A Disjunctive Model for Scheduling in a Manufacturing and Packing Facility with Intermediate Storage

The problem considered in this paper deals with the short term scheduling of a two stage continuous process with intermediate storage tanks. The major scheduling decisions in this problem are: a) the assignment of orders to various storage tanks; b) the sequence of orders in each unit; c) the timing of various operations in different stages. The problem is highly combinatorial in nature. The major challenge is to develop strong integer programming formulations and to devise efficient solution techniques. An initial model is presented in the form of a disjunctive program which is later transformed to a Mixed Integer Linear Programming (MILP) problem. A number of example problems are solved which highlight the limitations of this model as the number of orders increases. A heuristic based on partial preordering is considered which solves industrial sized problems very quickly. The objective function values for the heuristic solutions are within 7% of the optimal values.     

A batching and scheduling algorithm for the diffusion area in semiconductor manufacturing

This paper proposes an efficient heuristic algorithm for solving a complex batching and scheduling problem in a diffusion area of a semiconductor plant. Diffusion is frequently the bottleneck in the plant and also one of the most complex areas in terms of number of machines, constraints to satisfy and the large number of lots to manage. The purpose of this study is to investigate an approach to group lots in batches and to schedule these batches on machines. The problem is modelled and solved using a disjunctive graph representation. A constructive algorithm is proposed and improvement procedures based on iterative sampling and Simulated Annealing are developed. Computational experiments, carried out on actual industrial problem instances, show the ability of the iterative sampling algorithms to significantly improve the initial solution, and that Simulated Annealing enhances the results. Furthermore, our algorithm compares favourably to an algorithm reported in the literature for a simplified version of our problem. The constructive algorithm has been embedded in software and is currently being used in a semiconductor plant.     

ϵ-OA for the solution of bi-objective generalized disjunctive programming problems in the synthesis of nonlinear process networks

There has been an increasing interest in multicriteria optimization (MCO) of nonlinear process network problems in recent years. Several mathematical models have been developed and solved using MCO methodologies including ϵ-constraint, weighted sum, and minimum distance. In this paper, we investigate the bi-objective nonlinear network synthesis problem and propose an effective algorithm, ϵ-OA, based on augmented ϵ-constraint and logic-based outer approximation (OA). We provide theoretical characterization of the proposed algorithm and show that the solutions generated are efficient. We illustrate the effectiveness of our novel algorithm on two benchmark problems. The ϵ-OA is compared to the straightforward use of OA with augmented ϵ-constraint algorithm (ϵ-con + OA), the augmented ϵ-constraint without OA (ϵ-MINLP), and the traditional ϵ-constraint (T-ϵ-con). Based on the results, our novel algorithm is very effective in solving the bi-objective generalized disjunctive programming problems in the synthesis of process networks.     

The formulation of optimal mixtures with generalized disjunctive programming: A solvent design case study

Systematic approaches for the design of mixtures, based on a computer‐aided mixture/blend design (CAM^bD) framework, have the potential to deliver better products and processes. In most existing methodologies the number of mixture ingredients is fixed (usually a binary mixture) and the identity of at least one compound is chosen from a given set of candidate molecules. A novel CAM^bD methodology is presented for formulating the general mixture design problem where the number, identity and composition of mixture constituents are optimized simultaneously. To this end, generalized disjunctive programming is integrated into the CAM^bD framework to formulate the discrete choices. This generic methodology is applied to a case study to find an optimal solvent mixture that maximizes the solubility of ibuprofen. The best performance in this case study is obtained with a solvent mixture, showing the benefit of using mixtures instead of pure solvents to attain enhanced behavior. © 2016 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 62: 1616–1633, 2016     

Application of spatial statistics as a screening tool for sustainable flood retention basin management

In the context of climate change and the EU flood directive, this paper analyses and explores sustainable flood retention basins (SFRB) as adaptive structures contributing to water resources management and flood risk control. A dataset of 371 potential SFRB (including many operating reservoirs) characterized by 40 variables have been surveyed across central Scotland. However, the spatial properties of these SFRB, such as water storage (which relates to flooding depth) in different regions, are ambiguous. This paper uses geostatistics on the Scottish dataset. Spatial analysis showed that ordinary kriging, which is a spatial interpolation method, could be successfully applied to estimate numerical values for all key flood control variables everywhere in the study area. Moreover, the probability that certain threshold values relevant to flood control managers were exceeded can also be calculated by using disjunctive kriging. The findings provide an effective screening tool in assessing flood control using SFRB.     

