泊松损耗过程下共享租赁商品(R,Q)库存模型研究

Research on(R,Q)Inventory Model for Sharing Rental Goods Under Poisson Loss Process

针对共享租赁商品存在泊松损耗过程时的库存管理问题,应用M/M/m/m排队理论,建立了以利润最大化为目标的(R,Q)库存模型,分析了共享租赁商品的最优订货点以及最优订货批量的相关性质。研究结果表明:在订货点一定时,利润是关于订货批量的凹函数;订货点不断增大时,订货批量不断接近经济订货批量(EOQ);给定订货批量,当订货点足够大时,利润是关于订货点的线性递减函数。最后,通过数值分析验证了模型结果的正确性和有效性。

Considering the inventory management problem of sharing rental goods under Poisson loss process, by applying of M/M/m/m queuing theory, a(R,Q)inventory model with profit maximization is established, the related properties of optimal order point and optimal order batch are analyzed. The research results show that: when ordering point is certain, profit is a concave function of order batch;asorder point keeps increasing, the order batch approaches economic order quantity(EOQ);when the order point is large enough for a given order batch, the profit is a linear decreasing function of the order point. Finally, the correctness and effectiveness of the model results are verified by numerical analysis.