Earliness and tardiness production scheduling and planning (ETPSP) have been studied by a number of researchers in recent years. However, the existing researches have been limited to the study of machine scheduling, and the effects of multi-product production, with the considerations of machine scheduling and lot-size and capacity are not being investigated. One of the reasons for this is the complexity of solving large-scale discrete problems where restrictions of linearity, convexity and differentiability prevail. Classical optimization methods have proved inadequate and an alternative approach is investigated here. A new extensive model of ETPSP is developed in this paper to address the multi-product production environment. A genetic algorithm (GA) is applied in order to obtain an optimal solution for this large-scale problem. The investigation demonstrates the use of a comprehensive model to represent a real life manufacturing environment and illustrates the fact that a solution can be effectively and efficiently obtained using the GA approach.