Improved approximation algorithms for parallel machine scheduling with release dates and job rejection

Zhong, Xingming; Ou, Jinwen

doi:10.1007/s10288-016-0339-6

Cited by 25 publications

(6 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently, He et al [10] and Ou et al [11] independently designed an improved approximation algorithm with a running time of O(n log n). More related results can be found in the surveys [12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 65%

Single Machine Vector Scheduling with General Penalties

Liu

Zhu

2021

Mathematics

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 65%

Single Machine Vector Scheduling with General Penalties

Liu

Zhu

2021

Mathematics

View full text Add to dashboard Cite

show abstract

“…They developed a 2-approximation algorithm. This result is further improved by Zhong and Ou [4] who designed a PTAS. Li et al [5] designed a PTAS for a variant of MSR, where the objective is to minimize the makespan when the rejection cost is bounded by a given constant.…”

Section: Introductionmentioning

confidence: 87%

“…where the first inequality follows from t 1 ≤ t 2 , the second inequality follows from the submodularity of π(•), and the third inequality follows from inequality (4). It implies that…”

Section: Lemmamentioning

confidence: 95%

Approximation Algorithm for the Single Machine Scheduling Problem with Release Dates and Submodular Rejection Penalty

Liu

2020

Mathematics

View full text Add to dashboard Cite

In this paper, we consider the single machine scheduling problem with release dates and nonmonotone submodular rejection penalty. We are given a single machine and multiple jobs with probably different release dates and processing times. For each job, it is either accepted and processed on the machine or rejected. The objective is to minimize the sum of the makespan of the accepted jobs and the rejection penalty of the rejected jobs which is determined by a nonmonotone submodular function. We design a combinatorial algorithm based on the primal-dual framework to deal with the problem, and study its property under two cases. For the general case where the release dates can be different, the proposed algorithm have an approximation ratio of 2. When all the jobs release at the same time, the proposed algorithm becomes a polynomial-time exact algorithm.

show abstract

“…We have the following properties on

I'_{1}

. The proof makes use of some techniques in .LEMMA If

{\overset{Γ}{true}}_{1} \neq \emptyset

, then there is a feasible solution

{\overset{σ}{true}}_{2}

I'_{1}

in which (i) all jobs with

a'_{j} = m + 1

are rejected; and (ii) the makespan of the accepted jobs is no greater than

C^{*} + 4 Δ_{1}

. …”

Section: Bicriteria Problemsmentioning

confidence: 99%

“…They developed an efficient 2‐approximation, and an FPTAS with a time complexity of

O (n^{2 m + 1} / ε^{m})

with m being a given fixed number. Zhong and Ou studied the same model in and presented a faster 2‐approximation, a faster FPTAS, and a PTAS. Ou and Zhong considered PMSR with service level constraints, where the number of rejected jobs is not allowed to be greater than a predefined value.…”

Section: Introductionmentioning

confidence: 99%

Scheduling parallel machines with inclusive processing set restrictions and job rejection

Zhong

2016

Naval Research Logistics

Self Cite

View full text Add to dashboard Cite

In this article, we study a parallel machine scheduling problem with inclusive processing set restrictions and the option of job rejection. In the problem, each job is compatible to a subset of machines, and machines are linearly ordered such that a higher‐indexed machine can process all those jobs that a lower‐indexed machine can process (but not conversely). To achieve a tight production due date, some of the jobs might be rejected at certain penalty. We first study the problem of minimizing the makespan of all accepted jobs plus the total penalty cost of all rejected jobs, where we develop a ( 5 3 + ε ) ‐approximation algorithm with a time complexity of O ( n 2 / ε 2 ) . We then study two bicriteria variants of the problem. For the variant problem of minimizing the makespan subject to a given bound on the total rejection cost, we develop a ( 5 3 + ε ) ‐approximation algorithm with a time complexity of O ( n m ε 2 · log P ) . For the variant problem of maximizing the total rejection cost of the accepted jobs subject to a given bound on the makespan, we present a 0.5‐approximation algorithm with a time complexity of O ( n log n ) . © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 667–681, 2017

show abstract

Improved approximation algorithms for parallel machine scheduling with release dates and job rejection

Cited by 25 publications

References 19 publications

Single Machine Vector Scheduling with General Penalties

Single Machine Vector Scheduling with General Penalties

Approximation Algorithm for the Single Machine Scheduling Problem with Release Dates and Submodular Rejection Penalty

Scheduling parallel machines with inclusive processing set restrictions and job rejection

Contact Info

Product

Resources

About