考虑共享机器租借费用的在线订单加工策略及竞争分析

探究了拥有两台平行机资源的制造商在共享制造环境下的实时加工调度决策问题。结合租赁外部共享机器的固定成本与可变成本因素，运用在线理论与竞争分析方法构建了平行机调度over-list在线模型，其最小化目标是工件总完工时间与机器租赁总成本之和。针对工件均为单位长度的情形，分析了问题离线最优方案，进而证明了竞争比下界为■,其中，a为固定租赁成本系数，b(0≤b+时，该下界趋于4/3;同时，设计给出了在线策略TS,并证明当a=2时该策略竞争比为4/3;当a≥3时，其竞争比为1.89。     

三台平行机排序的一个复合半在线问题的算法

本文讨论一个三台平行机半在线排序问题.对预先知道工件的总加工时间和最大的工件的加工时间的复合半在线模型,我们证明了不存在半在线算法,其竞争比为4/3,并给出了一个竞争比为7/5的半在线算法,两者的差距小于0.067.     

在线社交网络虚假信息交互量最小化的边阻断策略研究

在线社交媒体的蓬勃发展改变了人们获取信息的模式,大量的信息通过社交平台传播,信息内容的真实性把关弱化,各类虚假信息依托社交媒体野蛮生长,网络空间治理,培育健康的网络生态意义重大。本文通过最小化用户之间的虚假信息交互量,研究社交网络中虚假信息传播路径的阻断策略。给定在线社交网络G=（V,E,P,H）,H表示用户之间信息交互量,已知虚假信息传播源集合S⊆V,虚假信息交互量最小化问题是从E中选取哪K条边,使得这些边被阻断之后,虚假信息在用户之间的交互总量最小。首先证明了该问题是NP-困难的,进而证明了问题的目标函数计算是#P-困难。其次,证明了该问题目标函数既不是次模函数也不是超模函数。再次,提出了两阶段贪婪算法（TSGA）来解决该问题,即先获取候选集合E^sa,然后选取阻断集合E'。最后,通过实际在线社交网络数据对模型和算法的有效性进行了分析,实验表明本文提出的算法比现有算法更加有效。     

无统计信息假设下的多阶段报童决策

在不对需求做任何统计假设的情形下,该文用理论计算科学兴起的集成专家意见的弱集成算法研究多阶段报童决策。弱集成算法是一种指数加权平均集成方法,在一定的初始权重下,根据损失函数在线调整专家意见的权重。基于收益损失函数和固定订购量的专家意见,得到了与从累积收益角度研究相一致的决策方法;并扩展研究了带有回收价值的情形。理论上证明了决策方法的累积收益损失几乎不超过最优专家意见的累积收益损失。通过数值算例验证了决策方法的可行性和合理性,探讨了卖出价和成本价等因素对竞争性能的影响,说明了回收价值的引入大大提高了决策方法的竞争性能,具有重要的现实意义。     

资源受限下平行工序顺序对优化的0-1规划模型

资源受限是工程项目时刻都可能面对的挑战。由于资源限制,需要将原项目计划中相互之间无优先关系的平行工序调整为顺序工序。平行工序顺序化可导致项目工期延迟,因此需考虑如何使项目工期延迟最小。该平行工序顺序优化问题是项目调度问题,也是排列组合问题,通常难度很大,包括一些NP-hard问题。本文主要研究该问题的一类典型子问题——平行工序顺序对优化,即如何将项目中某2n个平行工序调整为n个顺序工序对,并且对项目工期的影响最小。该问题的总方案数可达到（2n）!/n!。本文借助工序网络（如CPM网络）,运用简单的时间参数量化了平行工序顺序化对项目工期的影响,进而降低问题的求解难度,建立了纯0-1规划模型。实验验证了该模型的求解效率,求解100个平行工序规模的问题平均耗时0.2605秒,而求解500个平行工序规模的问题平均耗时10.66秒。     

考虑加工与运输协同调度的单机排序问题

在考虑加工与运输协同调度的单机排序问题中,每个工件尺寸不同,工件在一台机器加工后,由m辆有容量限制的运输工具运送到同一个顾客处,目标是极小化最后一个送到其顾客的工件的到达时间,本文给出了该问题的一个最优算法,并且证明了该算法的最坏情况界为3/2。     

可折旧设备在线租赁的随机性竞争策略

应用在线算法与竞争分析研究在线租赁问题是近年来国内外的一个研究热点.在一般设备在线租赁的基础上,提出了可折旧设备在线租赁问题.针对离线人具有遗忘性竞争对手的特点分别给出了可折旧设备在线租赁在有无利率情形下的随机性竞争策略.基于在线-离线成本比值矩阵分别证明了有无利率下随机性策略的竞争比,说明了折旧因素的引入使得可折旧设...     

预知两种信息带准备时间的平行机半在线排序

本文研究了P2,rj/sum & max/Cmax问题,即预知所有工件加工时间总和sum和最大工件加工时间max的两台处理器的带准备时间的半在线问题,并给出了竞争比为6/5的最优半在线算法.     

