Single facility siting involving allocation decisions

Single facility siting is often viewed as the most basic of location planning problems. It has been approached by many researchers, across a range of disciplines, and has a rich and distinguished history. Much of this interest reflects the general utility of single facility siting, but also the mathematical and computational advancements that have been made over past decades to support better decision making. This paper discusses a recently rediscovered form of Weber's classic single facility location problem that is both important and relevant in contemporary planning and decision making. This form of the Weber problem involves locating a production plant where there are multiple sources of each needed raw material (input) distributed throughout a region. This means that the selection of a given raw material source may vary depending on the plant location. In essence, this makes the problem non-convex, even when locating only one production plant. We review elements of the Weber problem that have been addressed in the literature along with proposed solution techniques. In doing so, we highlight elements of the problem originally noted by Weber, but to date have not been operationalized in practice––allocation selection among multiple sources of given raw material inputs. A problem formulation involving allocation decisions for this generalization is derived and an optimal solution approach is developed. Application results demonstrate the significance of addressing important planning characteristics and the associated nuances that result.