Computational Methods for Multi-Product Stochastic Inventory Control

这项拨款为开发有效的计算方法提供资金，以确定具有多种产品和相关需求的库存控制问题的最佳订购策略。对于单个产品案例来说，这个问题很容易解决，但由于问题的维度性，对多产品案例的跟踪方法面临着很大的挑战。为了避免维数的诅咒，本文提出了一种基于移动边界方法的方法。在移动边界框架下，人们首先对最优策略进行初步猜测，并估计使用该策略的价值。如果能够提出一种类似于政策改进、单调且保证收敛的边界更新程序，那么就可以在很大程度上简化解决多维问题所涉及的复杂性。随着研究的发展，还提出了一个库存控制博弈，参与者试图在随机需求存在的情况下控制多产品库存水平，不仅相互竞争，而且与最优策略竞争。这项工作的成功将在两个方面产生影响。在库存控制领域，这将是第一个可以解决具有大量产品类型的现实世界规模问题的计算方法。其次，该方法总体上发展了一种移动边界方法来解决脉冲控制问题。冲动控制问题出现在许多领域，包括金融、经济学和排队论。因此，研究人员将有可能在这些其他领域扩展或调整该方法以达到他们的目的。随机控制博弈可以直观地感受不确定条件下的决策挑战，丰富选修库存控制课程的学生的学习经验。

This grant provides funding for the development of efficient computational methods to determine optimal ordering policies for inventory control problems with multiple products and correlated demands. While the problem is fairly easy and well solved for the single product case, methods to tract the multiple product case face a significant challenge due to the dimensionality of the problem. To avoid the curse of dimensionality, this work proposes on developing a method based on the moving boundary approach. Under a moving boundary framework, one begins with an initial guess for the optimal policy and an estimate of the value of using that policy. If one can then come up with a boundary update procedure that is akin to policy improvement, is monotone and guarantees convergence, then one can to a large extent simplify the complexity involved in solving multi-dimensional problems. An inventory control game is also proposed alongside the development of the research where participants try controlling multi-product inventory levels in the presence of stochastic demand, competing not only against each other but also against the optimal policy.Success in this work would have an impact in two areas. In the area of inventory control, this would be the first computational method that can solve problems that are of the real-world size, with a large number of product types. Second, the proposed method in general develops a moving boundary approach to solving impulse control problems. Impulse control problems arise in a variety of areas that include finance, economics and queuing theory. Hence researchers would potentially be able to extend or adapt the method for their purposes in these other areas. The stochastic control game can provide a direct feel for the challenges in decision making under uncertainty and enrich the learning experience of students taking courses that cover inventory control.