Planning and Scheduling Under Uncertainties: Data Processing and Solution Strategy

Recent years, planning and scheduling are still great challenges in process optimization.  Moreover, uncertainty is the most critical issue. Individual technique such as scheduling or planning is insufficient to deal with the problem and uncertainty. With the concept of Enterprise Wide Optimization¹, techniques should be integrated.

Planning usually determines the production profile as well as the raw material procurement and production distribution with the horizon from a week to a month. Scheduling gives task allocation and unit utilization with the information given by planning. Its time period is usually from an hour to a day. Integration of planning and scheduling saves cost or increases revenue. However, the problem size increases dramatically and the problem becomes intractable even a small time horizon is considered. In this article, a two level optimization framework for a petrochemical optimization problem, which is inherited from Luo² is presented. The stochastic programming planning model at upper level is integrated with the scheduling model at lower level using heuristic rules. This approach reduces the binary number caused by integration.

Many researchers focus on the external uncertainties such as demand uncertainty, supply uncertainty and price fluctuation in planning or scheduling optimization. Few focus on the process inherent uncertainty, such as product yield fluctuation, flow rate variation. Most people assume this kind of uncertainty obeying normal or uniform distribution. However, such assumption is neither accurate nor convincible compared with real world application. Lacking of information about process inherent uncertainty makes such optimization a big problem. Because of the process inherent uncertainty, the process data may be far from the one calculated by optimization model, especially when time goes on. Some treatment should be made to deal with such case, not only the optimization approach but also the data processing method. In real world application, process data depends on the accuracy of instruments. Moreover, in some cases, not all the process data are measureable. Process data with gross error or random error will distort some key constraints in the optimization model. As a result, data rectification approach should be executed before optimization.

The aim of this work is to provide a solution strategy of the optimization framework under both process inherent uncertainty and external uncertainty for a petrochemical plant. A real-time optimization framework is proposed. Planning and scheduling are integrated in the framework in a rolling horizon manner. The planning model is a MILP model with two-stage stochastic programming approach and the scheduling one is based on heuristic rules. The uncertainty of product yield is from both the uncertain raw material composition and the uncertain process. Data rectification and other statistical method are executed to obtain the distribution of uncertain yield. At the beginning of each optimization period, process data such as product yield and initial inventory is updated. The accuracy of the process data is guaranteed by an improved MT-NT method³ for gross error detection and data reconciliation. 

Reference:

1.      Grossmann, I., Enterprise-wide optimization: A new frontier in process systems engineering. AIChE Journal 2005, 51, (7), 1846-1857.

2.      Luo, C.; Rong, G., Hierarchical Approach for Short-Term Scheduling in Refineries. Industrial & Engineering Chemistry Research 2007, 46, (11), 3656-3668.

3.      Wang, F.; Jia, X.; Zheng, S.; Yue, J., An improved MT-NT method for gross error detection and data reconciliation. Computers & Chemical Engineering 2004, 28, (11), 2189-2192.