Stochastic Control In Semiconductor Supply Chain

这项拨款为开发基于线性规划（LP）的方法来解决扩散控制问题提供了资金，该方法已被证明对许多过程的随机特性建模是实用和有效的，包括大型呼叫中心、按订单组装系统、半导体晶圆制造线等。扩散模型的主要优点之一是，当以精确形式分析困难且棘手的问题时，它提供了一种易于处理的方法来找到近似最优解。此外，使用扩散模型作为原始系统的近似值通常通过高流量限制定理证明是合理的。LP方法利用了40年来对线性优化的理论发展和计算工具的投资。它产生了一个近乎最优的策略，描述了在每种情况下采取的适当行动，以及最佳平均成本的下界。将问题表述为线性规划涉及到一种新的离散化方案，并且增加离散化的保真度产生渐近最优策略。所提出的方法有望将LP的实际计算能力用于管理供应链中可变性的紧迫和具有挑战性的问题。该方法最初将在一个理想化的环境中开发，在这种环境中，通过漂移控制和指定边界的瞬时控制来管理单产品、单阶段过程。在通过加入额外的约束和控制方案（如奇异控制和脉冲控制）来增强漂移控制模型的保真度之后，将解决扩展到多个产品和阶段的问题。如果成功，该方法将允许单个扩散控制问题的LP公式编织在一起，并集成到更大的多产品，多阶段供应链模型中，以解决当今半导体和其他行业面临的复杂战略和运营挑战。在随机环境中更有效的规划工具将有助于提高各种行业的产品可用性、产能利用率和资本回报率。所提出的工作将在很大程度上独立的随机控制和确定性优化研究领域之间建立一个更强大的桥梁。

This grant provides funding for the development of a linear programming (LP) based approach to solving diffusion control problems, which have proven practical and effective for modeling the stochastic nature of many processes including large call centers, assemble-to-order systems, semiconductor wafer fabrication lines, etc. One of the main advantages of diffusion models is that they provide a tractable way to find approximately optimal solutions when analyzing the problem in its exact form is difficult and intractable. Further, the use of a diffusion model as an approximation of the original system is often justified through heavy traffic limit theorems. The LP approach exploits 40 years of investments in theoretical developments and computational tools for linear optimization. It produces both a near-optimal policy describing appropriate actions to take in every circumstance and a lower bound on the best possible average cost. Formulating the problem as a linear program involves a novel discetization scheme and increasing the fidelity of the discretization produces asympotically optimal policies. The proposed approach promises to bring the practical computational power of LP to bear on the pressing and challenging problems of managing variability in the supply chain. The approach will initially be developed in an idealized setting in which a single-product, single-stage process is managed via drift controls and instantaneous controls at specified boundaries. After enhancing the fidelity of the drift control model by incorporating additional constraints and control regimens like singular control and impulse control, extensions to multiple products and stages will be addressed.If successful, the approach will allow LP formulations of individual diffusion control problems to be knitted together and integrated into the larger multi-product, multi-stage supply chain models that address the complex strategic and operational challenges facing the semiconductor and other industries today. More effective tools for planning in stochastic environments will help improve product availability, capacity utilization and return on capital in a variety of industries. The proposed work will forge a stronger bridge between the largely separate research areas of stochastic control and deterministic optimization.