基于极值理论的大规模装配系统库存与产能优化
Optimization of inventory and capacity in large-scale assembly systems using extreme-value theory
AI总结：
针对高科技装配系统零部件产能波动引发短缺延迟的问题，将生产系统建模为对称分叉-汇合排队网络，应用极值理论推导队列长度相关新结果，提出系统规模渐近最优方法，经测试对中等规模系统效果良好。
摘要：
高科技系统的生产通常分为两个阶段：1）使用专用设备和人员进行零部件生产；2）系统装配/集成。零部件生产产能存在波动，导致至少一种零部件出现短缺的风险很高，进而引发代价高昂的延迟。企业通过对过剩生产产能和零部件缓冲库存进行战略投资来对冲这一风险。要优化这些投资，明确零部件短缺风险与产能、库存投资之间的关系至关重要。我们假设在有限时间区间内，零部件生产产能和产品需求服从正态分布，据此将生产系统建模为对称fork-join（分叉-汇合）排队网络，该网络包含N个统计特性相同的队列，具有共同的到达过程和独立的服务过程。在对称成本结构的假设下，我们随后应用极值理论（extreme value theory）来获取该优化问题的解析见解。我们推导了该排队网络的若干新结果， notably N个稳态队列长度的缩放最大值依分布收敛于一个高斯随机变量。这些结果可转化为系统规模设计的渐近最优方法。在一系列问题上的测试表明，这些方法通常对中等规模的系统效果良好。
英文摘要：
High-tech systems are typically produced in two stages: 1) Production of components using specialized equipment and staff; 2) System assembly/integration. Component production capacity is subject to fluctuations, causing a high risk of shortages of at least one component, which results in costly delays. Companies hedge this risk by strategic investments in excess production capacity and in buffer inventories of components. To optimize these, it is crucial to characterize the relation between component shortage risk and capacity and inventory investments. We suppose that component production capacity and produce demand are normally distributed over finite time intervals, and we accordingly model the production system as a symmetric fork-join queueing network with $N$ statistically identical queues with a common arrival process and independent service processes. Assuming a symmetric cost structure, we subsequently apply extreme value theory to gain analytic insights into this optimization problem. We derive several new results for this queueing network, notably that the scaled maximum of $N$ steady-state queue lengths converges in distribution to a Gaussian random variable. These results translate into asymptotically optimal methods to dimension the system. Tests on a range of problems reveal that these methods typically work well for systems of moderate size.
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