A k-permutation algorithm for Fixed Satellite Service orbital allotments

A satellite system synthesis problem, the satellite location problem (SLP), is addressed in this paper. In SLP, orbital locations (longitudes) are allotted to geostationary satellites in the Fixed Satellite Service. A linear mixed-integer programming model is presented that views SLP as a combination of two problems: (1) the problem of ordering the satellites and (2) the problem of locating the satellites given some ordering. A special-purpose heuristic procedure, a k-permutation algorithm, that has been developed to find solutions to SLPs formulated in the manner suggested is described. Solutions to small example problems are presented and analyzed.