Magnetic Material Group Furnace Problem Modeling 

Grade, due date, priority, and demand are attributes of magnetic material products. Planners are required to seek the optimal combination of production work orders to minimize cost and improve efficiency based on these attributes. The magnetic material group furnace optimization problem is a generalization of the 1-D bin-packing problem wherein bins of varying sizes are used. Bin sizes are determined by the grade and demand of the grouped work orders. A mathematical model is established to solve the magnetic material group furnace optimization problem by using a specialized genetic algorithm (SGA).

In SGA, an initial population generation method is designed by following the sort criteria of the earliest completion date. The furnace charging weight is set according to several rules derived from work order attributes. An elite strategy and an improved greedy three-crossover operator are introduced to enhance convergence speed and precision. In addition, a reverse operator is applied to exploit the proposed algorithm. Simulation results based on practical production data show that the established model is suitable and that the presented algorithm is effective