无限齐次平面上转运设施的优化布局
Optimal Layout of Transshipment Facilities on An Infinite Homogeneous Plane
摘要：
本文研究了在无限均匀平面$\mathbb{R}^2$上，以设施设置、出库和入库补给运输总费用最小为目标的转运设施及相应服务区域的最优空间布局问题.这一问题在货运物流和过境系统设计方面具有重要意义。本文首先集中在一个欧几里德平面，并提出了一个新的证明已知的Gersho的猜想，该猜想指出，每个服务区的最佳形状应该是一个正六边形，如果入境运输成本被忽略。然而，当进站运输成本变得不可忽略时，我们证明了一个紧的上界可以通过一种类型的拉长的循环六边形来实现，而基于松弛和理想化的成本下界也得到了。分析上限和下界之间的差距在0.3%以内。本文然后表明，一个类似的细长的非循环六边形形状实际上是最佳的服务区域上的直线度量平面。数值实验和灵敏度分析进行验证的分析结果，并得出管理见解。
英文摘要：
This paper studies optimal spatial layout of transshipment facilities and the corresponding service regions on an infinite homogeneous plane $\mathbb{R}^2$ that minimize the total cost for facility set-up, outbound delivery and inbound replenishment transportation. The problem has strong implications in the context of freight logistics and transit system design. This paper first focuses on a Euclidean plane and presents a new proof for the known Gersho's conjecture, which states that the optimal shape of each service region should be a regular hexagon if the inbound transportation cost is ignored. When inbound transportation cost becomes non-negligible, however, we show that a tight upper bound can be achieved by a type of elongated cyclic hexagons, while a cost lower bound based on relaxation and idealization is also obtained. The gap between the analytical upper and lower bounds is within 0.3%. This paper then shows that a similar elongated non-cyclic hexagon shape is actually optimal for service regions on a rectilinear metric plane. Numerical experiments and sensitivity analyses are conducted to verify the analytical findings and to draw managerial insights.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
