Online and semi-online scheduling of two machines under a grade of service provision

Park, Jong-Ho; Chang, Soo Y.; Lee, Kangbok

doi:10.1016/j.orl.2005.11.004

Cited by 81 publications

(58 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They further analyze the case with seven machines showing that their gap is no more than 1/180 (≈ 0.00556). Park et al (2006) study online and semi-online scheduling on two machines. (Note that for two machines, arbitrary eligibility is equivalent to nested eligibility.)…”

Section: Arbitrary Eligibilitymentioning

confidence: 99%

Makespan minimization in online scheduling with machine eligibility

2010

Self Cite

View full text Add to dashboard Cite

In this paper we provide a survey of online scheduling in parallel machine environments with machine eligibility constraints and the makespan as objective function. We first give a brief overview of the different parallel machine environments and then survey the various types of machine eligibility constraints, including treehierarchical processing sets, Grade of Service processing sets, interval processing sets, and nested processing sets. We furthermore describe the relationships between the various different types of processing sets. We proceed with describing two basic online scheduling paradigms, namely online over list and online over time. For each one of the two paradigms we survey all the results that have been recorded in the literature with regard to each type of machine eligibility constraints. We obtain also

show abstract

Section: Arbitrary Eligibilitymentioning

confidence: 99%

Makespan minimization in online scheduling with machine eligibility

2010

Self Cite

View full text Add to dashboard Cite

show abstract

“…Park et al [11] and Jiang et al [9] independently presented an optimal algorithm with a competitive ratio of 5/3 for the integral model on two identical machines. When two machines have different speeds, Chassid and Epstein [4] proved the optimal algorithm has a competitive ratio 1+2s+s 2 1+s+s 2 for the fractional model, Tan and Zhang [12] proved the optimal algorithm has a competitive ratio of…”

Section: Introductionmentioning

confidence: 99%

A Mathematical Programming Approach for Online Hierarchical Scheduling

Tan

Zhang

2009

Combinatorial Optimization and Applications

View full text Add to dashboard Cite

Abstract. This paper considers an online hierarchical scheduling problem on parallel identical machines. We are given a set of m machines and a sequence of jobs. Each machine has a different hierarchy, and each job also has a hierarchy associated with it. A job can be assigned to a machine only if its hierarchy is no less than that of the machine. The objective is to minimize makespan. Two models are studied in the paper. For the fractional model, we present an improved algorithm and lower bounds. Both algorithm and lower bounds are based on solutions of mathematical programming. For any given m, our algorithm is optimal by numerical calculation. For the integral model, we present both a general algorithm for any m, and an improved algorithm with better competitive ratios of 2.333 and 2.610 for m = 4 and 5, respectively.

show abstract

“…Park, Chang and Lee [13] and independently Jiang, He and Tang [12] studied the problem on two identical speed hierarchical machines. They both designed 5 3 -competitive algorithms and showed that this ratio is best possible.…”

Section: Introductionmentioning

confidence: 99%

“…They both designed 5 3 -competitive algorithms and showed that this ratio is best possible. In [13], the semi-online variant where the sum of job processing times is known in advance was studied as well. A 3 2 -competitive algorithm was designed.…”

Section: Introductionmentioning

confidence: 99%

The hierarchical model for load balancing on two machines

Chassid

Epstein

2007

J Comb Optim

View full text Add to dashboard Cite

Following previous work, we consider the hierarchical load balancing model on two machines of possibly different speeds. We first focus on maximizing the minimum machine load and show that no competitive algorithm exists for this problem. We overcome this barrier in two ways, both related to previously known models. The first one is fractional assignment, where each job can be arbitrarily split between the machines. The second one is a semi-online model where the sum of jobs is known in advance. We design algorithms of best possible competitive ratios for both these cases. Furthermore, we show that the combination of the two models leads to the existence of an optimal algorithm (i.e., an algorithm of competitive ratio 1). This algorithm is clearly optimal for the makespan minimization problem as well. For the latter problem, we consider the fractional assignment model and design an algorithm of best possible competitive ratio for it.

show abstract

Online and semi-online scheduling of two machines under a grade of service provision

Cited by 81 publications

References 8 publications

Makespan minimization in online scheduling with machine eligibility

Makespan minimization in online scheduling with machine eligibility

A Mathematical Programming Approach for Online Hierarchical Scheduling

The hierarchical model for load balancing on two machines

Contact Info

Product

Resources

About