Xie, W.Ouyang, Y.2018-07-252018-07-252015-05-010191-2615http://hdl.handle.net/10919/84390This 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.74 - 88 (15) page(s)application/pdfenIn CopyrightSocial SciencesScience & TechnologyTechnologyEconomicsEngineering, CivilOperations Research & Management ScienceTransportationTransportation Science & TechnologyBusiness & EconomicsEngineeringLocationRoutingTransshipmentCyclic hexagonVoronoi diagramDISRUPTIONSINVENTORYDESIGNSYSTEMCOSTSRISKArticle - Refereedhttps://doi.org/10.1016/j.trb.2015.02.00175Xie, W [0000-0001-5157-1194]