Multiobjective optimization of multiproduct batch plants scheduling under environmental and economic concerns

In batch process scheduling, production trade‐offs arise from the simultaneous consideration of different objectives. Economic goals are expressed in terms of plant profitability and productivity, whereas the environmental objectives are evaluated by means of metrics originated from the use of life cycle assessment methodology. This work illustrates a novel approach for decision making by using multiobjective optimization. In addition, different metrics are proposed to select a possible compromise based on the distance to a nonexistent utopian solution, whose objective function values are all optimal. Thus, this work provides a deeper insight into the influence of the metrics selection for both environmental and economic issues while considering the trade‐offs of adopting a particular schedule. The use of this approach is illustrated through its application to a case study related to a multiproduct acrylic fiber production plant, special attention is put to the influence of product changeovers. © 2010 American Institute of Chemical Engineers AIChE J, 57: 2766–2782, 2010     

Optimal operation of process plants under partial shutdown conditions

A systematic strategy for optimal plant operation during partial shutdowns is proposed. We consider the situation where one or more process units are shut down due to failure or maintenance but where the remaining units are able to continue operation to some degree. The goal of the strategy is to manipulate the plant degrees‐of‐freedom—during and after the shutdown—such that production is restored in a cost‐optimal fashion while meeting safety and operational constraints. Optimal control trajectories are obtained through the solution of a dynamic optimization problem. A novel multitiered optimization approach allows the prioritization of multiple competing objectives and the specification of trade‐offs between them. Uncertainty in the downtime estimate, a crucial parameter in shutdown optimization, is addressed through reoptimization. We employ a transient predictive control algorithm for implementing the computed control policy under feedback. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4151–4168, 2013     

A property‐based approach to the synthesis of material conservation networks with economic and environmental objectives

This article presents a multiobjective optimization model for the recycle and reuse networks based on properties while accounting for the environmental implications of the discharged wastes using life‐cycle assessment. The economic objective function considers fresh sources and treatment costs, whereas the environmental objective function is measured through the eco‐indicator 99. The model considers constraints in the process sinks as well as in the environment based on stream properties such as pH, chemical oxygen demand, toxicity, density, and color, in addition to the composition of the waste streams. A global optimization procedure is developed by indirectly tackling properties through property operators and by segregating the process streams before treatment. Three examples are included, and the results show that it is possible to consider simultaneously the trade‐offs between the total annual costs and the overall environmental impact using the proposed methodology. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Minimization of the nonrenewable energy consumption in bioethanol production processes using a solar‐assisted steam generation system

The multiobjective optimization of a corn‐based bioethanol plant coupled with a solar‐assisted steam generation system with heat storage is described. Our approach relies on the combined use of process simulation, rigorous optimization tools, and economic and energetic plant analysis. The design task is posed as a bicriteria nonlinear programming problem that considers the simultaneous optimization of the plant profitability and the energy consumption. The capabilities of the proposed methodology are illustrated through a 120,000,000 kg/year corn‐based bioethanol plant considering weather data of Tarragona (Spain). © 2013 American Institute of Chemical Engineers AIChE J 60: 500–506, 2014     

Integrated Scheduling and Dynamic Optimization of Sequential Batch Processes with Online Implementation

An efficient decomposition method to solve the integrated problem of scheduling and dynamic optimization for sequential batch processes is proposed. The integrated problem is formulated as a mixed‐integer dynamic optimization problem or a large‐scale mixed‐integer nonlinear programming (MINLP) problem by discretizing the dynamic models. To reduce the computational complexity, we first decompose all dynamic models from the integrated problem, which is then approximated by a scheduling problem based on the flexible recipe. The recipe candidates are expressed by Pareto frontiers, which are determined offline by using multiobjective dynamic optimization to minimize the processing cost and processing time. The operational recipe is then optimized simultaneously with the scheduling decisions online. Because the dynamic models are encapsulated by the Pareto frontiers, the online problem is a mixed‐integer programming problem which is much more computationally efficient than the original MINLP problem, and allows the online implementation to deal with uncertainties. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2379–2406, 2013     

Teaching mathematical modeling software for multiobjective optimization in chemical engineering courses

