This work addresses the modeling, verification, planning and scheduling problems of non-cycle discrete systems with emphasis on Flexible Manufacturing Systems. We introduce a special type of Petri nets, the Conflict-Free nets with Input and Output transitions (CFIO nets) that provide a much needed platform on which all these problems can be tackled in a unified manner. It is shown that CFIO nets are live, reversible, if consistent, and can be kept bounded under certain conditions. We develop reduction rules which facilitate the detection of the above properties. We then take advantage of the qualitative properties of CFIO nets and use those models to develop a linear programming formulation of the production planning problem. Finally we use the CFIO nets, along with the production planning results, to develop the production schedule of the Flexible Manufacturing system.