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Abstract: We show that over unbounded domain no algorithm can be created for the integer programming, nonlinear equations, continuous global optimization and constraint satisfaction problems. [Copyright &y& Elsevier]

Abstract: In this paper, the partner selection problem with a due date constraint in virtual enterprises is proved to be an NP-complete problem. So it cannot have any polynomial time solution algorithm at present. A nonlinear integer programming model for this problem is established. The objective function and a constraint function of the model have monotone properties. Based on the above observations, a Branch & Bound algorithm is constructed to solve the problem. Numerical experiments show that the algorithm is efficient. [Copyright &y& Elsevier]