This chapter aims to at least partially fill that void and should be of interest to both developers and users of Lagrangian relaxation algorithms. In many large-scale optimization problems for planning in production, feasibility of the optimization problems present in linear programming allows the determination of optimal solution by first decomposing a problem into smaller subproblems and then solving the subproblems almost independently. Many variants of Lagrange relaxation have been posed by researchers in power systems operation for unit commitment. The technique has been developed to take advantage of iterative technique and eliminate certain coupling constraints by adding them to the master problem thereby enabling the independent and simultaneous solutions of many resulting subproblems. Lagrangian relaxation is based upon the observation that many difficult programming problems can be modeled as relatively easy problems complicated by a set of side constraints.