Convex Optimization Based Methods For Steel Material Allocation Planning

Steel material allocation problems in this thesis are to allocate the surplus material to customer orders such that the inventory is reduced and the material utilization is improved. Taking the practical production process of a domestic steel enterprise as background, this thesis studies the deterministic slab matching problem for in-stock slab and robustness slab matching problem for preconcerted slab arising from the hot rolling stage. For both problems, solution methods based on convex optimization are designed. Furthermore, a logistics balancing problem arising from the downstream cold rolling stage is also studied. The main contents are as follows:(1) Taking the in-stock slabs as input, a deterministic matching problem is investigated. Taking the matching relations between slabs and orders as decision variables, the problem is formulated as a 0-1 integer quadratic programming model. The objective is not only to minimize the matching cost quantified by a linear penalty, but also to minimize the slab shuffles quantified by a quadratic penalty. To solve the problem, the model is first equivalently transformed to a Semidefinite Programming (SDP) model. Then the SDP model is relaxed by using the rank semidefinite relaxation technique. Finally, a semidefinite relaxation algorithm is proposed to solve the original problem. The result of numerical experiment demonstrates the effectiveness of the proposed algorithm.(2) Taking the preconcerted slabs as input, a robustness matching problem is investigated. Compared to the deterministic matching problem, the main feature of this robustness problem is that the weight of preconcerted slab is uncertain. For this problem, we build a robust linear programming model with the consideration that the parameter of preconcerted slab weight belongs to a uncertainty elliptical set. The model is equivalently transformed to a second-order cone programming model through the conic optimization approach. Then the new model is solved by the standard package MOSEK. The result of numerical experiment demonstrates the effectiveness of the proposed solution methods.(3) Taking the cold rolling stage as background, the logistics balancing planning problem of the cold rolling process is studied. The main feature of this problem is that the coordination between production and inventory for multiple stages is considered. For this problem, a mixed integer programming model is built with the decisions on whether each order in is produced on a unit in a given period or not. The objective is to minimize production costs and inventory costs such that the equipment capacity and safety inventory constraints are satisfied. Finally, the model is solved by CPLEX optimization software to verify its effectiveness.(4) Based on the above research, an optimization system for the muti-line slab-order matching and a decision support system for logistics planning in cold rolling stage are designed and developed. The function modules of the muti-line slab-order matching system mainly include data processing module, the matching plan generation module and data uploading module. The decision support system for logistics planning in cold rolling stage mainly includes data processing module, capability allocation generation module and data uploading module.