Using Branch-and-Price Algorithm to Solve Raw Materials Logistics Planning Problem in Iron and Steel Industry

Based on the analysis to the logistics process of raw materials in iron and steel industry, this paper formulates a two level mathematical model to its planning problem. At the subordinate level, a shortest path that represents a feasible distribution plan of preparing mixed raw materials for production is determined for each machine after accepting the dual variables from the superior level. At the superior and coordinating level, the transportation and the inventory quantities of raw materials are determined in order to meet the flow conservation. The objective is to minimize the total cost and try to find tradeoff among inventory, transportation and production. Using branch and price algorithm, the model is solved by column generation technique, which means only columns with negative reduced costs are added to the superior level. Heuristic branch and Depth-First-Search are used to find feasible and approximate optimal integer solution as quickly as possible. The small duality gap of numerical experiment indicates the high quality of the obtained solution. This means the solution method is effective.