Optimal Layout of Transshipment Facilities on An Infinite Homogeneous Plane

Weijun Xie; Yanfeng Ouyang

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arXiv · 1401.2415

Optimal Layout of Transshipment Facilities on An Infinite Homogeneous Plane

Weijun Xie·Yanfeng Ouyang

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Abstract

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.

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BibTeX RIS

Weijun Xie, Yanfeng Ouyang. 2014-01-10. Optimal Layout of Transshipment Facilities on An Infinite Homogeneous Plane. https://arxiv.org/abs/1401.2415

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