A new model of generalized assignment problem and its method

The traditional assignment problem assumes that the number of persons is equal to that of the tasks, beyond that, one person is allowed to undertake only one task and one task must be accomplished by one person. However, in practical situation, a real task usually calls for more than one person, in some cases, those persons are required to work at the same time. If so, the classical assignment model will not be able to describe the problem accurately. In view of this situation, a new generalized assignment model based on nonlinear integer programming is presented in this paper. The new model gives a unified description of the generalized assignment problems in which one or more persons are required to work at the same time to complete a single task. As a result, it makes up for the deficiency of the existing generalized assignment model. Moreover, for the case of binary quadratic programming, a new branch and bound method is also proposed. The numerical results indicate that the generalized assignment model and method proposed are valid.