Organizing agents into disjoint groups is a crucial challenge in artificial intelligence, with many applications where quick runtime is essential. The Simultaneous Coalition Structure Generation and Assignment (SCSGA) problem involves partitioning a set of agents into coalitions and assigning each coalition to a task, with the goal of maximizing social welfare. However, this is an NP-complete problem, and only a few algorithms have been proposed to address it for both small and large-scale problems. In this paper, we address this challenge by presenting a novel algorithm that can efficiently solve both small and large instances of this problem. Our method is based on a new search space representation, where each coalition is codified by an index. We have developed an algorithm that can explore this solution space effectively by generating index vectors that represent coalition structures. The resulting algorithm is anytime and can scale to large problems with hundreds or thousands of agents. We evaluated our algorithm on a range of value distributions and compared its performance against state-of-the-art algorithms. Our experimental results demonstrate that our algorithm outperforms existing methods in solving the SCSGA problem, providing high-quality solutions for a wide range of problem instances.