Approximation algorithms for precedence-constrained identical machine scheduling with rejection

Zhang, Xianzhao; Xu, Dianguo; Du, Donglei; Wu, Chenchen

doi:10.1007/s10878-016-0044-6

Cited by 21 publications

(7 citation statements)

References 19 publications

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“…This means that the penalty function is a submodular function, where the submodular function is a special set function, which has decreasing marginal returns. Combination optimizations with submodular penalties have been proposed and studied, and recently, Zhang et al [34] proposed a 3-approximation algorithm for precedence-constrained scheduling with submodular rejection on parallel machines. Liu et al [35] proposed an O( √ n)-approximation combinatorial algorithm for the submodular load balancing problem with submodular penalties.…”

Section: Introductionmentioning

confidence: 99%

Single Machine Vector Scheduling with General Penalties

Liu

Zhu

2021

Mathematics

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In this paper, we study the single machine vector scheduling problem (SMVS) with general penalties, in which each job is characterized by a d-dimensional vector and can be accepted and processed on the machine or rejected. The objective is to minimize the sum of the maximum load over all dimensions of the total vector of all accepted jobs and the rejection penalty of the rejected jobs, which is determined by a set function. We perform the following work in this paper. First, we prove that the lower bound for SMVS with general penalties is α(n), where α(n) is any positive polynomial function of n. Then, we consider a special case in which both the diminishing-return ratio of the set function and the minimum load over all dimensions of any job are larger than zero, and we design an approximation algorithm based on the projected subgradient method. Second, we consider another special case in which the penalty set function is submodular. We propose a noncombinatorial ee−1-approximation algorithm and a combinatorial min{r,d}-approximation algorithm, where r is the maximum ratio of the maximum load to the minimum load on the d-dimensional vector.

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Section: Introductionmentioning

confidence: 99%

Single Machine Vector Scheduling with General Penalties

Liu

Zhu

2021

Mathematics

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“…It follows that when the option of job-rejection is valid, the scheduler may decide to process only a subset of the jobs, and those jobs which are not processed (i.e., totally rejected or outsourced) are penalized. The importance and practicality of job-rejection are demonstrated in the following selection of recently published papers, addressing various machine settings and cost functions: Zou and Miao (2016), Gerstl and Mosheiov (2017), Strusevich (2017), Fiszman and, Huang et al (2018), Mor and Mosheiov (2018), Zhang et al (2018), Dabiri et al (2019, Kovalyov et al (2019), Mor and Shapira (2019), Koulamas, and Kyparisis (2020), , Mor and Shapira (2020a, b), , Mosheiov and Pruwer (2020) and Wang et al (2020).…”

Section: Introductionmentioning

confidence: 99%

Single machine scheduling to maximize the weighted number of on-time jobs with job-rejection

Mor

Mosheiov

2021

Oper Res Int J

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We study a single machine scheduling problem, where the goal is to maximize the weighted number of jobs completed exactly at their due-dates. The option of jobrejection is considered, i.e., the scheduler may perform only a subset of the jobs. An upper bound on the total permitted rejection cost is assumed. The problem is proved to be NP-hard, and a pseudo-polynomial dynamic programming algorithm is introduced. Our numerical tests indicate that the proposed algorithm performs well: medium size instances (of up to 100 jobs) are solved in less than 1 s.

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“…Liu and Li [14] considered parallel-machine scheduling with submodular penalties and proposed a (2 − 1 m )-approximation algorithm based on the greedy method and list scheduling algorithm. Zhang et al [15] considered precedence-constrained scheduling with submodular rejection on parallel machines, and proposed a 3-approximation algorithms. Based on the primal-dual method, Liu and Li presented a 2-approximation algorithm for [16] single machine scheduling with release dates and submodular rejection penalty.…”

Section: Introductionmentioning

confidence: 99%

A Combinatorial 2-Approximation Algorithm for the Parallel-Machine Scheduling with Release Times and Submodular Penalties

Wang

Liu

2021

Mathematics

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In this paper, we consider parallel-machine scheduling with release times and submodular penalties (P|rj,reject|Cmax+π(R)), in which each job can be accepted and processed on one of m identical parallel machines or rejected, but a penalty must paid if a job is rejected. Each job has a release time and a processing time, and the job can not be processed before its release time. The objective of P|rj,reject|Cmax+π(R) is to minimize the makespan of the accepted jobs plus the penalty of the rejected jobs, where the penalty is determined by a submodular function. This problem generalizes a multiprocessor scheduling problem with rejection, the parallel-machine scheduling with submodular penalties, and the single machine scheduling problem with release dates and submodular rejection penalties. In this paper, inspired by the primal-dual method, we present a combinatorial 2-approximation algorithm to P|rj,reject|Cmax+π(R). This ratio coincides with the best known ratio for the parallel-machine scheduling with submodular penalties and the single machine scheduling problem with release dates and submodular rejection penalties.

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Approximation algorithms for precedence-constrained identical machine scheduling with rejection

Cited by 21 publications

References 19 publications

Single Machine Vector Scheduling with General Penalties

Single Machine Vector Scheduling with General Penalties

Single machine scheduling to maximize the weighted number of on-time jobs with job-rejection

A Combinatorial 2-Approximation Algorithm for the Parallel-Machine Scheduling with Release Times and Submodular Penalties

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