考虑完成期限的电子商务在线订单分批模型及算法

在电子商务在线订单拣选系统中,订单到达时间和订购商品等信息未知。针对拣选设备容量、员工人数等资源有限约束情况,研究在何时、对多少订单进行分批优化,以保证在订单完成期限前以最短的时间拣出最多的订单。构建考虑订单完成期限的在线订单分批混合整数规划模型,以最小化平均有效订单服务时间,采用改进的固定时间窗订单分批启发式规则求解模型,定义剩余操作时间在[前置时间,配送准备时间]内的订单为紧急订单,构建综合考虑紧急程度和相似度因素的在线订单分批算法。采用某配送中心14：00～18：00时间段内以泊松分布（λ＝17）随机生成的订单进行数据实验,将实验结果与传统固定时间窗在线订单分批算法进行比较。研究结果表明,考虑完成期限时,系统拣选配送的订单数量更多,总服务时间和平均有效订单服务时间更短,且出现延迟订单的数量更少,延迟时间更短。拣选员工人数的增多在不同程度上提高配送率,且考虑完成期限时,配送率提高幅度要大于传统算法;但随着人数的增加,配送率的提高幅度呈降低趋势。     

时间窗口约束下基于改进蚁群算法的协同制造调度研究

与传统调度模式不同，协同制造模式下企业之间的调度模式极其复杂。协同企业间的加工工序路线并不固定，且不同类型产品具有不同的加工路线网络。为此本文针对平衡型、瓶颈型、跳跃型、混合型四类具有典型特点的协同制造网络G_p进行分析和设计；考虑制造企业同类产品合并加工策略，构建基于连续加工量的分段生产成本函数；通过设计合理的订单最早交货时间和最晚交货时间，对订单交货进行时间窗口约束，并在此基础上构建了由制造商生产成本W_c^m、订单等待W_s^k（Q_k， T'_k）和提前完工库存成本W_s^k（Q_k， T″_k）、延期惩罚成本构成W_l^k（Q_k， T'″_k）的目标函数。为求解该模型，创新性将蒙特卡洛思想引入蚁群算法，提高蚂蚁选择合理性，避免局部最优；同时，采用移动窗口[min， max]奖励机制，并且对信息素奖励乘以平衡系数k（N）提高奖励可信度，加快搜索速度并提高求解性能。仿真结果表明，本文构建调度模型合理，可以获得优化的调度结果；同时，本文提出的蚁群改进寻优算法具有良好的求解速度和收敛性，算法具有较好的稳定性。     

Single machine batch scheduling with release times

Motivated by a high-throughput logging system, we investigate the single machine scheduling problem with batching, where jobs have release times and processing times, and batches require a setup time. Our objective is to minimize the total flow time, in the online setting. For the online problem where all jobs have identical processing times, we propose a 2-competitive algorithm and we prove a corresponding lower bound. Moreover, we show that if jobs with arbitrary processing times can be processed in any order, any online algorithm has a linear competitive ratio in the worst case. A preliminary version of a part of this paper was presented at the 31st International Symposium on Mathematical Foundations of Computer Science (MFCS 2006). We gratefully acknowledge reviewers’ comments that helped to improve the presentation of this work. Supported by the Swiss SBF under contract no. C05.0047 within COST-295 (DYNAMO) of the European Union. Research carried out while B. Weber was affiliated with the Institute of Theoretical Computer Science, ETH Zurich.     

From theory to practice: maximizing revenues for on-line dial-a-ride

We consider the on-line dial-a-ride problem, where a server fulfills requests that arrive over time. Each request has a source, destination, and release time. We study a variation of this problem where each request also has a revenue that the server earns for fulfilling the request. The goal is to serve requests within a time limit while maximizing the total revenue. We first prove that no deterministic online algorithm can be competitive unless the input graph is complete and edge weights are unit. We therefore focus on these graphs and present a 2-competitive algorithm for this problem. We also consider two variations of this problem: (1) the input graph is complete bipartite and (2) there is a single node that is the source for every request, and present a 1-competitive algorithm for the former and an optimal algorithm for the latter. We also provide experimental results for the complete and complete bipartite graphs. Our simulations support our theoretical findings and demonstrate that our algorithms perform well under settings that reflect realistic dial-a-ride systems.     

Online MapReduce processing on two identical parallel machines

In this work we investigate the online over-list MapReduce processing problem on two identical parallel machines, aiming at minimizing the makespan. Jobs are revealed one by one, and each job consists of one map task and one reduce task. The map task can be arbitrarily split and processed on both machines simultaneously, while the reduce task has to be processed on a single machine and it cannot be started unless the map task has been completed. We first show that the general case of the problem reduces to the classical two machine online scheduling model with an optimal competitive ratio of 3/2. For a special case where the map task is at least as long as the reduce task, we prove that no online algorithm can be less than 4/3-competitive. An optimal Greedy algorithm with a matching competitive ratio is proposed as well.     

