Congestion in Facilities Location and Layout: Deterministic and Stochastic Models

该项目旨在建立一个共同的理论基础，在设施选址和设施布局的背景下模拟移动和由此产生的拥堵。其动机源于关于设施布局和设施选址的两大文献总体上是分开发展的。我们的目标是通过明确考虑减速、拥堵、流量和精确距离，生产出一类优秀的模型，期望在实际应用中提供更好的性能。研究工作主要有三个方面的任务。第一个问题称为广义拥堵区域的平面设施选址问题，通过对障碍(无交通，无位置)、禁区(无位置)和拥堵区域(无位置和有额外费用的旅行)的共同建模，改进并统一了现有的受限设施选址文献。在这个问题的动态/随机版本中，拥堵成本可能随着一天中的时间而变化(以表示高峰时间的交通)，或者是一个随机变量。第二个研究任务称为连接选址问题，其中“连接”用于定义制造设施的连接部分或连接不同部门/单元或设施集的城市流量网络。该任务的随机版本涉及连接的选择/位置和服务速率(以及分配流)，以最小化考虑拥塞影响的固定连接安装成本、排队延迟成本和材料移动成本的总和。第三个任务是体现教育材料研究的理论成果。第一个任务的智力优势是研究工厂不同部分距离测量不同的工厂布局问题，并在一个同时考虑障碍、禁区和拥堵区域的建模框架中考虑选址问题。第二项任务将允许对过道容量和摆放位置进行建模，并大大增加这一领域现有的有限文献。

The project aims at developing a common theory base to model movement and resultant congestion in the context of facilities location and facilities layout. The motivation stems from the fact that the two bodies of literature in facility layout and facility location have generally evolved separately. The objective is to produce a superior class of models that are expected to provide better performance in real-life applications via the explicit consideration of slow-downs, congestion, flow capacity, and accurate distances. The research work has three main tasks. The first one is called the Planar Facility Location Problem with Generalized Congested Regions that advances and unifies existing restricted facility location literature by common modeling of: Barriers (no travel, no location), Forbidden Regions (no location), and Congested Regions (no location and travel with additional cost). In the dynamic/stochastic version of this problem the congestion cost might change with time of day (to represent rush hour traffic) or be a random variable. The second research task is called the Connection Location Problem, where ``connection'' is used to define a connected part of a manufacturing facility or an urban flow network that links different sets of departments/cells or facilities. The stochastic version of this task concerns selection/location and the service rate of the connections (and to assign the flows) so as to minimize the sum of the fixed connection installation costs, the queuing delay cost, and the material movement cost, that take into consideration the congestion effects. The third task is to embody the theoretical results of the study in Educational material.The intellectual merit of the first task is the study the plant layout problem in which distance measures vary in different sections of the plant, and also consider location problems in a modeling framework that simultaneously allows for barriers, forbidden regions and congested regions. The second task would allow for modeling of aisle capacities and placement and add significantly to the limited literature available in this area.