二次订购报童模型的理论和算法研究

发布时间：2019-02-17 19:32

【摘要】：报童问题又被称为单周期库存问题，它是对短周期产品的订购量做出最优决策以满足利润最大或成本最小的随机规划模型。自从1888年著名经济学家Edgeworth应用中心极限定理解决银行的最优储备金(cash reserves)问题后，该模型逐渐受到国内外研究者的重视，目前已被广泛地应用在生产、服务、物流、管理和金融等领域。由于报童模型中含有多种不确定变量，确定最优订购量历来是研究者们研究的主要问题。为了确定最优订购量，使决策者获得更大的利润空间，如何平衡订购过量与订购不足之间的矛盾已成为一个研究热点。在销售期结束前允许一次追加订购能有效解决这一问题，这就是本文研究的主要内容——二次订购的报童模型。针对二次订购模型如何求解的问题，本文应用两阶段方法建立了有补偿的二次订购报童模型，证明了补偿模型与完全信息下的分段模型是等价的，并给出了模型的L型算法；针对决策者可能面临的市场需求是未知分布函数的情形，研究了自由分布的二次订购报童模型，，并得到了最优订购量与最优利润值的表达式，经过与经典报童模型做比较分析，得到二次订购的确能使决策者的期望利润增加的结论；最后基于随机模糊理论，建立了随机模糊需求环境下自由分布的二次订购模型，并分析了最优解的性质，最后通过算例验证了不确定性的增加使得最优订购量增大，同时最有可能获得的利润期望值减小的结论。
[Abstract]:The newsboy problem is also called the single-cycle inventory problem. It is a stochastic programming model which makes the optimal decision on the order quantity of the short-period product to satisfy the maximum profit or the minimum cost. Since the famous economist Edgeworth applied the limit theorem of center to solve the (cash reserves) problem of bank's optimal reserve in 1888, the model has been paid more and more attention by domestic and foreign researchers, and has been widely used in production, service and logistics. Areas such as management and finance Because there are many uncertain variables in the newsboy model, the determination of the optimal order quantity has always been the main problem studied by researchers. In order to determine the optimal order quantity and make the decision makers gain more profit space, how to balance the contradiction between excessive ordering and insufficient ordering has become a hot research topic. Allowing one additional order before the end of the sales period can effectively solve this problem, which is the main content of this paper-the newsboy model of secondary order. Aiming at the problem of how to solve the quadratic ordering model, this paper applies the two-stage method to establish a compensated second-order newsboy model. It is proved that the compensation model is equivalent to the piecewise model with complete information, and the L-type algorithm of the model is given. In view of the situation that the market demand that decision makers may face is unknown distribution function, the free distribution quadratic order newsboy model is studied, and the expressions of optimal order quantity and optimal profit value are obtained, which are compared with the classical newsboy model. Get the conclusion that the second order can increase the expected profit of the decision maker; Finally, based on the stochastic fuzzy theory, a quadratic ordering model with free distribution in the environment of random fuzzy demand is established, and the properties of the optimal solution are analyzed. Finally, an example is given to verify that the increase of uncertainty makes the optimal order quantity increase. At the same time the most likely profit expectations to reduce the conclusion.
【学位授予单位】：华北电力大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F253

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