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:There are a number of weapons and a number of targets. The weapons are of type <math> i = 1, \ldots, m </math>. There are <math> W_{i} </math> available weapons of type <math>i</math>. Similarly, there are <math> j = 1, \ldots, n </math> targets, each with a value of <math> V_{j} </math>. Any of the weapons can be assigned to any target. Each weapon type has a certain probability of destroying each target, given by <math> p_{ij} </math>.
Notice that as opposed to the classic [[assignment problem]] or the [[generalized assignment problem]], more than one [[agent]]{{dn|date=April 2014}} (i.e., weapon) can be assigned to each ''task'' (i.e., target) and not all targets are required to have weapons assigned. Thus, we see that the WTA allows one to formulate optimal assignment problems wherein tasks require cooperation among agents. Additionally, it provides the ability to model probabilistic completion of tasks in addition to costs.
Both static and dynamic versions of WTA can be considered. In the static case, the weapons are assigned to targets once. The dynamic case involves many rounds of assignment where the state of the system after each exchange of fire (round) in considered in the next round. While the majority of work has been done on the static WTA problem, recently the dynamic WTA problem has received more attention.
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