This chapter presents a new direction to the scheduling problem by exploring the Moore-Hodgson algorithm. This algorithm is used within the context of integer programming to come up with complementarity conditions, more biding constraints, and a strong lower bound for the scheduling problem. With Moore-Hodgson Algorithm, the alternate optimal solutions cannot be easily generated from one optimal solution; however, with integer formulation, this is not a problem. Unfortunately, integer formulations are sometimes very difficult to handle as the number jobs increases. Therefore, the integer formulation presented in this chapter uses infeasibility to verify optimality with branch and bound related algorithms. Thus, the lower bound was obtained using pre-processing and shown to be highly accurate and on its own can be used in those situations where quick scheduling decisions are required

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