We focus on the weapon target assignment and fire scheduling problem (WTAFSP) with the objective of minimizing the makespan, i.e., the latest completion time of a given set of firing operations. In this study, we assume that there are m available weapons to fire at n targets (> m). The artillery attack operation consists of two steps of sequential procedure : assignment of weapons to the targets; and scheduling firing operations against the targets that are assigned to each weapon. This problem is a combination of weapon target assignment problem (WTAP) and fire scheduling problem (FSP). To solve this problem, we define the problem with a mixed integer programming model. Then, we develop exact algorithms based on a dynamic programming technique. Also, we suggest how to find lower bounds and upper bounds to a given problem. To evaluate the performance of developed exact algorithms, computational experiments are performed on randomly generated problems. From the results, we can see suggested exact algorithm solves problems of a medium size within a reasonable amount of computation time. Also, the results show that the computation time required for suggested exact algorithm can be seen to increase rapidly as the problem size grows. We report the result with analysis and give directions for future research for this study. This study is meaningful in that it suggests an exact algorithm for a more realistic problem than existing researches. Also, this study can provide a basis for developing algorithms that can solve larger size problems.