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Ordinal Semi On-line Scheduling for Jobs with Arbitrary Release Times on Identical Parallel Machines

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Intelligent Information Management 2017年第6期9卷 245-254页

作者： Sai Ji rongheng li Yunxia Zhou Key Laboratory of High Performance Computing and Stochastic Information Processing Department of Mathematics Hunan Normal University Changsha China Department of Computer Hunan Normal University Changsha China

In this paper, we investigate the problem of semi-on-line scheduling n jobs on m identical parallel machines under the assumption that the ordering of the jobs by processing time is known and the jobs have arbitrary release times. Our aim is to minimize the maximum completion time. An ordinal algorithm is investigated and its worst case ratio is analyzed.

关键词： Schedule Algorithm Worst Case Ratio Parallel Machines

On-line Scheduling for Jobs with Arbitrary Release Times on Parallel Related Uniform Machines

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Intelligent Information Management 2016年第4期8卷 98-102页

作者： Xiayan Cheng rongheng li Yunxia Zhou Department of Mathematics Hunan First Normal University Changsha China Department of Mathematics Key Laboratory of High Performance Computing and Stochastic Information Processing Hunan Normal University Changsha China Department of Computer Hunan Normal University Changsha China

A parallel related uniform machine system consists of m machines with different processing speeds. The speed of any machine is independent on jobs. In this paper, we consider online scheduling for jobs with arbitrary release times on the parallel uniform machine system. The jobs appear over list in terms of order. An order includes the processing size and releasing time of a job. For this model, an algorithm with competitive ratio of 12 is addressed in this paper.

关键词： Online Scheduling Uniform Machine Competitive Ratio Approximation Algorithm

<i>LPT</i>Algorithm for Jobs with Similar Sizes on Three Machines

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Applied Mathematics 2019年第11期10卷 947-955页

作者： Yajie Ma rongheng li Yunxia Zhou Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education) School of Mathematics and Statistics Hunan Normal University Changsha China College of Information Science and Engineering Hunan Normal University Changsha China

In this paper, LPT (largest processing time) algorithm is considered for scheduling jobs with similar sizes on three machines. The objective function is to minimize the maximum completion time of all machines. The worst case performance ratio of the LPT algorithm is given as a piecewise linear function of r if job sizes fall in [1, r]. Our result is better than the existing result. Furthermore, the ratio given here is the best. That means our result cannot be improved any more.

关键词： LPT Algorithm Parallel Machine Performance Ratio Schedule

Better Algorithm of Ordinal Online Schedule for Jobs with Similar Sizes on Two Machines

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American Journal of Operations Research 2019年第5期9卷 235-243页

作者： limin Wang rongheng li Yunxia Zhou Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education) Department of Mathematics School of Mathematics and Statistics Hunan Normal University Changsha China College of Information Science and Engineering Hunan Normal University Changsha China

Ordinal online schedule for jobs with similar sizes in on two parallel machines system is considered. Firstly it is proved that the worst case performance ratio of the existing algorithm P2 cannot be improved even if the job processing times are known in for any . Then a better algorithm named S is developed and its worst case performance ratio is given for? .

关键词： Semi-Online Scheduling Pm Algorithm S Algorithm Worst Performance Ratio

Facility Location Problem with Different Type of Clients

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Intelligent Information Management 2011年第3期3卷 71-74页

作者： lisheng Wang rongheng li Jingui Huang 不详

This paper proposes a new model of facility location problem referred to as k-product uncapacitated facility location problem with multi-type clients. The k-product uncapacitated facility location problem with multi- type clients consists of two set of sites, one is the set of demand points where clients are located and the other is the set of sites where facilities of unlimited capacities can be set up to serve the clients. Each facility can provide only one kind of products. Each client needs to be served by a set of facilities depending on which products it needs. Each facility can be set up only for one of the k products with a non-negative fixed cost determined by the product it is designated to provide. There is also a nonnegative cost of shipping goods between each pair of locations. The problem is to determine the set of facilities to be set up and to find an assignment of each client to a set of facilities so that the sum of the setup costs and the shipping costs is minimized. Under the assumption that the setting costs is zero and the shipping costs are in facilities centered metric space, it is shown that the problem with two kinds of clients is NP-complete. Furthermore a heuristic algorithm with worst case performance ratio not more than 2-1/k is presented for any integer k.

关键词： Heuristic Algorithm Complexity Facility Location

The proof of FFD(L)≤11/9OPT(L) +7/9

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Chinese Science Bulletin 1997年第15期42卷 1262-1265页

作者： li rongheng, YUE Minyi1. Department of Mathematics, Hunan Normal University, Changsha 410081, China 2. Institute of Applied Mathematics, Chinese Academy of Sciences, Beijing 100080, China Department of Mathematics Hunan Normal University Changsha China Institute of Applied Mathematics Chinese Academy of Sciences Reijing China

THE one-dimensional bin-packing problem is defined as follows: for a given list L={p1, p2,…, Pn}, where 0i≤1 denotes the item and its size as well, we are to pack all the items in-to bins, each of which has a capacity 1, and the goal is to minimize the number of bins *** first-fit-decreasing （FFD） algorithm is a famous approximate algorithm for the bin-pack-ing problem. The FFD algorithm first sorts all the list into non-increasing order and then pro-cesses the pieces in that order by placing each item into the first bin into which it fits.

