A constrained multiple raw materials manufacturing batch sizing problem

The purpose of this research is to determine an optimal batch size for a product, and the purchasing policy of associated raw materials, for a manufacturing firm. Like any other practical situation, this manufacturing firm has a limited storage space, and transportation fleet of known capacity. The mathematical formulation of the problem indicates that the model is a constrained nonlinear integer program. Considering the complexity of solving such a model, we investigate the use of genetic algorithms (GAs) for solving this model. We develop both binary and real coded genetic algorithms with six different penalty functions. In addition, we develop a new procedure to solve constrained optimization models using penalty function based GAs. The real coded genetic algorithms work well for the batch sizing problem. The detailed computational experiences are presented.