Integrated model for two-stage production planning and its genetic algorithm design

An integrated problem was studied for a two-stage production planning, in which the upper-stage was a capacitated lot sizing problem and the lower-stage was a parallel two-machine scheduling problem. A single model was proposed to describe the whole problem. The objective of the model consists of three parts: the inventory cost, the shortage cost and the overtime cost. A genetic algorithm was designed to solve this problem based on monolithic method, within which every individual contained all the information of lot sizing and scheduling, and the infeasible solutions were avoided through the design of genetic operator. Numerical simulations were conducted, including the computation of three different sizes and the analysis of solutions. The result shows the feasibility and validity of our genetic algorithm.