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Here, we revisit the bounded batch scheduling problem with nonidentical job sizes on single and parallel identical machines, with the objective of minimizing the makespan. For the single machine case, we present an algorithm which calls an online algorithm (chosen arbitrarily) for the one‐dimensional bin‐packing problem as a sub‐procedure, and prove that its worst‐case ratio is the same as the absolute performance ratio of . Hence, there exists an algorithm with worst‐case ratio , which is better than any known upper bound on this problem. For the parallel machines case, we prove that there does not exist any polynomial‐time algorithm with worst‐case ratio smaller than 2 unless P = NP, even if all jobs have unit processing time. Then we present an algorithm with worst‐case ratio arbitrarily close to 2. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 351–358, 2014 相似文献
393.
Previous research on the scheduling of multimachine systems has generally focused on the optimization of individual performance measures. This article considers the sequencing of jobs through a multimachine flow shop, where the quality of the resulting schedule is evaluated according to the associated levels of two scheduling criteria, schedule makespan (Cmax) and maximum job tardiness (Tmax). We present constructive procedures that quantify the trade-off between Cmax and Tmax. The significance of this trade-off is that the optimal solution for any preference function involving only Cmax and Tmax must be contained among the set of efficient schedules that comprise the trade-off curve. For the special case of two-machine flow shops, we present an algorithm that identifies the exact set of efficient schedules. Heruistic procedures for approximating the efficient set are also provided for problems involving many jobs or larger flow shops. Computational results are reported for the procedures which indicate that both the number of efficient schedules and the error incurred by heuristically approximating the efficient set are quite small. 相似文献
394.
Donald L. Bott 《海军后勤学研究》1977,24(3):407-416
In an inventory model, the distribution of total units demanded can be considered as a compound distribution arising from the distributions of demand occurrence and individual demand size. Three such compound distributions are considered, where the number of demands is Poisson distributed. The demand size distribution will depend on the observed or desired variance-to-mean ratio. An approximation using the gamma distribution is given in terms of the cumulants of the compound distribution for both fixed and stochastic lead times. 相似文献
395.
Consider a regulated monopolist whose current profits would be maximized if they could charge a price p?, where p? exceeds the current market price. By reducing production below current consumer demand the monopolist can create an illusion of a shortage and induce the regulator to allow a price increase. Conditions are given for which the production rate that maximizes the monopolist's expected discounted profits over an infinite horizon will have the property that the amount of unsatisfied consumer demand will be a non-increasing function of current market price. 相似文献
396.
A computationally feasible matrix method is presented to find the first-passage probabilities in a Markov chain where a set of states is taboo during transit. This concept has been used to evaluate the reliability of a system whose changes in strength can be thought of as a Markov chain, while the environment in which it is functioning generates stresses which can also be envisaged as another Markov chain. 相似文献
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关于振荡器相位噪声引起的GNSS接收机载波跟踪数字锁相环相位抖动,目前的解析结论仍是基于模拟锁相环的,不能说明相位抖动大小与中频积累时间的关系,因此不能有效指导高灵敏度、高精度载波跟踪锁相环参数设计.本文首先推导中频积累输出的频率白噪声、频率游走噪声序列的功率谱,然后基于数字二阶锁相环离散线性模型导出了环路相位抖动公式并进行了仿真验证,最后对公式进行了解析和数值分析.分析结果表明:频率白噪声、频率游走噪声引起的二阶载波跟踪锁相环相位抖动,均随中频积累时间单调递增,随环路带宽先递减后递增.本文推得的相位抖动公式及其随参数变化特征的分析结论,可用于具体指导GNSS载波跟踪锁相环参数设计. 相似文献