Research Initiation: Coordinating the Production of Components and Assemblies When Demands and Yields are Random

本项目的目标是研究当组件产量和对组件的需求是随机的情况下，协调组件座的生产和生产组件所需的组件的问题。这是一个工厂间的协调问题，因为部件和组件通常在不同的工厂生产。该项目的动机是半导体制造中的一个问题，即使用一组芯片(组件)来生产不同的热导体模块(组件)。这个问题被表述为一个随机规划。研究工作被分成几种近似方案，这些方案利用分解过程的特殊结构，分两个阶段解决问题。一个重要的工具是关于一组随机变量的最小值的期望的新的下界。适当的工厂协调应导致更高的预期利润(效用)和更高的能力，以满足对组件的需求。此外，它应该通过以正确的组合释放用于生产的零部件来减轻生产零部件的工厂的负担。

The objective of this project is to study the problem of coordinating the production of a seat of assemblies and of the components required to produce them when the component production yields and the demand for the assemblies are random. This problem is one of inter-plant coordination since the components and the assemblies are usually produced in different plants. The project is motivated by a problem in semiconductor manufacturing where a set of chips (components) is used to produce different thermo- conductor modules (assemblies). The problem is formulated as a stochastic program. The research effort is divided between approximation schemes that exploit special structures of decomposition procedure that solves the problems in two stages. An important tool is a new lower bound on the expectation of the minimum of a set of random variables. Proper plant coordination should result in higher expected (utility of) profit and in an increased ability to satisfy demand for the assemblies. Moreover, it should reduce the burden for the plants producing components by releasing components for production in the right mix.