We address the problem of optimal path finding for multiple agents where agents must not collide and their total travel cost is minimized. Previous work used traditional single-agent search variants of the A* algorithm. We present a novel formalization for this problem which includes a search tree called increasing cost tree (ICT) and a corresponding search algorithm that finds optimal solutions. We analyze this new formalization and compare it to the traditional A* search formalization. Experimental results on various domains show the benefits and drawbacks of this approach. A speedup of up to 3 orders of magnitude was obtained in a number of cases.