Microblogging platforms such as Twitter are widely used by eyewitnesses and affected people to post situational updates during mass convergence events such as natural and man-made disasters. These crisis-related messages disperse among multiple classes/categories such as infrastructure damage, shelter needs, information about missing, injured, and dead people etc. Side by side, we observe that sometimes people post information about their missing relatives, friends with details like name, last location etc. Such kind of information is time-critical in nature and their pace and quantity do not match with other kind of generic situational updates. Also, requirement of different stakeholders (government, NGOs, rescue workers etc.) vary a lot. This brings two-fold challenges -(i). extracting important high-level situational updates from these messages, assign them appropriate categories, finally summarize big trove of information in each category and (ii). extracting small-scale time-critical sparse updates related to missing or trapped persons. In this paper, we propose a classification-summarization framework which first assigns tweets into different situational classes and then summarizes those tweets. In the summarization phase, we propose a two stage extractive-abstractive summarization framework. In the first step, it extracts a set of important tweets from the whole set of information, develops a bigram-based word-graph from those tweets, and generates paths by traversing the word-graph. Next, it uses an Integer-linear programming (ILP) based optimization technique to select the most important tweets and paths based on different optimization parameters such as informativeness, coverage of content words etc. Apart from general class-wise summarization, we also show the customization of our summarization model to address time-critical sparse information needs (e.g., missing relatives). Our proposed method is time and memory efficient and shows better performance than state-of-the-art methods both in terms of quantitative and qualitative judgement.