Competitive analysis for make-to-order scheduling with reliable lead time quotation

This paper makes extended studies on the discrete problem of online scheduling and reliable lead time quotation (discrete Q-SLTQ) introduced by Keskinocak et al. (Manag. Sci. 47(2):264–279, 2001). We first relax the assumption on revenue function from a linear decreasing function to any decreasing function. We present an online deterministic strategy which is optimal in competitiveness for concave revenue functions. The above results are further extended to the continuous Q-SLTQ model where orders are released at arbitrary time points. For the discrete Q-SLTQ problem, if orders are with nonuniform lengths, we prove the nonexistence of online strategies with bounded competitive ratios; otherwise if orders are with unit length but various weights, we present an optimal online strategy.     

Dynamic work hour optimization for casual workers

An original online problem named the work-break problem is proposed to optimize the work hours of casual workers. The algorithm for our problem has to answer for a casual worker about when he should have a break for his efficiency declines with the growing duration of current work period. We consider the online uncertainty of the work efficiency and present a periodic algorithm for the problem. Then our algorithm is proved to be 2-competitive by a novel form of competitive analysis.     

Online interval scheduling: randomized and multiprocessor cases

We consider the problem of scheduling a set of equal-length intervals arriving online, where each interval is associated with a weight and the objective is to maximize the total weight of completed intervals. An optimal 4-competitive algorithm has long been known in the deterministic case, but the randomized case remains open. We give the first randomized algorithm for this problem, achieving a competitive ratio of 3.5822. We also prove a randomized lower bound of 4/3, which is an improvement over the previous 5/4 result. Then we show that the techniques can be carried to the deterministic multiprocessor case, giving a 3.5822-competitive 2-processor algorithm, and a 4/3 lower bound for any number of processors. We also give a lower bound of 2 for the case of two processors. A preliminary version of this paper appeared in the Proceedings of COCOON 2007, LNCS, vol. 4598, pp. 176–186. The work described in this paper was fully supported by a grant from City University of Hong Kong (SRG 7001969), and NSFC Grant No. 70525004 and 70702030.     

Randomized Online Scheduling with Delivery Times

We study one of the most basic online scheduling models, online one machine scheduling with delivery times where jobs arrive over time. We provide the first randomized algorithm for this model, show that it is 1.55370-competitive and show that this analysis is tight. The best possible deterministic algorithm is 1.61803-competitive. Our algorithm is a distribution between two deterministic algorithms. We show that any such algorithm is no better than 1.5-competitive. To our knowledge, this is the first lower bound proof for a distribution between two deterministic algorithms.     

Online integrated production–distribution scheduling problems without preemption

We study an integrated production–distribution scheduling problem where jobs are released by customers to a manufacturer over time. The jobs are released online, that is, at any time the information of the number, release and processing times of future jobs is unknown, and the processing time of a job becomes known when the job is released. The manufacturer processes the jobs on a single machine. During the processing of jobs preemption is not allowed. Completed jobs are delivered in batches to customers via sufficient capacitated vehicles. For the objective of minimizing the sum of the total delivery time and the total distribution cost, we present a 3-competitive algorithm for the single-customer case and then extend the result to the multi-customer case. A lower bound of two on the competitive ratio of the problem is also given.     

On-Line Scheduling Algorithms for a Batch Machine with Finite Capacity

We study the problem of on-line scheduling jobs with release dates on a batch machine of finite capacity with the objective of minimizing the makespan. We generalize several existing algorithms for the problem to a class of on-line algorithms that are 2-competitive for any arbitrary finite machine capacity. Then, we show that one of these generalized algorithms is in fact 7/4-competitive for machine capacity 2. This is the first on-line algorithm for a finite machine capacity with competitive ratio less than 2.This research is substantially supported by a grant from City Univ. of Hong Kong (Grant No. 7001119). The second author is supported by this grant and by the Natural Science Foundation of China.     

A Tighter Extra-Resource Analysis of Online Deadline Scheduling

This paper is concerned with online algorithms for scheduling jobs with deadlines on a single processor. It has been known for long that unless the system is underloaded, no online scheduling algorithm can be 1-competitive, i.e., matching the performance of the optimal offline algorithm. Nevertheless, recent work has revealed that some online algorithms using a moderately faster processor (or extra processors) can guarantee very competitive performance Kalyanasundaram and Pruhs, 2000 or even be 1-competitive Koo et al., 2002; Lam and To, 2001. This paper takes a further step to investigate online scheduling algorithms with an even higher performance guarantee (i.e., better than 1-competitive algorithms) and in particular, presents an extra-resource analysis of the earliest-deadline-first strategy (EDF) with respect to such a higher performance guarantee.A preliminary version of this paper has been accepted by The Australian Theory Symposium on Computing, 2004.This research was supported in part by Hong Kong RGC Grant HKU-7024/01E.