In this work a new assignment problem with the name "Artillery Target Assignment Problem (ATAP)" is defined. ATAP is about assigning artillery guns to targets at different time instances while some objective functions are to be optimized. Since an assignment made for any time instance effect the value of the shooting ATAP is harder than the classical assignment problem. For two variations of ATAP genetic algorithm solutions with customized representations and genetic operators are developed and presented. © 2011 Springer Science+Business Media B.V.