RoboCup Soccer Simulation 2D League challenges teams to smartly and stably out-perform their opponents. Designing a reliable defense is important for reducing opportunities of the opponent to score points. The team developed by the authors uses a defense system called one-to-one mark system. During a set-play, the system builds assignment plans providing guidelines to the players about which opponent's player to mark. From one assignment plan to another, targets that players have to mark can be reconsidered. If too many modifications occur, the markers only wander around the soccer field without having the possibility to reach their target. So, minimizing it would result in a more reliable defense. In this paper, we propose a method for minimizing the change in the mark assignment by formulating the assignment plan as a minimum cost flow problem. Our previous work solved the assignment plan by using the Hungarian method. However, this method requires to consider all possible targets, while some of them should be ignored for some strategic reasons in the domain of soccer simulation. In order to reduce the search space, we used the Ford-Fulkerson algorithm that can handle incomplete bipartite graphs. A series of computational experiments were conducted to examine the performance of the proposed method and we observed promising results about the reduction of assignment modification's frequency.