【摘要】：報童問題又被稱為單周期庫存問題，它是對短周期產(chǎn)品的訂購量做出最優(yōu)決策以滿足利潤最大或成本最小的隨機規(guī)劃模型。自從1888年著名經(jīng)濟學(xué)家Edgeworth應(yīng)用中心極限定理解決銀行的最優(yōu)儲備金(cash reserves)問題后，該模型逐漸受到國內(nèi)外研究者的重視，目前已被廣泛地應(yīng)用在生產(chǎn)、服務(wù)、物流、管理和金融等領(lǐng)域。 由于報童模型中含有多種不確定變量，確定最優(yōu)訂購量歷來是研究者們研究的主要問題。為了確定最優(yōu)訂購量，使決策者獲得更大的利潤空間，如何平衡訂購過量與訂購不足之間的矛盾已成為一個研究熱點。在銷售期結(jié)束前允許一次追加訂購能有效解決這一問題，這就是本文研究的主要內(nèi)容——二次訂購的報童模型。 針對二次訂購模型如何求解的問題，本文應(yīng)用兩階段方法建立了有補償?shù)亩斡嗁張笸Ｐ�，證明了補償模型與完全信息下的分段模型是等價的，并給出了模型的L型算法；針對決策者可能面臨的市場需求是未知分布函數(shù)的情形，研究了自由分布的二次訂購報童模型，，并得到了最優(yōu)訂購量與最優(yōu)利潤值的表達式，經(jīng)過與經(jīng)典報童模型做比較分析，得到二次訂購的確能使決策者的期望利潤增加的結(jié)論；最后基于隨機模糊理論，建立了隨機模糊需求環(huán)境下自由分布的二次訂購模型，并分析了最優(yōu)解的性質(zhì)，最后通過算例驗證了不確定性的增加使得最優(yōu)訂購量增大，同時最有可能獲得的利潤期望值減小的結(jié)論。
[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.
【學(xué)位授予單位】：華北電力大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：F224;F253

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