Integrated planning and scheduling under production uncertainties: Bi-level model formulation and hybrid solution method

We propose a novel method for integrating planning and scheduling problems under production uncertainties. The integrated problem is formulated into a bi-level program. The planning problem is solved in the upper level, while the scheduling problems in the planning periods are solved under uncertainties in the lower level. The planning and scheduling problems are linked via service level constraints. To solve the integrated problem, a hybrid method is developed, which iterates between a mixed-integer linear programming solver for the planning problem and an agent-based reactive scheduling method. If the service level constraints are not met, a cutting plane constraint is generated by the agent-based scheduling method and appended to the planning problem which is solved to determine new production quantities. The hybrid method returns an optimality gap for validating the solution quality. The proposed method is demonstrated by two complicated problems which are solved efficiently with small gaps less than 1%.     

Development of refinery scheduling system using mixed integer programming and expert system

This paper presents a hybrid refinery scheduling system combining mathematical programming model and expert system. Mixed-integer linear programming models for crude oil movement between units are merged into the expert system that is for qualitative issues concerning crude vessel unloading operations. The target problem ranging from the crude unloading to the crude charging to distillation towers is decomposed into several module problems for efficiency. Compared with existing scheduling approaches for oil movement, the proposed hybrid refinery scheduling system is very effective in dealing with timing decisions involving vessel unloading operations due to the advantages of an expert system. Since the proposed scheduling system can generate solutions so fast, it is expected to play a key role in the real processes. This paper is dedicated to Professor Wha Young Lee on the occasion of his retirement from Seoul National University.     

Production scheduling in a steelmaking-continuous casting plant

In this paper we describe an optimization procedure for planning the production of steel ingots in a steelmaking-continuous casting plant. The strict requirements of the production process defeated most of the earlier approaches to steelmaking-continuous casting production scheduling, mainly due to the lack of information in the optimization models. Our formulation of the problem is based on the alternative graph, which is a generalization of the disjunctive graph of Roy and Sussman. The alternative graph formulation allow us to describe in detail all the constraints that are relevant for the scheduling problem. We then solve the problem by using a beam search procedure, and compare our results with a lower bound of the optimal solutions and with the actual performance obtained in the plant. Computational experience shows the effectiveness of this approach.     

MILP scheduling model for multipurpose batch processes considering various intermediate storage policies

MILP (Mixed Integer Linear Programming) scheduling models for non-sequential multipurpose batch processes are presented. Operation sequences of products have to be made in each unit differently by considering production route of each product under a given intermediate storage policy to reduce idle time of units and to raise the efficiency of the process. We represent the starting and finishing time of a task in each unit with two coordinates for a given storage policy. One is based on products, and the other is based on operation sequences. Then, using binary variables and logical constraints, we match the variables used in the two coordinates into one. We suggest MILP models considering sequence dependent setup times to guarantee the optimality of the solutions. Two examples are presented to show the effectiveness of the suggested models.     

Model-Based Analysis of Convective Grain Drying Processes

ABSTRACT

Simulation results for convective drying processes in cross-flow packed bed grain dryers are discussed in this article. A mathematical model developed in order to enable easier design of convective dryers and optimization of operating conditions for agricultural materials (wheat, corn, sunflower seed, etc.) is used in the study. On the basis of calculated values of the state variables of the gas phase and the solids, a clear image of the process itself can be obtained, as well as an overview of advantages and disadvantages of a specific design, supporting and facilitating decisions about the choice of dryer type and operating scheme. The case of double passing of drying agent, with and without additional heating, for a cross-flow continuous dryer, as well as the case of different materials processed in a series of cross-flow batch dryers, is analyzed.     

A novel MILP formulation for short-term scheduling of multi-stage multi-product batch plants with sequence-dependent constraints

This paper presents a continuous-time mixed-integer linear programming (MILP) model for short-term scheduling of multi-stage multi-product batch plants. The model determines the optimal sequencing and the allocation of customer orders to non-identical processing units by minimizing the earliness and tardiness of order completion. This is a highly combinatorial problem, especially when sequence-dependent relations are considered such as the setup time between consecutive orders. A common approach to this scheduling problem relies on the application of tetra-index binary variables, i.e. (order, order, stage, unit) to represent all the combinations of order sequences and assignments to units in the various stages. This generates a huge number of binary variables and, as a consequence, much time is required for solutions. This paper proposes a novel formulation that replaces the tetra-index binary variables by one set of tri-index binary variables (order, order, stage) without losing the model's generality. By the elimination of the unit index, the new formulation requires considerably fewer binary variables, thus significantly shortening the solution time.     

Application of gain scheduling for modeling the nonlinear dynamic characteristics of NO<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> emissions from utility boilers

A hierarchical gain scheduling (HGS) approach is proposed to model the nonlinear dynamics of NO _x emissions of a utility boiler. At the lower level of HGS, a nonlinear static model is used to schedule the static parameters of local linear dynamic models (LDMs), such as static gains and static operating conditions. According to upper level scheduling variables, a multi-model method is used to calculate the predictive output based on lower-level LDMs. Both static and dynamic experiments are carried out at a 360 MW pulverized coal-fired boiler. Based on these data, a nonlinear static model using artificial neural network (ANN) and a series of linear dynamic models are obtained. Then, the performance of the HGS model is compared to the common multi-model in predicting NO _x emissions, and experimental results indicate that the proposed HGS model is much better than the multi-model in predicting NO _x emissions in the dynamic process. This paper was presented at the 7 ^th China-Korea Workshop on Clean Energy Technology held at Taiyuan, Shanxi, China, June 25–28, 2008.     

含局部流水的柔性作业车间调度研究

针对含有局部流水生产的柔性作业车间生产调度问题,首先在柔性作业车间调度问题的基础上建立调度模型,然后提出一种基于模拟退火法的调度算法,同时对加工路径和加工顺序进行优化,并实现最小化完工时间的调度目标。最后通过实例进行仿真,结果表明了算法的可行性和有效性。     

基于遗传算法的高职化工院校排课系统的设计与实现

排课问题是一个有约束的、多目标的组合优化问题,并且已经被证明是一个NP完全问题。遗传算法是一种随机搜索算法,非常适合于解决NP问题。本文将遗传算法应用于求解课表问题,采用优化编码结构组合的方法减少排课冲突,降低算法的复杂度;对排课问题的关键参数进行量化分析,针对染色体编码完成各个遗传算子的设计和开发任务,最后集成排课的整体优化算法。     

调度自动化实时系统与MIS系统间数据交换

在化工系统实际运行中,调度自动化实时系统与管理信息系统间存在数据交换的技术开发问题。以华鲁恒升集团调度自动化OASYS的系统的工程实际为基础,介绍一种实时SCADA系统与管理信息MIS系统间交换数据的实现方式。