Extensions to the Weber problem

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One of the classics in the field of Location Science is the book on the theory of industrial location by Weber (1909). Weber used a simple construct comprised of a 3-point triangle to describe important issues, including where raw materials for manufacturing are sourced. Virtually all of the research conducted in the last 50 years related to Weber’s construct has overlooked major elements of his work. This includes the issue of sourcing needed raw materials, which can be limited, as an integral part the location problem. This paper explores one form of raw material sourcing first described by Weber in which each raw material source is limited by a fixed capacity. We show that most instances of this location problem are non-convex as well as propose a solution procedure. We also explore a related problem where the facility itself can be of limited capacity and not all demands can be served. These two models can serve as building blocks for a greater exploration of many of the important problem facets proposed by Weber in his seminal work.