仓库容量有限条件下的随机存贮管理

The Optimization of Random Storage Management on a Condition of Limited Storage Capacity

讨论了仓库容量有限条件下的随机存贮管理优化问题,认为时间是连续分布的.对于存贮一种商品的问题,根据订货点和自己仓库容量的关系分两种情况讨论,得到平均损失费与订货点、到货时间之间的关系式,利用实测数据拟合出到货时间的概率密度,建立了以平均损失费用的数学期望为目标函数的最优化模型,并使用MATLAB数学软件进行求解,得到三种商品的最优订货点分别为41,37和36.经过分析得知仓库容量与销售速率的比例、单位商品的损失费均对确定订货点都有重要影响.对于存贮多种商品的问题,根据到货时间的取值范围与两个时间临界点(销售完租借仓库中某种商品的时间和销售完所有该种商品的时间)之间的位置关系,将每种商品分为六种情况,m种商品组合起来,就有6m种不同情况,在此基础上,以m种商品的总体平均损失费用的数学期望作为目标函数,建立问题的最优化模型.针对题目中给出的三种商品的情形进行求解,得到最优订货点L*=4.807.最后,对销售速率随机的情形建立模型并进行了讨论.

This paper discusses the optimization of random storage management on a condition of limited storage capacity, in which time is considered to be consecutive. The discussion, concerning the problem of one commodity storage, can be put into two catalogs according to the relationship between ordering point and storage capability. The relationship between average loss, ordering point and commodity＇s arrival time is revealed in this essay. The establishment of optimization model, which takes the expectation of average loss as the objective function, is based on the probability density of arrival time fitted from the data recorded. Three optimum ordering points, 41,37 and 36,are achieved with the application of MATLAB to solve the model. The analysis demonstrates that the determination of ordering point is signiticandy influenced by the ratio between storage capability and sales＇ rate and by the unit loss of commodity. For the problem of multi - commodity storage, there are 6 possibilities for every commodity according to the relation between the range of arrival time and two critical time points. The various possibilities will be as many as 6^m when ra kinds of commodities are stored together. A mathematical model on this issue can be set up with the expectation of the overall average loss of all these m commodities to be the objective function. The optimum ordering point for the problem of three commodities, L^＊ = 4.807, is obtained with this model. Finally, another model for the situation of random sale rate is developed and further discussed.