheduling on identical parallel machines via network flow techniques

Shioura,

Strusevich,

Shakhlevich

2023

Networks

View full text Add to dashboard Cite

We study the use of flow‐based algorithmic and proof techniques applied to preemptive scheduling of jobs on parallel identical machines. For the classical problem in which the jobs have individual release dates and must be finished by a common deadline, we present and prove unified necessary and sufficient conditions for the existence of a feasible schedule by examining the structure of minimum cuts in a special network. We then study an enhanced model that allows the presence of additional resources, provided that some jobs at any time of their processing require one unit of a particular resource. We extend our argument developed for the classical case to this enhanced model. The generalized necessary and sufficient conditions for the existence of a feasible schedule are presented and proved using the max‐flow/min‐cut reasoning.

show abstract

Scheduling of parallel identical machines to maximize the weighted number of just-in-time jobs

Cited by 52 publications

References 3 publications

Models and algorithms for energy-efficient scheduling with immediate start of jobs

Models and algorithms for energy-efficient scheduling with immediate start of jobs

Comparing the Performance of Different Meta-Heuristics for Unweighted Parallel Machine Scheduling

Generalizing Horn's conditions for preemptive scheduling on identical parallel machines via network flow techniques

Contact Info

Product

Resources

About