关键词： bin-packing minimal counter-example weigtht-function FFD-algorithm.

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黄芪对肾小球疾病物质代谢紊乱的调节作用

中草药 1999年第5期30卷 386-388页

作者：周钦李荣亨重庆医科大学附属第-医院 400016

黄芪对肾小球疾病的物质代谢紊乱有调节作用。它能通过提高血浆白蛋白水平，降低尿蛋白排出量，增加肌肉蛋白贮备，提供必需氨基酸，从整体上改善肾小球疾病蛋白质代谢紊乱；其持久的降脂效应能有效地防治肾小球硬化；黄芪还可降低血糖... 详细信息

黄芪对肾小球疾病的物质代谢紊乱有调节作用。它能通过提高血浆白蛋白水平，降低尿蛋白排出量，增加肌肉蛋白贮备，提供必需氨基酸，从整体上改善肾小球疾病蛋白质代谢紊乱；其持久的降脂效应能有效地防治肾小球硬化；黄芪还可降低血糖，防治糖尿病性肾损害。

关键词：黄芪肾小球疾病蛋白质物质代谢紊乱

带有线性惩罚的鲁棒k-种产品设施选址问题的近似算法

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运筹学学报 2021年第4期25卷 31-44页

作者：李小玮成夏炎李荣珩湖南师范大学数学与统计学院湖南长沙410081 湖南第一师范学院信息科学与工程学院湖南长沙410205

k-种产品设施选址问题是指存在一组客户和一组可以建设设施的地址。现有k种不同的产品,每一客户均需要k种不同的产品,且每一设施最多只能生产一种产品。问题的要求是从若干地址中选择一组地址来建立设施,对所要建立的设施指定其生产的产... 详细信息

k-种产品设施选址问题是指存在一组客户和一组可以建设设施的地址。现有k种不同的产品,每一客户均需要k种不同的产品,且每一设施最多只能生产一种产品。问题的要求是从若干地址中选择一组地址来建立设施,对所要建立的设施指定其生产的产品,并为每一个客户提供一组指派确保每一客户都有k个设施来为其提供k种不同的产品,使得设施建设费用与运输费用之和最小。对于k-种产品设施选址问题,我们通常简写为k-PUFLP,其中,当所有设施建设费用为0时,记为k-PUFLPN。本文对k-PUFLPN进行线性舍入,通过分析最优分数解特殊结构,当k≥3时分析算法将k-PUFLPN的近似比从3k/2-1提升到了3k/2-3/2。鲁棒k-种产品设施选址问题是指在该问题中,最多有q个客户可以不被服务。我们首次对无容量限制下建设费用为0时的鲁棒k-种产品选址问题建立模型,当k≥3,得到了3k/2-3/2近似算法。对顾客伴有线性惩罚的鲁棒k-种产品设施选址问题,本文同时考虑异常值与惩罚性,利用k-PUFLPN中最优整数解与最优分数解的关系,得到了3k/2-3/2近似算法。

关键词：近似算法设施选址线性惩罚

带有次模惩罚的k-种产品设施选址问题近似算法

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应用数学学报 2022年第3期45卷 307-321页

作者：李小玮成夏炎李荣珩计算与随机数学教育部重点实验室复杂系统的控制与优化湖南省高校重点实验室湖南师范大学数学与统计学院长沙410081 湖南第一师范大学数学与统计学院长沙410205

本文我们研究了设施建设费用为零时的带线性惩罚的k-种产品设施选址问题与带次模惩罚的k-种产品设施选址问题.在带线性惩罚的k-种产品设施选址问题中,每一客户均对应一定的惩罚费用,目标是选择一个开设的设施集合,将一部分客户连接到开... 详细信息

本文我们研究了设施建设费用为零时的带线性惩罚的k-种产品设施选址问题与带次模惩罚的k-种产品设施选址问题.在带线性惩罚的k-种产品设施选址问题中,每一客户均对应一定的惩罚费用,目标是选择一个开设的设施集合,将一部分客户连接到开设的设施,使得这些客户对k种产品的需要均得到满足,同时对另一部分客户进行惩罚,并使得客户连接费用与客户惩罚费用之和最小.针对该问题特殊结构,当k≥3时我们得到了(3k/2)-(3/2)近似算法.在带次模惩罚的k-种产品设施选址问题中,客户的每个子集都对应一定的次模惩罚费用,我们给出了该问题的数学规划模型,结合问题的次模性,利用原始对偶算法,当k≥3时得到了(3k/2)-(3/2)近似算法.

关键词：近似算法设施选址原始对偶