Research On The Optimal Scheduling Method For The Productive Process Of Steelmaking- Refining-Continuous Casting

The process of steelmaking-refining-continuous casting in modern large steel plant is composed by using multiple converters, multiple refining machines and multiple casting machines with different refining modes. The molten steel is poured into steel ladles, which are the containers for the molten steel. The molten steel in each ladle is called a charge. Steel ladles with molten steel are transported to the refining position by trolleys and shop travelers for the process of single or multiple refining mode (single refining mode denotes that a charge is processed by one refining machines, multiple refining mode denotes that a charge is processed by multiple refining machines). The refined molten steel is poured into the tundishes, which are the containers for the molten steel. The molten in each tundish is called a cast. The tundish with molten steel is sent to the continuous casting machines. Finally, the molten steel becomes slabs by the process of continuous cast.Suppose the process path (the total number of manufacturing procedure and the selected machine type in each manufacturing procedure) of each charge is given. There are four performance indexes in steelmaking plant. They are as follows:the consecutive charges in each cast should be processed continuously-no break cast, the consecutive processed charges in the same machine cannot conflict-no confliction, the summation of the difference-value between the actual beginning time and the ideal beginning time of the casts in the casters, the summation of the waiting time for all charges in all procedures. The constraints are to satisfy the machine capacity for each machine and the processing time requirement for each charge. The schedule of steelmaking-refining-continuous casting is to decide the beginning time in each procedure for each charge and the related selected machine for each charge in each procedure, and form the table of steelmaking-refining-continuous casting, that is the schedule of steelmaking-refining-continuous casting process.When composing the optimal schedule for the process of steelmaking-refining-continuous casting, the multiple machines and multiple stages in the refining procedure lead to the index level combination of paths for each charge. All these paths for all the charges could cause multiple possible conflicts and uncertain conflicts. These made the performance index-no confliction hard to be described by mathematical model. At the same time, the process of the optimal schedule for multiple charges should consider many performance indexes. Traditional method, which transformed the multiple targets problem into single target problem by adding weights, cannot satisfy the multiple performance indexes for the process of steelmaking-refining-continuous casting and easily causes the conflicts of performance indexes. The evolutional algorithm also cannot acquire an optimal schedule under the premise of keeping all the performance indexes. The paper proposed the two stages strategy which was composed by the machine assignment and the time optimization to get the optimal schedule of steelmaking-refining-continuous casting. The stage of machine assignment strategy fixed the assignment for each charge in the stage of steelmaking LD, refining RH, refining CAS first, and then optimized the schedule time. This kind of method could be easily lead to the results into local optimization results. Meanwhile, this method separated all the performance indexes by two stages and set the performance index-no break as adjustable performance index, this method could not ensure the final schedule optimal results is effective for the real production.In order to solve the problems mentioned above based on the support from the National 863 Project (2004AA412010)-The Key Technology (EMS-EAM-IPS) Research and Application of MES in Iron and Steel Industry, this paper focuses on the research in one of the largest steel plant in China, which has three converters, seven refining furnaces, three casters and three refining modes. This paper proposes the optimal scheduling method for the productive process of steelmaking-refining-continuous casting with the lagrangian relaxation framework. The major contributions are listed as follows:1. Under the condition that there are three converters, seven refining furnaces, three casters and three refining modes in one of the large steel plant, the performance indexes of no break and no confliction are transformed into constraints. The beginning time in each procedure for each charge and the machine type in each procedure are set as the decision variables. The minimization of the the difference value between the actual beginning time of the casts in the casters and the ideal beginning time of the cast in the casters and the minimization of the waiting time for all charges in all procedures are set as the mathematical objective function. This paper builds the no confliction constraint equations by introducing the 0-1 decision variables and the time variables. After that, the paper gives the analysis of the complexity for the constructed mathematical model.2. After constructed the global optimal mathematical model, this paper proposes the two stages strategy to solve this problem. The first stage transforms the model which is based on the relaxation of the constraints "no break and no confliction" by using the lagrangian relaxation method. The second stage proposes the lagrangian relaxation framework to optimize the schedule of steelmaking-refining-continuous casting. In the process of model transformation, the relaxed constraint equations are transformed into the performance indexes by introducing the lagrangian relaxation multipliers to relax the no break and no confliction constraint equations. The original mathematical model is transformed into the subproblems for all charges with the lagrangian multipliers. The optimal method for the process of steelmaking-refining-continuous casting with lagrangian relaxation framework is composed by four parts. Setting the initial value of the lagrangian multipliers, the algorithm for solving the subproblems based on the backward dynamic programming, updating the multipliers based on the surrogate subgradient method (SSG) and Setting the end condition. Considering the difficulty of optimizing subproblems, we introduce the backward dynamic programming algorithm to get the optimal schedule for each charge in a limited time. Based on the optimal results for all charges, we get the lower bound by the value of the dual problem and the upper bound by the value of feasible solution, which is got by the two stages heuristic method. Then, the surrogate subgradient method which can get a proper direction without solving all the separated charge's schedule to optimize dual functions for separable steel-making and continuous casting schedule problems is introduced to update the lagrangian relaxation multipliers by using the proper step-size and subgradient. Finally, we get the near optimal schedule solution by adjusting the duality gap between the lower bound and the upper bound.3. The industrial experiments for the proposed approach is taken based on the data from the real industry. First, compare with paper,the results shows that the average time to generate the schedule is 2 seconds in this paper which is much shorter than 6 seconds in paper. The maximum waiting time of the charges in front of the caster do not exceed 11 minutes; the maximum of deviation to the targeted casting time is 2 minutes which is better than the optimal results in paper. Meanwhile, for the different problems, which includes the large scale, input charges and the different scale machines (continuous casting machine). We take the experiments. The results shows that the average time to generate the schedule is 2.4 seconds; the maximum waiting time of the charges in front of the caster do not exceed 14 minutes; the maximum of deviation to the targeted casting time is 3 minutes which is better than the optimal results in paper. The test demonstrates that the method in this paper is reasonable and effective, especially for the large steelmaking plant, which has more equipment and more input charges. The mathematical model and the algorithm has a wide application in the steelmaking industry.