论文标题
在随机再生模型中对离散产品库存的最佳管理问题的研究，并连续消耗和随机延迟
A study of the problem of optimal management of discrete product inventory in the stochastic regeneration model with continuous consumption and random delivery delay
论文作者
论文摘要
本文认为，在再生方案中具有离散产品库存的最佳控制问题，并具有客户需求的泊松流。在系统中，允许递延需求，其数量受给定值的限制。控制参数是股票的水平，在该股票上，有必要在该股票上订购补货。管理有效性的指标是一个再生期内获得的平均特定利润。最佳控制问题是基于关于离散概率分布集对分数线性积分功能的极差的陈述解决的。这项工作的重要内容是分析表示的推导，以实现在再生期间获得的利润功能的数学期望。获得的分析表示使我们能够明确确定控制效率的固定成本指标，这是在研究的第一部分中引入的。因此，在所考虑的模型中，有可能在数值上解决库存的最佳控制问题。
The paper considers the optimal control problem of inventory of a discrete product in regeneration scheme with a Poisson flow of customer requirements. In the system deferred demand is allowed, the volume of which is limited by a given value. The control parameter is the level of the stock, at which achievement it is necessary to make an order for replenishment. The indicator of management effectiveness is the average specific profit received in one regeneration period. The optimal control problem is solved on the basis of the statement about the extremum of a fractional-linear integral functional on the set of discrete probability distributions. The significant content of the work is the derivation of analytical representations for the mathematical expectation of the increment of the functional of profit obtained during the regeneration period. The obtained analytical representations enable us to explicitly determine the stationary cost indicator of control efficiency, which was introduced in the first part of the research. Thus, it becomes possible to numerically solve the optimal control problem of inventory in the model under consideration.