This paper expects to give undergraduate students some guidelines about how to incorporate environmental considerations in a chemical supply chain and how the introduction of these concerns have an important effect on the results obtained in the multiobjective optimization problem where both economic and environmental aspects are considered simultaneously.To extend the economic and environmental assessment outside the chemical plant and to identify the tradeoffs associated with the reality of chemical and petrochemical industries, a simplified problem of a chemical supply chain is proposed as a case study.The inclusion of environmental concerns to this economic problem make this new case study a good example for undergraduate students interested in implementing simultaneous economic and environmental considerations in the chemical process design incorporating mathematical modeling software for solving this multiobjective problem.Thus, the final objective of this paper is to show to undergraduate students how environmental together with economic considerations could have an important impact in the logistics of a supply chain and how multiobjective optimization could be used to make better decisions in the design of chemical processes including its supply chain.To reach our purpose, the Pareto curve of the supply chain is obtained using the ?-constraint method. In addition, the tradeoffs of this multiobjective optimization have been identified and analyzed and ultimately a good decision based on the set of ‘equivalent’ optimal solutions for this chemical supply chain problem determined.     

Short-term scheduling and recipe optimization of blending processes

The main objective of this paper is to develop an integrated approach to coordinate short-term scheduling of multi-product blending facilities with nonlinear recipe optimization. The proposed strategy is based on a hierarchical concept consisting of three business levels: Long-range planning, short-term scheduling and process control. Long-range planning is accomplished by solving a large-scale nonlinear recipe optimization problem (multi-blend problem). Resulting blending recipes and production volumes are provided as goals for the scheduling level. The scheduling problem is formulated as a mixed-integer linear program derived from a resource-task network representation. The scheduling model permits recipe changeovers in order to utilize an additional degree of freedom for optimization. By interpreting the solution of the scheduling problem, new constraints can be imposed on the previous multi-blend problem. Thus bottlenecks arising during scheduling are considered already on the topmost long-range planning level. Based on the outlined approach a commercial software system has been designed to optimize the operation of in-line blending and batch blending processes. The application of the strategy and software is demonstrated by a detailed case study.     

Sustainable design and synthesis of algae‐based biorefinery for simultaneous hydrocarbon biofuel production and carbon sequestration

The superstructure optimization of algae‐based hydrocarbon biorefinery with sequestration of CO₂ from power plant flue gas is proposed. The major processing steps include carbon capture, algae growth, dewatering, lipid extraction and power generation, and algal biorefinery. We propose a multiobjective mixed‐integer nonlinear programming (MINLP) model that simultaneously maximizes the net present value (NPV) and minimizes the global warming potential (GWP) subject to technology selection constraints, mass balance constraints, energy balance constraints, technoeconomic analysis constraints, and environmental impact constraints. The model simultaneously determines the optimal decisions that include production capacity, size of each processing unit, mass flow rates at each stage of the process, utility consumption, economic, and environmental performances. We propose a two‐stage heuristic solution algorithm to solve the nonconvex MINLP model. Finally, the bicriteria optimization problem is solved with ε‐constraint method, and the resulting Pareto‐optimal curve reveals the trade‐off between the economic and environmental criteria. The results show that for maximum NPV, the optimal process design uses direct flue gas, a tubular photobioreactor for algae growth, a filtration dewatering unit, and a hydroprocessing pathway leading to 47.1 MM gallons of green diesel production per year at $6.33/gal corresponding to GWP of 108.7 kg CO₂‐eq per gallon. © 2013 American Institute of Chemical Engineers AIChE J, 59: 1599–1621, 2013     

Economic model predictive control for inventory management in supply chains

In this paper, we propose economic model predictive control with guaranteed closed-loop properties for supply chain optimization. We propose a new multiobjective stage cost that captures economics as well as risk at a node, using a weighted sum of an economic cost and a tracking stage cost. We also demonstrate integration of scheduling with control using a supply chain example. We integrate a scheduling model for a multiproduct batch plant with a control model for inventory control in a supply chain. We show recursive feasibility of such integrated control problems by developing simple terminal conditions.     

