Raw Material Purchasing Optimization Using Column Generation

The raw material purchasing (RMP) problem is to determine the purchasing quantities of raw materials in given periods or cycles. Raw material purchasing optimization is crucial for large-scale steel plants because it is closely related to the supply of raw materials and cost savings. The raw material purchasing of large-scale steel enterprises is characterized by many varieties, large quantities, and high costs. The RMP objective is to minimize the total purchasing cost consisting of the price of raw materials, purchasing set-up costs, and inventory costs and meet product demand. We present a mixed integer linear programming (MILP) model and a column generation (CG) solution for the resulting optimization problem. The column generation algorithm is the generalization of the branch & bound algorithm with solving the linear programming (LP) relaxation of MILP using column generation (CG), and its advantage is to handle large-sized MILPs. Experimental results show the effectiveness and efficiency of the solution.