I am reviewing the facility location problem (FLP) literature. Here, Daskin and Dean (2004) provided a short literature on discrete space FLPs, which was useful to distinguish different types of models with varying objectives. Chopra and Meindl (2013) showed a small example of an FLP over continuous space with a single facility selection, which they called gravity location model, in the book titled: "Supply chain management: strategy, planning, and operation."
I am in search of a review paper or select papers that formulated FLP over continuous space with multiple facility selections. Also, the problem was formulated with a nonlinear model in Chopra and Meindl (2013) because they considered Euclidean distance between a demand node and possible facility coordinates. Have you ever encountered a paper formulating the problem with a linear model? Is this even possible?
To better describe the problem, assume there is a polynomially-sized set of demand nodes and we would like to locate facilities to completely meet the demand while minimizing costs of facilities and services. Each facility has a circular service range, and facility cost is the same across locations. Since facilities are not capacity constrained and there is no incentive of meeting a portion of the demand by another facility, we can assume each demand node will be fully-served by the closest facility, and finding the ramifications is not at interest. We can further assume that the Euclidean distance is the prevailing driver of the service cost calculation.
I am also interested in the discretely-spaced facility version of the above described problem. In particular, I am looking for algorithms that can handle covering up to 2 millions of demand nodes in a reasonable amount of computational time, say less than a day. Otherwise, models presented in Daskin and Dean (2004) provide a reasonable sketch to build on.