Weapon target assignment problem

The weapon target assignment problem (WTA) is a class of

combinatorial optimization Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, where the set of feasible solutions is discrete or can be reduced to a discrete set. Typical combi ...

problems present in the fields of

optimization Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...

and

operations research Operations research ( en-GB, operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a discipline that deals with the development and application of analytical methods to improve dec ...

. It consists of finding an optimal assignment of a set of

weapon A weapon, arm or armament is any implement or device that can be used to deter, threaten, inflict physical damage, harm, or kill. Weapons are used to increase the efficacy and efficiency of activities such as hunting, crime, law enforcement, ...

s of various types to a set of targets in order to maximize the total expected damage done to the opponent. The basic problem is as follows: :There are a number of weapons and a number of targets. The weapons are of type

i = 1, \ldots, m

. There are

W_

available weapons of type

i

. Similarly, there are

j = 1, \ldots, n

targets, each with a value of

V_

. Any of the weapons can be assigned to any target. Each weapon type has a certain probability of destroying each target, given by

p_

. Notice that as opposed to the classic

assignment problem The assignment problem is a fundamental combinatorial optimization problem. In its most general form, the problem is as follows: :The problem instance has a number of ''agents'' and a number of ''tasks''. Any agent can be assigned to perform any t ...

or the generalized assignment problem, more than one agent (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