A reactive optimization strategy for the simultaneous planning,scheduling and control of short-period continuous reactors

The efficient and economic operation of processing systems ideally requires a simultaneous planning, scheduling and control framework. Even when the optimal simultaneous solution of this problem can result in large scale optimization problems, such a solution can represent economic advantages making feasible its computation using optimization decomposition and/or few operating scenarios. After reducing the complexity of the optimal simultaneous deterministic solution, it becomes feasible to take into account the effect of model and process uncertainties on the quality of the solution. In this work we consider those changes in product demands that take place once the process is already under continuous operation. Therefore, a reactive strategy is proposed to meet the new product demands. Based on an optimization formulation for handling the simultaneous planning, scheduling, and control problem of continuous reactors, we propose a heuristic strategy for dealing with unexpected events that may appear during operation of a plant. Such a strategy consists of the rescheduling of the products that remain to be manufactured after the given disturbance hits the process. Such reactive strategy for dealing with planning, scheduling and control problems under unforeseen events is tested using two continuous chemical reaction systems.     

A computational framework and solution algorithms for two‐stage adaptive robust scheduling of batch manufacturing processes under uncertainty

A novel two‐stage adaptive robust optimization (ARO) approach to production scheduling of batch processes under uncertainty is proposed. We first reformulate the deterministic mixed‐integer linear programming model of batch scheduling into a two‐stage optimization problem. Symmetric uncertainty sets are then introduced to confine the uncertain parameters, and budgets of uncertainty are used to adjust the degree of conservatism. We then apply both the Benders decomposition algorithm and the column‐and‐constraint generation (C&CG) algorithm to efficiently solve the resulting two‐stage ARO problem, which cannot be tackled directly by any existing optimization solvers. Two case studies are considered to demonstrate the applicability of the proposed modeling framework and solution algorithms. The results show that the C&CG algorithm is more computationally efficient than the Benders decomposition algorithm, and the proposed two‐stage ARO approach returns 9% higher profits than the conventional robust optimization approach for batch scheduling. © 2015 American Institute of Chemical Engineers AIChE J, 62: 687–703, 2016     

An approximate mathematical framework for resource-constrained multistage batch scheduling

A rigorous representation of the multistage batch scheduling problem is often useless to even provide a good feasible schedule for many real-world industrial facilities. In order to derive a much simpler scheduling methodology, some usual features of multistage batch plants should be exploited. A common observation in industry is that multistage processing structures usually present a bottleneck stage (BS) controlling the plant output level. Therefore, the quality of the production schedule heavily depends on the proper allocation and sequencing of the tasks performed at the stage BS. Every other part of the processing sequence should be properly aligned with the selected timetable for the bottleneck tasks. A closely related concept with an empirical basis is the usual existence of a common batch sequencing pattern along the entire processing structure that leads to define the constant-batch-ordering rule (CBOR). According to this rule, a single sequencing variable is sufficient to establish the relative ordering of two batches at every processing stage in which both have been allocated to the same resource item. This work introduces a CBOR-based global precedence formulation for the scheduling of order-driven multistage batch facilities. The proposed MILP approximate problem representation is able to handle sequence-dependent changeovers, delivery due dates and limited manufacturing resources other than equipment units. Optimal or near-optimal solutions to several large-scale examples were found at very competitive CPU times.     

Reactor modeling and recipe optimization of polyether polyol processes: Polypropylene glycol

The reactor modeling and recipe optimization of conventional semibatch polyether polyol processes, in particular for the polymerization of propylene oxide to make polypropylene glycol, is addressed. A rigorous mathematical reactor model is first developed to describe the dynamic behavior of the polymerization process based on first‐principles including the mass and population balances, reaction kinetics, and vapor‐liquid equilibria. Next, the obtained differential algebraic model is reformulated by applying a nullspace projection method that results in an equivalent dynamic system with better computational performance. The reactor model is validated against plant data by adjusting model parameters. A dynamic optimization problem is then formulated to optimize the process recipe, where the batch processing time is minimized, given a target product molecular weight as well as other requirements on product quality and process safety. The dynamic optimization problem is translated into a nonlinear program using the simultaneous collocation strategy and further solved with the interior point method to obtain the optimal control profiles. The case study result shows a good match between the model prediction and real plant data, and the optimization approach is able to significantly reduce the batch time by 47%, which indicates great potential for industrial applications. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2515–2529, 2013     

Optimization issues of the broke management system in papermaking

This paper presents an optimization strategy for the design and operation of a broke management system in a papermaking process. A stochastic model based on a two-state Markov process is presented for the broke system and a multiobjective and bi-level stochastic optimization model is developed featuring (i) a multiobjective operational subproblem for the optimization of the broke dosage and (ii) a multiobjective design problem formulation. An efficient optimization strategy is proposed for the operational subproblem along with a simulation based Pareto optimal solution for the design problem, and illustrated with a detailed case study.     

