This paper considers low-complexity implementation of energy-efficient cooperative transmission in wireless sensor networks. In particular, an optimization framework is considered which, for a given configuration of the source, destination and relay nodes, performs optimal relay selection and power allocation subject to signal-to-noise ratio constraints. While the proposed framework gives the optimal solution, considering simple platforms of sensing nodes, solving the corresponding mixed-integer linear programming problem is computationally complex. To overcome this hurdle, an explicit solution to the optimization problem at hand is presented by invoking the theory of multi-parametric programming. This technique provides the solution as a function of measurable parameters in an off-line manner. The piecewise-constant values in such a solution can be stored in a memory chip and the online computational tasks are reduced to finding the parameters and evaluating simple functions to obtain the optimal solution.