Design,synthesis and scheduling of multipurpose batch plants via an effective continuous-time formulation

Design, synthesis and scheduling issues are considered simultaneously for multipurpose batch plants. An earlier proposed continuous-time formulation for scheduling is extended to incorporate design and synthesis. Processing recipes are represented by the State-Task Network (STN). The superstructure of all possible plant designs is constructed according to the potential availability of all processing/storage units. The proposed model takes into account the trade-offs between capital costs, revenues and operational flexibility. Computational studies are presented to illustrate the effectiveness of the proposed formulation. Both linear and nonlinear models are included, resulting in MILP and mixed-integer nonlinear programming (MINLP) problems, respectively. The MILP problems are solved using a branch and bound method. Globally optimal solutions are obtained for the nonconvex MINLP problems based on a key property that arises due to the special structure of the resulting models. Comparisons with earlier approaches are also presented.     

Generic mathematical programming formulation and solution for computer-aided molecular design

This short communication presents a generic mathematical programming formulation for computer-aided molecular design (CAMD). A given CAMD problem, based on target properties, is formulated as a mixed integer linear/non-linear program (MILP/MINLP). The mathematical programming model presented here, which is formulated as an MILP/MINLP problem, considers first-order and second-order molecular groups for molecular structure representation and property estimation. It is shown that various CAMD problems can be formulated and solved through this model.     

An MILP-MINLP decomposition method for the global optimization of a source based model of the multiperiod blending problem

The multiperiod blending problem involves binary variables and bilinear terms, yielding a nonconvex MINLP. In this work we present two major contributions for the global solution of the problem. The first one is an alternative formulation of the problem. This formulation makes use of redundant constraints that improve the MILP relaxation of the MINLP. The second contribution is an algorithm that decomposes the MINLP model into two levels. The first level, or master problem, is an MILP relaxation of the original MINLP. The second level, or subproblem, is a smaller MINLP in which some of the binary variables of the original problem are fixed. The results show that the new formulation can be solved faster than alternative models, and that the decomposition method can solve the problems faster than state of the art general purpose solvers.     

多产品间歇过程的分层次在线调度--一种数学规划与遗传算法的混合算法

In this contribution we present an online scheduling algorithm for a real world multiproduct batch plant. The overall mixed integer nonlinear programming (MINLP) problem is hierarchically structured into a mixed integer linear programming (MILP) problem first and then a reduced dimensional MINLP problem, which are optimized by mathematical programming (MP) and genetic algorithm (GA) respectively. The basis idea relies on combining MP with GA to exploit their complementary capacity. The key features of the hierarchical model are explained and illustrated with some real world cases from the multiproduct batch plants.     

Optimal design of reverse-osmosis networks for wastewater treatment

An optimization study of reverse-osmosis networks (RON) for wastewater treatment has been carried out by describing the system as a nonconvex mixed-integer nonlinear problem (MINLP). A mixed-integer linear problem (MILP) is derived from the original nonlinear problem by the convex relaxation of the nonconvex terms in the MINLP to provide bounds for the global optimum. The MILP model is solved iteratively to supply different initial guesses for the nonconvex MINLP model. It is found that such a procedure is effective in finding local optimum solutions in reasonable time and overcoming possible convergence difficulties associated with MINLP local search methods. Examples of water desalination and wastewater treatment from the pulp and paper industry are considered as case studies to illustrate the proposed solution strategy.     

