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31.
We consider the problem of scheduling a set of n jobs on a single batch machine, where several jobs can be processed simultaneously. Each job j has a processing time pj and a size sj. All jobs are available for processing at time 0. The batch machine has a capacity D. Several jobs can be batched together and processed simultaneously, provided that the total size of the jobs in the batch does not exceed D. The processing time of a batch is the largest processing time among all jobs in the batch. There is a single vehicle available for delivery of the finished products to the customer, and the vehicle has capacity K. We assume that K = rD, where and r is an integer. The travel time of the vehicle is T; that is, T is the time from the manufacturer to the customer. Our goal is to find a schedule of the jobs and a delivery plan so that the service span is minimized, where the service span is the time that the last job is delivered to the customer. We show that if the jobs have identical sizes, then we can find a schedule and delivery plan in time such that the service span is minimum. If the jobs have identical processing times, then we can find a schedule and delivery plan in time such that the service span is asymptotically at most 11/9 times the optimal service span. When the jobs have arbitrary processing times and arbitrary sizes, then we can find a schedule and delivery plan in time such that the service span is asymptotically at most twice the optimal service span. We also derive upper bounds of the absolute worst‐case ratios in both cases. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 470–482, 2015 相似文献
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计算了一类二次Hamilton微分系统的一阶Mel’nikov函数,通过此方法对该系统在三次多项式扰动下分岔的极限环个数进行了估计。 相似文献
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介绍了可以用扩展可靠性框图表示的系统的可靠性参数的仿真算法。首先,对扩展可靠性框图进行了介绍,提出了利用树状结构来描述扩展可靠性框图的结构。其次,对基于扩展可靠性框图的系统行为进行了分析。然后,依据离散事件系统仿真思想,分别给出了计算可修系统可靠性参数的仿真算法与不可修系统可靠性参数的仿真算法。最后,给出了计算实例。该仿真算法不仅可以对状态独立系统进行可靠性参数计算,而且可以对具有冷储备关系以及冷储备嵌套关系的状态相关系统进行可靠性参数计算,具有很强的通用性与实用性。 相似文献
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We consider the problem of nonparametric multi-product dynamic pricing with unknown demand and show that the problem may be formulated as an online model-free stochastic program, which can be solved by the classical Kiefer-Wolfowitz stochastic approximation (KWSA) algorithm. We prove that the expected cumulative regret of the KWSA algorithm is bounded above by where κ1, κ2 are positive constants and T is the number of periods for any T = 1, 2, … . Therefore, the regret of the KWSA algorithm grows in the order of , which achieves the lower bounds known for parametric dynamic pricing problems and shows that the nonparametric problems are not necessarily more difficult to solve than the parametric ones. Numerical experiments further demonstrate the effectiveness and efficiency of our proposed KW pricing policy by comparing with some pricing policies in the literature. 相似文献
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D J L Moore 《Whitehall Papers》2013,80(1):13-22
Abstract David Moore analyses the role of the Treasury in detemining and controlling defence policy and expenditure, and the place of the MoD within this function. 相似文献
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This paper considers the production of two products with known demands over a finite set of periods. The production and inventory carrying costs for each product are assumed to be concave. We seek the minimum cost production schedule meeting all demands, without backlogging, assuming that at most one of the two products can be produced in any period. The optimization problem is first stated as a nonlinear programming problem, which allows the proof of a result permitting the search for the optimal policy to be restricted to those which produce a product only when its inventory level is zero. A dynamic programming formulation is given and the model is then formulated as a shortest route problem in a specially constructed network. 相似文献