Process Discovery amounts to determine a process model from an event log of a business process. Many process discovery algorithms try to synthesize a Petri net representing the log by finding places and arcs that relate the event classes. Bergenthum et al. (2007) and van der Werf et al. (2008) propose formulations for this problem discover one place at a time, in which each basic solution of the set of inequalities represents a candidate place. We propose a global integer programming formulation that, given a log, determines all places and arcs defining a Petri net. This model simplifies the selection of places but has an efficiency problem due to a large number of integer variables used. We also propose a decomposition method for the global ILP model to treat each place and their associated constraints as a separate sub-problem. We can run the algorithm on large synthetic instances, which is unprecedented for this kind of process miner.