Sequential methodology for integrated optimization of energy and water use during batch process scheduling

Though commonly encountered in practice, energy and water minimization simultaneously during batch process scheduling has been largely neglected in literature. In this paper, we present a novel framework for incorporating simultaneous energy and water minimization in batch process scheduling. The overall problem is decomposed into three parts - scheduling, heat integration, and water reuse optimization - and solved sequentially. Our approach is based on the precept that in any production plant, utilities (energy and water) consumption is subordinate to the production target. Hence, batch scheduling is solved first to meet an economic objective function. Next, alternate schedules are generated through a stochastic search-based integer cut procedure. For each resulting schedule, minimum energy and water reuse targets are established and networks identified. As illustrated using two well-known case studies, a key feature of this approach is its ability to handle problems that are too complex to be solved using simultaneous methods.     

Integrated design of agricultural and industrial processes: A case study of combined sugar and ethanol production

Bioethanol production from molasses has advantages in greenhouse gas emissions because of its energy acquisition from bagasse. However, the improvement of bioethanol productivity is challenging; while each elemental technology option can be greatly improved, the trade‐offs between the production of raw sugar and bioethanol are complex. This issue should be addressed through the optimization of the whole system, including both agricultural and industrial processes. In this study, we constructed a model of combined raw sugar and bioethanol production from sugarcane considering agricultural and industrial technology options. Data were acquired through a detailed investigation of actual sugar mills. Case studies on the redesign of combined raw sugar and bioethanol production demonstrated that the simultaneous implementation of both technology options increases production of food, materials, and energy from plant‐derived renewable resources, thus demonstrating the effectiveness of the interdisciplinary approach. © 2016 American Institute of Chemical Engineers AIChE J, 63: 560–581, 2017     

考虑环境影响的多产品间歇化工过程优化排序

提出一种用于多产品厂排序的多目标优化模型 ,其目标函数同时考虑了总生产时间和废物对环境的影响 ,定义了关于废物的环境影响因子及决策因子 ,用以对总生产时间和废物及其对环境的影响进行权衡 .采用改进的模拟退火算法对具有不同决策因子和环境影响因子情况下的算例进行了求解 ,结果表明 ,该模型能够较好地反映环境因素在多产品厂排序问题中的影响 ,使排序结果达到生产时间和环境影响的综合最优     

多因素不确定条件下的间歇生产调度优化

不确定条件下的间歇生产调度优化是生产调度问题研究中具有挑战性的课题。提出了一种基于混合整数线性规划(MILP)的鲁棒优化模型,来优化不确定条件下的生产调度决策。考虑到生产过程中的操作成本和原料成本,建立了以净利润最大为调度目标的确定性数学模型。然后考虑需求、处理时间、市场价格三种不确定因素,建立可调整保守程度的鲁棒优化模型并转换成鲁棒对应模型。实例结果表明,鲁棒优化的间歇生产调度模型较确定性模型利润减少,但生产任务数量增加,设备空闲时间缩短,从而增强了调度方案的可靠性,实现了不确定条件下生产操作性和经济性的综合优化。     

Full Superstructure for Multiobjective Optimization of Multicolumn Chromatography for Ternary Separations

In the past decades, many multicolumn chromatographic processes have been proposed and studied for multicomponent continuous separation. In this study, the optimal operation for ternary multicolumn chromatographic separation is obtained from a full superstructure which embeds many different operations. A multiobjective optimization problem was solved to analyze the trade‐off between the throughput and the purity of the target component. It was found that the throughput of the optimal operation found from the full superstructure is significantly higher than that of the generalized full cycle scheme in our former publication in 2012.