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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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影响图建模算法的改进 总被引:1,自引:0,他引:1
影响图建模方法是一种规范化的复杂系统建模方法,其实质是将表征复杂系统的参量及参量间的耦合关系进行分类,并以此为基础建立系统的数学模型.影响图建模算法就是将系统的参量及参量间的耦合关系进行分类的算法.目前使用的算法是James R.Burns于1979年提出的.该算法仅考虑了最小的反馈回路,而没有考虑影响图中存在的一般反馈回路,且一些操作造成了不必要的循环.在分析该算法的基础上,考虑了一般的反馈回路,并对原算法的操作步骤进行了优化重组. 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
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This paper gives a new organization of the theoretical results of the Generalized Transportation Problem with capacity constraints. A graph-theoretic approach is utilized to define the basis as a one-forest consisting of one-trees (a tree with an extra edge). Algorithmic development of the pivot-step is presented by the representation of a two-tree (a tree with two extra edges). Constructive procedures and proofs leading to an efficient computer code are provided. The basic definition of an operator theory which leads to the discussion of various operators is also given. In later papers we will present additional results on the operator theory for the generalized transportation problem based on the results in the present paper. 相似文献
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This paper investigates the effect on the optimum solution of a (capacitated) transportation problem when the data of the problem (the rim conditions-i. e., the warehouse supplies and market demands-the per unit transportation costs and the upper bounds) are continuously varied as a (linear) function of a single parameter. An operator theory is developed and algorithms provided for applying rim and cost operators that effect the transformation of optimum solution associated with changes in rim conditions and unit costs. Bound operators that effect changes in upper bounds are shown to be equivalent to rim operators. The discussion in this paper is limited to basis preserving operators for which the changes in the data are such that the optimum basis structures are preserved. 相似文献