论文总字数：25997字

摘 要

许多处于供应链中的公司往往需要同时管理现金和库存，与此同时它们也需要和其上下游的企业进行交易。在本文中，我们考虑一个随机的库存控制问题，建立一家可以同时进行金融决策和库存决策的企业。一方面，它可以进行存贷款决策，该公司获得现金的利息，并对其债务支付利息；另一方面，企业可以在合理的时间内延迟向其供应商付款，相应的，它也有可能延迟收到货款。也就是说，买方在采购后可以在几个周期之后支付采购成本。因此，买方可以进行投资并从客户产生的现金产生额外的利润。企业的每个时期的状态由当前时期的现金流水平和库存水平来衡量，最终目标是在有限的规划期结束时最大化公司资本的预期价值。在本文中，我们首先通过数学推导得出了一些普适性的结论，证明了最优策略的存在性和唯一性并得出了最优策略的结构。接着考虑特殊情况，即从延迟付款期限为1开始分析，扩展至延迟付款期限大于1 的情形。当延迟付款期限大于1的时候，我们采用数值实验的方式进行灵敏度分析，分析不同变量对结果的影响。研究表明，在同等情况下，持有现金比持有库存更具有价值。

关键词：随机库存，延迟支付，现金流

Abstract

Many companies in the supply chain often need to manage cash and inventory at the same time. At the same time, they also need to deal with their upstream and downstream companies. In this paper, we consider a random inventory control problem and establish a company that can make both financial and inventory decisions. On the one hand, it can make deposit and loan decisions. The company receives interest on cash and pays interest on its debts. On the other hand, the company can delay payment to their suppliers within a reasonable time. Correspondingly, the payment from its downstream company may be also delayed. That is to say, the buyer can pay for the purchase after several time periods after purchase. Therefore, the buyer can make an investment and generate additional profits from the cash generated by the customer. The status of each period of an enterprise is measured by the current period's cash flow level and inventory level. The ultimate goal is to maximize the expected value of the company's capital at the end of a limited planning period. In this paper, we first derive some general conclusions through mathematical derivation, and prove the existence and uniqueness of the optimal strategy and draw the structure of the optimal strategy. Then we consider the special case. The analysis begins with a delay payment period of 1 and extend it to a period with a deferred payment period of more than one.When the delay payment period is greater than 1, we use a numerical experiment to analyze the sensitivity and analyze the impact of different variables on the results. Research shows that holding cash is more valuable than holding inventory in the same situation.

KEY WORDS: stochastic inventory，cash flow，payment delay

目录

摘要..............................................................................................................................................I

Abstract.......................................................................................................................................II

第一章 引言............................................................................................................................ 1

1.1 研究背景.................................................................................................................1

1.2 研究内容.................................................................................................................1

第二章 文献综述....................................................................................................................3

2.1 国内外研究现状.....................................................................................................3

2.2 相关理论.................................................................................................................5

2.2.1 报童模型..........................................................................................................5

2.2.2 动态规划基本原理..........................................................................................6

第三章 考虑支付期和账期的多周期库存模型....................................................................8

3.1 模型建立.................................................................................................................8

3.2 特殊情况...............................................................................................................12

3.3 数值实验...............................................................................................................14

3.3.1 不同需求分布的影响...................................................................................,14

3.3.2 需求函数方差的影响....................................................................................17

3.3.3 均匀分布区间的影响....................................................................................19

3.3.4 不同期限条件的影响................................................................................... 19

第四章 结论与展望..............................................................................................................21

致谢............................................................................................................................................22

参考文献....................................................................................................................................23

附录............................................................................................................................................25

引言

1.1 研究背景

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