基于库存价值改变和随机需求的经济订货批量模型

Economic Order Quantity Model for Value Change Inventory with Random Demand

大多数库存研究的重点都集中在各种复杂的限制条件和模型的变换上,没有考虑到库存本身可能发生贬值或增值的情况,而实际中库存本身常常会发生价值变化。针对以往库存模型中没有考虑库存价值变化的问题,提出了在需求为随机连续分布、库存价值发生变化情况下的单周期经济订货批量模型,给出了最优订货策略。模型中以先进先出为假设条件,基于报童模型的思想,以订货量为决策变量、期望收益为目标函数,结合随机需求的分布情况得到最优订货量和最大期望收益,并给出了相应的数学证明。通过算例对模型进行说明,并对影响最优订货批量和最大期望收益的各个参数进行敏感性分析。

Most of research on inventory control focus on the complex restrictions and transforms of mathematical model, without considering the situation that the value of inventory may add or depreciate. However, inventory value will increase or reduce in the real world. To solve this problem, this paper set up a single cycle economic order quantity model under the condition that the value changing of inventory will happen. According to the stochastic demand, the optimal order policy was given. Based on the assumption of first-in-first-out, the model combined the idea of newsboy problems, used the order quantity as the decision variable, set up an objective function for expected profit and provided mathematical proof, with considering the stochastic demand, optimal order quantity and optimal expected profit. The results were illustrated with numerical examples and sensitivity analysis was provided for related parameters.