This paper focuses on scheduling problems arising in the military. In planned artillery attack operations, a large number of threatening enemy targets should be destroyed to minimize fatal loss to the friendly forces. We consider a situation in which the number of available weapons is smaller than the number of targets. Therefore it is required to develop a new sequencing algorithm for the unplanned artillery attack operation. The objective is to minimize the total loss to the friendly forces from the targets, which is expressed as a function of the fire power potential, after artillery attack operations are finished. We develop an algorithm considering the fire power potential and the time required to destroy the targets. The algorithms suggested in this paper can be used in real artillery attack operations if they are modified slightly to cope with the practical situations.