Assignment problem

The problem of optimally assigning m individuals to m jobs, so that each individual is assigned to one job, and each job is filled by one individual. The problem can be formulated as a linear-programming problem with the objective function measuring the (linear) utility of the assignment as follows:

The problem is a special form of the transportation problem and, as such, has an optimal solution in which each variable is either zero or one. The problem can be solved by the simplex method, but special assignment problem algorithms tend to be computationally more efficient. Hungarian method; Transportation problem; Transportation-simplex method.