Calculating solution-value bounds for a geostationary-satellite location problem

Bounds are developed on the solution value to the satellite location problem (SLP). In SLP, orbital locations in the geostationary orbit are alloted to satellites so as to minimize the sum of the absolute deviations between the locations prescribed for the satellites and their specified desired locations, subject to service arc and electromagnetic interference constraints. SLP is formulated as a mixed-integer program. We show that SLP is NP-complete and that the bound from the linear-programming (LP) relaxation of SLP is zero in many cases. We establish three a priori bounds that dominate the bound from the LP relaxation under a mild condition and illustrate the usefulness of decomposition in calculating bounds for SLP. Three procedures for decomposing SLP are described, and numerical results for SLP examples are presented. Finally, we suggest that the bounds and decomposition schemes be used to construct valid inequalities for SLP.