Optimal Method of Capacitated Lot-Sizing Planning in Manufacturing Systems

This paper analyzes the capacitated lot-sizing problem considering an individual machine’s production capacity using a two-layer hierarchical method to minimize the sum of the dynamic inventory cost and the overtime penalty cost. The genetic algorithm, the parameter linear programming method, and a heuristic method were used in the developed method. The method uses the genetic operator to define the lot-sizing matrix (the first layer), linear programming to determine each machine's schedule (the second layer) according to the lot-sizing matrix, and the heuristic method to verify the feasibility of the solutions by adjusting them to meet the constraint requirements. The scheduling of machines in a press shop demonstrates the effectiveness of the algorithm. The result shows that the algorithm is convergent.