High-quality alignment between movie scripts and plot summaries is an asset for learning to summarize stories and to generate dialogues. The alignment task is challenging as scripts and summaries substantially differ in details and abstraction levels as well as in linguistic register. This paper addresses the alignment problem by devising a fully unsupervised approach based on a global optimization model. Experimental results on ten movies show the viability of our method with 76% F1-score and its superiority over a previous baseline. We publish alignments for 914 movies to foster research in this new topic.