A novel precedence-based and heuristic approach for short-term scheduling of multipurpose batch plants

Many continuous-time formulations have been proposed during the last decades for short-term scheduling of multipurpose batch plants. Although these models establish advantages over discrete-time representations, they are still inefficient in solving moderate-size problems, such as maximization of profit in long horizon, and minimization of makespan. Unlike existing literature, this paper presents a new precedence-based mixed integer linear programming (MILP) formulation for short-term scheduling of multipurpose batch plants. In the new model, multipurpose batch plants are described with a modified state-task network (STN) approach, and binary variables express the assignments and sequences of batch processing and storing. To eliminate the drawback of precedence-based formulations which commonly include large numbers of batches, an iterative procedure is developed to determine the appropriate number of batch that leads to global optimal solution. Moreover, four heuristic rules are proposed to selectively prefix some binary variables to 0 or 1, thereby reducing the overall number of binary variables significantly. To evaluate model performance, our model and the best models reported in the literature (S&K model and I&F model) are utilized to solve several benchmark examples. The result comparison shows that our model is more effective to find better solution for complex problems when using heuristic rules. Note that our approach not only can handle unlimited intermediate storage efficiently as well as the I&F model, but also can solve scheduling problems in limited intermediate storage more quickly than the S&K model.     

Simultaneous targeting and design for cooling water systems with multiple cooling water supplies

This paper presents a technique for simultaneous targeting and design in cooling water systems comprising of at least two cooling towers and several cooling water using operations. The presented technique is based on a superstructure from which a mathematical formulation is derived using system specific variables and parameters. It is demonstrated that in a system like this, true optimality can only be realized by a holistic consideration of the entire cooling water system. Consideration of individual subsets of cooling towers with their dedicated cooling water operations yields suboptimal results. Four operational cases are considered and structural considerations of corresponding mathematical formulations presented. The first case results in a linear programming (LP) formulation, the second case yields a mixed integer linear programming (MILP) formulation whilst the other two cases yield mixed integer nonlinear programming (MINLP) formulations which cannot be exactly linearized. However, in all cases significant improvements in excess of 40% were realized in targeting, without compromising the heat duty of the cooling water using operations. The main objective of this investigation is to debottleneck the overall cooling water supply for the cooling water network.     

Design of multipurpose production facilities: A RTN decomposition-based algorithm

A general mathematical formulation for the design of multipurpose facilities has recently been presented by Barbosa-Póvoa and Pantelides (1997). The model proposed permits a detailed consideration of the design problem taking account of trade-offs between capital costs, revenues and operational flexibility. The optimal solution involves the selection of the required processing and storage equipment items and the required levels of provision of other production resources such as utilities, manpower, cleaning and transportation equipment.In order to guarantee solution optimality, the above design formulation has to consider a large number of equipment items, out of which it will select the ones that will actually be incorporated in the plant. This may result in large mixed-integer linear programming (MILP) problems that are expensive to solve.This paper presents a decomposition approach for the solution of large batch process design problems. The approach involves the iterative solution of a master problem (representing a relaxation of the original design problem) and a design sub-problem (in which several of the design decisions are already fixed).An example illustrating the effectiveness of the proposed decomposition approach is presented.     

Recipe determination and scheduling of gasoline blending operations

Gasoline is a major contributor to the profit of a refinery. Scheduling gasoline‐blending operations is a critical and complex routine task involving tank allocation, component mixing, blending, product storage, and order delivery. Optimized schedules can maximize profit by avoiding ship demurrage, improving order delivery, minimizing quality give‐aways, avoiding costly transitions and slop generation, and reducing inventory costs. However, the blending recipe and scheduling decisions make this problem a nonconvex mixed‐integer nonlinear program (MINLP). In this article, we develop a slot‐based MILP formulation for an integrated treatment of recipe, specifications, blending, and storage and incorporate many real‐life features such as multipurpose product tanks, parallel nonidentical blenders, minimum run lengths, changeovers, piecewise constant profiles for blend component qualities and feed rates, etc. To ensure constant blending rates during a run, we develop a novel and efficient procedure that solves successive MILPs instead of a nonconvex MINLP. We use 14 examples with varying sizes and features to illustrate the superiority and effectiveness of our formulation and solution approach. The results show that our solution approach is superior to commercial solvers (BARON and DICOPT). © 2009 American Institute of Chemical Engineers AIChE J, 2010     

化工过程系统综合问题新的模块化求解策略和算法

针对过程系统综合问题中求解混合整数非线性规划（MINLP）问题传统解法的不足提出了在[JP+1]模块化环境中过程系统综合问题新的求解策略,同时提出相对应的算法.实例证明了该策略的正确性和新算法的有效性.     

