The satellite constellation design problem with discontinuous coverage is an emerging research area arising in aerospace applications. In this problem we aim to design a constellation comprised of the minimum number of satellites guaranteeing the observability of several targets on the Earth surface with a constrained revisit time. In this communication we describe exact and heuristic methodology to solve the satellite constellation design problem, in particular we present mixed integer (non)linear approaches based on a feasibility pump heuritic followed by a post-processing procedure in order to improve the quality of the solution. Preliminary results with randomly generated targets on the Earth surface show the capabilities of the previous algorithms in terms of CPU time and memory usage.