零部件检查与预防性更换的最优化模型

An Optimizing Model for Checking and Preventive Parts Changing

运用随机性数学模型的概率分布建模方法 ,对于如何解决生产部门的设备在长期运行时 ,由于零部件损坏而使其不能正常运行 ,从而造成经济损失的问题 ,提出了一种结合零部件的检查和预防性更换的模型 ,使得在所获得的检查间隔和预防性更换周期下 ,生产单位产品的损失费用期望值达到最小 .在建模过程中 ,我们把双变量求极值问题转化为求单变量极值问题 ,大大减少了计算量 .文中把模型应用于 1999年数模竞赛题目的一个实际问题中 ,介绍了如何根据实际情况应用本模型及进一步简化运算的方法 。

In the production process, the equipment will be out of work because of the damage of the parts, causing economic loss. To deal with this problem, we set up a mathematical model which combines the checking model and preventive changing model by using the probability distribution modeling method. Using this model, we get the checking interval as well as preventive changing period and minimize the expected loss of per unit product. In the process of modeling, we change the bivariable extremum problem to a single variable extremum one, which decreases the computing load. In addition, we apply the model to a practical problem of MCM China 1999 and introduce how to use it according to the practice as well as how to simplify the calculation. We get a good result.