Global optimization for scheduling refinery crude oil operations

In this work we present an outer-approximation algorithm to obtain the global optimum of a nonconvex mixed-integer nonlinear programming (MINLP) model that is used to represent the scheduling of crude oil movement at the front-end of a petroleum refinery. The model relies on a continuous time representation making use of transfer events. The proposed algorithm focuses on effectively solving a mixed-integer linear programming (MILP) relaxation of the nonconvex MINLP to obtain a rigorous lower bound (LB) on the global optimum. Cutting planes derived by spatially decomposing the network are added to the MILP relaxation of the original nonconvex MINLP in order to reduce the solution time for the MILP relaxation. The solution of this relaxation is used as a heuristic to obtain a feasible solution to the MINLP which serves as an upper bound (UB). The lower and upper bounds are made to converge to within a specified tolerance in the proposed outer-approximation algorithm. On applying the proposed technique to test examples, significant savings are realized in the computational effort required to obtain provably global optimal solutions.     

一种改进的顺序型多目的间歇工厂生产调度的MILP模型

分析了顺序型多目的工厂间歇生产的特点,建立了一种新的混合整数线性规划（MILP）模型.该模型以操作活动序列作为建模的依据,将整个间歇生产过程分解成若干个子系统.在对各子系统建模的基础上,实现了顺序型多目的工厂间歇调度的全局性优化.并通过算例验证了该模型求解结果的正确性和可行性.然后将新模型运用到更大规模的调度问题上,均求解出了有效的调度方案.     

Simultaneous subtour elimination model for single-stage multiproduct parallel batch scheduling with sequence dependent changeovers

In this paper a mixed-integer linear programming (MILP) model is presented to minimize makespan of single-stage multiproduct parallel batch production with sequence dependent changeovers. The computational inefficiency and suboptimal problems are addressed by the tight and rigorous formulation of the proposed model. Subtours (subcycles) are eliminated simultaneously so that the optimal solution is obtained in one step. The proposed model is tested with two examples. The results show that the model obtains the global optimal solutions with significant improvement in solution time.     

Optimal storage design for a multi-product plant: A non-convex MINLP formulation

We discuss a tank design problem for a multi product plant, in which the optimal cycle time and the optimal campaign size are unknown. A mixed-integer nonlinear programming (MINLP) formulation is presented, where non-convexities are due to the tank investment cost, storage cost, campaign setup cost and variable production rates. The objective of the optimization model is to minimize the sum of the production cost per ton per product produced. A continuous-time mathematical programming formulation is proposed and several extensions are discussed. The model is implemented in GAMS and computational results are reported for the two global MINLP solver BARON and LINDOGlobal as well as several nonlinear solvers available in GAMS.     

A discretization-based approach for the optimization of the multiperiod blend scheduling problem

In this paper, we introduce a new generalized multiperiod scheduling version of the pooling problem to represent time varying blending systems. A general nonconvex MINLP formulation of the problem is presented. The primary difficulties in solving this optimization problem are the presence of bilinear terms, as well as binary decision variables required to impose operational constraints. An illustrative example is presented to provide unique insight into the difficulties faced by conventional MINLP approaches to this problem, specifically in finding feasible solutions. Based on recent work, a new radix-based discretization scheme is developed with which the problem can be reformulated approximately as an MILP, which is incorporated in a heuristic procedure and in two rigorous global optimization methods, and requires much less computational time than existing global optimization solvers. Detailed computational results of each approach are presented on a set of examples, including a comparison with other global optimization solvers.     

