论文标题
生产控制模型中的最佳策略
Optimal strategies in a production-inventory control model
论文作者
论文摘要
假设客户需求的累积过程是由复合泊松过程给出的，那么我们考虑具有有限容量和两个不同生产率的生产控制模型。在任何时候都可以从不同的生产率转换，但是当库存过程达到存储最大容量时，必须关闭。我们考虑举行，生产，短缺和转换成本。该模型是由Doshi，Van der Duyn Schouten和Talman于1978年推出的。我们的目的是将预期的折扣累积成本最小化至无限级的所有可接受的切换策略。我们表明，不同生产率的最佳成本功能满足粘度意义上相应的方程式汉密尔顿 - 雅各比 - 贝尔曼系统，并证明了验证定理。最佳成本函数解决不同变异不平等的方式给出了最佳策略的开关区域，因此它仅取决于当前的生产率和库存水平。我们定义了有限的频段策略的概念，并使用量表函数来得出，这是带有一个或两个频段的频段策略不同成本的公式。我们还证明了Doshi等人提出的切换策略的例子。不是最佳策略。
We consider a production-inventory control model with finite capacity and two different production rates, assuming that the cumulative process of customer demand is given by a compound Poisson process. It is possible at any time to switch over from the different production rates but it is mandatory to switch-off when the inventory process reaches the storage maximum capacity. We consider holding, production, shortage penalty and switching costs. This model was introduced by Doshi, Van Der Duyn Schouten and Talman in 1978. Our aim is to minimize the expected discounted cumulative costs up to infinity over all admissible switching strategies. We show that the optimal cost functions for the different production rates satisfy the corresponding Hamilton-Jacobi-Bellman system of equations in a viscosity sense and prove a verification theorem. The way in which the optimal cost functions solve the different variational inequalities gives the switching regions of the optimal strategy, hence it is stationary in the sense that depends only on the current production rate and inventory level. We define the notion of finite band strategies and derive, using scale functions, the formulas for the different costs of the band strategies with one or two bands. We also show that there are examples where the switching strategy presented by Doshi et al. is not the optimal strategy.
