Adaptive Inventory Control for Partially Observed, Non-Stationary Demand

9813127Sox该项目将解决部分观察到的非平稳随机需求的库存控制问题。当需求在给定时间段内的概率分布不确定时，需求过程是部分观察到的。相反，它只是通过之前的随机变量的需求观察部分观察到的。需求过程是非平稳的，即需求的概率分布可能在一个时间段内随机变化，这种变化是未知的，而是通过随机需求观测间接观察到的。该问题被建模为一个复合状态、部分观察的马尔可夫决策过程。最优控制策略的结构结果将发展为广泛的问题，包括延期订购，销售损失，零和非零固定订单成本，以及积极的交货时间。由于计算最优策略需要计算和内存，因此该项目还将开发一系列次优控制策略，这些策略在工业中具有更大的应用潜力。这些策略将在广泛的问题实例上进行测试，并与最优策略或下界进行比较。这些政策还将与工业中通常使用的战略进行比较，以评估其潜在的工业影响。随着产品生命周期的不断缩短，以及竞争和产品扩散等市场因素增加了单个产品需求的波动性，这个问题变得越来越重要。在这种环境下，经典的库存模型是无效的。信息的价值和信息在控制策略构建中的有效利用是这一问题中的重要问题。该项目的研究结果将对供应链规划中的相关问题以及其他具有类似不确定性结构的问题（如过程控制、维护和产量规划）产生更广泛的影响。这个项目的直接实际效益将是制定库存控制政策，在面对极不确定的客户需求时，改善客户服务，降低库存和生产成本。

9813127Sox This project will address inventory control problems with partially observed, non-stationary random demand. A demand process is partially observed when the probability distribution of demand in a given time period is not known with certainty. Instead, it is only partially observed through the previous demand observations which are random variables. The demand process is non-stationary in that the probability distribution of demand may randomly change from one time period to the next, and such a change is not known but is indirectly observed through the random demand observations. The problem is modeled as a composite-state, partially observed Markov decision process. Structural results for optimal control policies will be developed for a wide range of problems that include backordering, lost sales, zero and non-zero fixed order cost, and positive lead times. Because of the computational and memory requirements to compute optimal policies, the project will also develop a range of suboptimal control policies that will have greater potential for use in industry. These policies will be tested on a wide range of problem instances and compared either with an optimal policy or a lower bound. These policies will also be compared with strategies typically used in industry in order to evaluate their potential industrial impact. This problem is becoming more important as the length of product life cycles continues to decrease and as market factors such as competition and product proliferation increase the volatility of individual product demand. In this environment, classical inventory models are ineffective. The value of information and the effective use of information in constructing control policies are important issues in this problem. The results of this project will have a broader impact on related problems in supply chain planning and other problems that have a similar structure of uncertainty such as process control, maintenance, and yield planning. The immediate practical benefit of this project will be the development of inventory control policies that will improve customer service and reduce inventory and production costs in the face of extremely uncertain customer demand.