Simulation based approach for optimal scheduling of fuel gas system in refinery

In refineries, fuel gas, which is continuously produced during the production process, is one of the most important energy sources. In this paper, a brief introduction of fuel gas system is given. The main problems concerned by the fuel gas system scheduler, such as the compressor operation strategy and the fuel assignment decision, are presented. A logical modeling method, which is called generalized disjunctive programming (GDP), is introduced to model the operation of compressors and the flow of branching structure pipeline network in the fuel gas system. The main purpose of this method is to make the modeling process more easily and systematically. In order to effectively deal with the flow rate proportion of loop structure pipeline network in the fuel gas system, an iterative procedure based on pipeline network simulation is proposed. Thus, the solution of a complex MINLP formulation is replaced by the sequential MILP problem. The efficiency of this method, which requires very low computational requirements, is illustrated with a case study.     

Multilevel strategies for the retrofit of large‐scale industrial water system: A brewery case study

This article presents an approach to designing a large‐scale water system, which integrates water‐using operations and wastewater treatment units in different production sections within the same network. This approach uses a mixed‐integer nonlinear programming (MINLP) model for water reuse and regeneration reuse in batch and semicontinuous processes. The application of this mathematical formulation to large‐scale industrial problems with changing daily production schedule leads to huge and complex mathematical models. Two alternative multilevel strategies are proposed to solve such problems by means of temporal decomposition. The approach is illustrated with a brewery case study that integrates water consumers in two production sections. The results obtained show that, despite the high piping cost, integration of both sections yields better result than the separate water network design in each section. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Mathematical programming approaches to the synthesis of chemical process systems

This paper presents a review of advances that have taken place in the mathematical programming approach to process design and synthesis. A review is first presented on the algorithms that are available for solving MINLP problems, and its most recent variant, Generalized Disjunctive Programming models. The formulation of superstructures, models and solution strategies is also discussed for the effective solution of the corresponding optimization problems. The rest of the paper is devoted to reviewing recent mathematical programming models for the synthesis of reactor networks, distillation sequences, heat exchanger networks, mass exchanger networks, utility plants, and total flowsheets. As will be seen from this review, the progress that has been achieved in this area over the last decade is very significant.     

DESIGN OF BATCH GRAPE DRYERS

The mathematical model describing the batch operation of industrial dryers with trucks and trays is presented and analysed for the case of grape dehydrators. The optimum flowsheet configuration and operation conditions for the specific mode of operation and type of dryer employed, are sought and verified by appropriate formulation of design and optimization strategies. The optimization objective is the total annual cost of the plant, subject to constraints imposed by the operation of the dryer, thermodynamics, and construction reasoning. The decision variables were the number of trucks and the drying air stream conditions involving temperature and humidity. The MINLP nature of the design problem required mathematical programming techniques for its solution. The optimization was carried out for a wide range of production capacities, and the optimal points were evaluated in each case. A characteristic design study was presented in order to demonstrate the effectiveness of the proposed approach.     

Scheduling of displacement batch digesters using discrete time formulation

This paper provides mathematical programming based optimization model and computational results for short-term scheduling of displacement batch digesters in a pulp industry. The scheduling problem involves development of an optimal solution that yields the best sequence of operations in each of the parallel batch digesters sharing common resources. The constraints are imposed on meeting the demand of pulp of different qualities within a specified time horizon. The problem comprises of both fixed-time and variable time durations of the tasks, different storage policies, zero-wait and finite wait times, and handling of shared resources. The scheduling problem is formulated using a state-task-network (STN) representation of production recipes, based on discrete time representation resulting in a mixed-integer linear programming (MILP) problem which is solved using GAMS software. The basic framework is adapted from the discrete-time model of Kondili et al. (Comput. Chem. Eng., 1993, 17, 211–227). Different case studies involving parallel digesters in multiple production lines are considered to demonstrate the effectiveness of the proposed formulation using two different objective functions.