Efficient optimal facility location determination method for convex position demand point

A method for arranging facilities performed at a computing system having one or more processors and memory, the method comprising:

• receiving, by the one or more processors, information regarding a plurality of facilities to be arranged, wherein arranging the plurality of facilities with no restrictions on positioning represents an NP-hard problem;
• for each facility of the plurality of facilities, determining, by the one or more processors, whether the facility is arranged so that an optimal distance, which is a distance from a plurality of demand locations with a farthest distance to the facility, is less than or equal to a given distance, wherein the determination comprises:
• performing a first type of determination in accordance with a determination that the plurality of facilities does not exceed a threshold number, wherein performing the first type of determination comprises determining whether there is a circle that covers points of a chain function;
• and
• performing a second type of determination in accordance with a determination that the plurality of facilities does exceed the threshold number, the second type of determination being different than the first type of determination, wherein performing the second type of determination comprises applying a binary search;
• for each facility of the plurality of facilities, calculating, by the one or more processors, an optimal facility location by applying a parametric search function so that a distance between the facility and the plurality of demand locations becomes the optimal distance;
• and
• providing, by the one or more processors, arrangement information for the plurality of facilities, the arrangement information including respective optimal facility locations for the plurality of facilities.