A modeling strategy for integrated batch process development based on mixed-logic dynamic optimization

This paper introduces an optimization-based approach for the simultaneous solution of batch process synthesis and plant allocation, with decisions like the selection of chemicals, process stages, task-unit assignments, operating modes, and optimal control profiles, among others. The modeling strategy is based on the representation of structural alternatives in a state-equipment network (SEN) and its formulation as a mixed-logic dynamic optimization (MLDO) problem. Particularly, the disjunctive multistage modeling strategy by Oldenburg and Marquardt (2008) is extended to combine and organize single-stage and multistage models for representing the sequence of continuous and batch units in each structural alternative and for synchronizing dynamic profiles in input and output operations with material transference. Two numerical examples illustrate the application of the proposed methodology, showing the enhancement of the adaptability potential of batch plants and the improvement of global process performance thanks to the quantification of interactions between process synthesis and plant allocation decisions.     

Synthesis of complex thermally coupled distillation systems including divided wall columns

The design of thermally coupled distillation sequences explicitly including the possibility of divided wall columns (DWC) is described. A DWC with a single wall can be considered thermodynamically equivalent to a fully thermally coupled (FTC) subsystem formed by three separation tasks (a Petlyuk configuration in the case of three‐component mixtures). It is shown how to systematically identify all the sequences of separation tasks that can produce configurations that include at least a DWC. Feasible sequences that explicitly include DWCs are enforced through a set of logical relationships in terms of Boolean variables. These logical relationships include as feasible alternatives from conventional columns (each column must have a condenser and a reboiler) to FTC systems (only one reboiler and one condenser in the entire system). A comprehensive disjunctive programming formulation for finding the optimal solution is presented. The model is based on the Fenske, Underwood Gilliland equations. However, the disjunctive formulation allows easily the use of any other shortcut, aggregated or even rigorous model without modifying much the structure of the model. Two illustrative examples illustrate the procedure. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1139–1159, 2013     

基于广义析取动态优化模型综合间歇精馏系统

基于数学规划技术提出间歇精馏过程设计与操作同步优化方法。首先,在原状态空间超级结构基础上嵌入时间维度,形成状态-时-空间超级结构,扩大间歇精馏过程优化空间。其次,将广义析取规划的思想引入间歇精馏动态优化模型,增加模型的直观性和可扩展性,并通过逻辑与析取约束,对方程进行合理分类,有效降低冗余方程导致的计算复杂度。新的优化策略采用严格模型,去除了恒摩尔流等简化假设,通过综合权衡设备投资、公用工程费用和操作周期等因素,一步获得最佳的间歇精馏塔型配置、结构参数和决策变量的动态控制方案。最后,以不同条件下苯-甲苯二元物系的间歇精馏分离为例展示了其有效性。     

Ordered model trees: A normal form for disjunctive deductive databases

Model trees were conceived as a structure-sharing approach to represent information in disjunctive deductive databases. In this paper we introduce the concept ofordered minimal model trees as a normal form for disjunctive deductive databases. These are model trees in which an order is imposed on the elements of the Herbrand base. The properties of ordered minimal model trees are investigated as well as their possible utilization for efficient manipulation of disjunctive deductive databases. Algorithms are presented for constructing and performing operations on ordered model trees. The complexity of ordered model tree processing is addressed. Model forests are presented as an approach to reduce the complexity of ordered model tree construction and processing.This research was supported by the National Science Foundation, under the grant Nr. IRI-89-16059, the Air Force Office of Scientific Research, under the grant Nr. AFOSR-91-0350, and the Fulbright Scholar Program.This work was done while visiting at the University of Maryland Institute for Advanced Computer Studies.     

Scheduling of a job-shop problem with limited output buffers

ABSTRACT

This article addresses a job-shop problem with limited output buffers (JS-LOB) with the objective of minimizing the process makespan. An integer nonlinear mathematical programming model is proposed to describe this problem. Based on the model, a two-stage algorithm consisting of obtaining feasible solutions and a local search is proposed to solve the JS-LOB problem. The local search has two operators: the first is a neighbourhood structure based on a disjunctive graph model, and the second is similar to crossover in the genetic algorithm to avoid falling into local optima. Computational results are presented for a set of benchmark tests. The results show the effectiveness of the proposed algorithm and indicate whether the processing time of the job conforms to a uniform distribution. When the proportion between the capacity of the buffer and the number of jobs is larger than 20%, the influence of the buffer becomes very small.