Optimal layout of transshipment facility locations on an infinite homogeneous plane

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Date

2015-05-01

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Publisher

Pergamon-Elsevier

Abstract

This paper studies optimal spatial layout of transshipment facilities and the corresponding service regions on an infinite homogeneous plane R2 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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Keywords

Social Sciences, Science & Technology, Technology, Economics, Engineering, Civil, Operations Research & Management Science, Transportation, Transportation Science & Technology, Business & Economics, Engineering, Location, Routing, Transshipment, Cyclic hexagon, Voronoi diagram, DISRUPTIONS, INVENTORY, DESIGN, SYSTEM, COSTS, RISK

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