Research the bound of the option value of MIP by Lagrangian relaxation

According to study the a Maximal Lifetime with Constrained Energy problem (MLCE)in a sensors net, we discuss the bound of the option value of mix integer program (MIP). Since the Maximun of the MIP is NP complete problem, so the exact solution can not be obtained, but the bound of the option value is exist. This paper use Lagrangian relaxation method to derive theoretical upper bound on the optimal value of the MIP problem.