Twitter is a valuable source of information to keep users up to date on topics they care about. However, timely following the development of long-running events is too difficult due to the velocity and the volume of the published information. Automatically generating a concise summary containing relevant and non-redundant posts that capture key aspects of information need, is one solution to keep users up to date. In this paper, we propose a novel approach that formulates the summary generation as an optimization problem modeled using Integer Linear Programming whereas the majority of traditional methods generate the summary by selecting iteratively top weighted tweets and ignores the mutual relation among messages. To overcome this issue, the generation of the summary is formulated as an optimization problem to select a subset of tweets that maximizes the global summary relevance and fulfills constraints related to non-redundancy, coverage, temporal diversity and summary length. Our experiments on TREC RTF 2015 and TREC RTS 2016 datasets have shown the effectiveness of our approach.