基于ε-约束与区间数线性规划的钢铁供应链能源优化模型

An Energy Optimization Model of Iron and Steel Supply Chain Using ε-Constraint Method and Interval Linear Programming Approach

由于二次能源的存在,钢铁供应链上的能源流在不同工序过程之间进行交互,存在着正向和逆向的能源流动。对钢铁供应链上能源流的优化,可以显著提高二次能源的利用效率,从而降低钢铁企业的综合能源消耗。首先,研究了钢铁供应链上的能源流情况,建立了钢铁供应链能源流模型,在此基础上考虑钢铁供应链能源优化的两重目标及相关约束因素,构建了钢铁供应链能源优化模型;其次,组合运用ε-约束方法和区间数线性规划方法对模型进行求解;最后,典型算例验证了该模型可以有效降低钢铁企业的能源消耗,提升能源利用效率。

The production system of iron and steel enterprises can be conceptualized into two processes： material flow transformation and energy flow transformation. The operation of these two processes consumes a great amount of resource, energy consumption and waste emissions. Due to the generation of secondary energy, energy flow in the iron and steel supply chain interacts among different production processes and runs forward and backward respectively, which has an important impact on the energy utilization for an iron and steel enterprise. Therefore, it is necessary to study the energy optimization of an iron and steel supply chain from the perspective of secondary energy recycling with the aim of reducing energy consumption and energy costs in the supply chain and improving energy efficiency through the optimal allocation of secondary energy.In order to clarify the flowing process of secondary energy in an iron and steel supply chain as well as the actual impact of secondary energy recycling on energy optimization of the iron and steel supply chain, an energy optimization model is proposed based on the detailed analysis of energy flows. Then, the ？-constraint method and interval linear programming approach are introduced to the process of solving the model. Finally, the research result that the model can effectively reduce the energy consumption of an iron and steel enterprise and improve energy utilization efficiency has been demonstrated through a typical case study. This paper is composed of the following four parts： Firstly, this paper analyzes the energy flow in an iron and steel supply chain. There are 7 strands of energy flows in a single process：（1） the energy input from the upstream;（2） the energy output from the present process;（3） the energy input from the outside;（4） the wasted energy;（5） the recycling energy for own use;（6） the recycling energy for others＇ use; and（7） the energy reversing from the downstream process. Energy flow in all single process can be integrated into a more complicated energy flow network system. It is clear that the energy flows not only in a single process but also in different processes in upstream and downstream activities. Secondly, an energy optimization model is constructed in this paper. The interval coefficients are used to express uncertain information of the objective function and its constraints. A multi-objective optimization model for an iron and steel supply chain is constructed. The objective function includes energy consumption minimization and energy cost minimization. The related constraints include basic demands for energy when producing iron and steel products, conserving input energy and output energy, requiring production capacity and technical parameters, increasing energy efficiency of a cogeneration system, demanding limits for secondary energy, having a constraint for the amount of electric output and emission limits, such as CO2, and non-negativity for some parameters. Thirdly, the solution based on ？-constraint method and interval linear programming is given. We change a multi-objective optimization problem into a single-objective optimization problem using ？-constraint method. A single-objective optimization model for an iron and steel supply chain is changed from a multi-objective optimization model. We solve the single-objective optimization model using interval linear programming. Finally, this paper implements a deeply empirical analysis based on a large Chinese iron and steel enterprise. There are three findings in this study. First, the energy from the outside has been reduced, and the efficiency for recycling secondary energy has been improved. Second, by optimization of secondary energy, the total annual energy consumption is reduced from 10.94GJ/t-steel to 6.55~8.28GJ/t-steel in 2010, and the efficiency of energy conservation is about 24.31%~40.13%. Thus, the result is quite significant. On the other hand, the total energy cost is decreased from 122.47USD/t-steel to 88.25USD/t-steel in 2010.The savings rate reaches up to 27.94%. It helps enterprises to economize the energy cost. Third, the energy optimization model has a relatively stability. In summary, we can optimize resource and energy allocation using the constructed energy optimization model of iron and steel supply chain that is based on ？-constraint method and interval linear programming approach. In addition, we can improve the awareness to recycle the secondary energy. All of these measures can reduce the energy consumption from the outside and improve the efficiency for recycling secondary energy in an iron and steel supply chain. Thus, for an iron and steel enterprise the efficiency of energy conservation could be improved and the energy cost could be reduced. Therefore, an enterprise should adjust their supply chain systems to strengthen the recycling and utilization of secondary energy by optimizing and improving their manufacturing process.