Design and planning of infrastructures for bioethanol and sugar production under demand uncertainty

In this paper, we address the strategic planning of integrated bioethanol–sugar supply chains (SC) under uncertainty in the demand. The design task is formulated as a multi-scenario mixed-integer linear programming (MILP) problem that decides on the capacity expansions of the production and storage facilities of the network over time along with the associated planning decisions (i.e., production rates, sales, etc.). The MILP model seeks to optimize the expected performance of the SC under several financial risk mitigation options. This consideration gives a rise to a multi-objective formulation, whose solution is given by a set of network designs that respond in different ways to the actual realization of the demand (the uncertain parameter). The capabilities of our approach are demonstrated through a case study based on the Argentinean sugarcane industry. Results include the investment strategy for the optimal SC configuration along with an analysis of the effect of demand uncertainty on the economic performance of several biofuels SC structures.     

A generalized cutting-set approach for nonlinear robust optimization in process systems engineering

We propose a novel computational framework for the robust optimization of highly nonlinear, non-convex models that possess uncertainty in their parameter data. The proposed method is a generalization of the robust cutting-set algorithm that can handle models containing irremovable equality constraints, as is often the case with models in the process systems engineering domain. Additionally, we accommodate general forms of decision rules to facilitate recourse in second-stage (control) variables. In particular, we compare and contrast the use of various types of decision rules, including quadratic ones, which we show in certain examples to be able to decrease the overall price of robustness. Our proposed approach is demonstrated on three process flow sheet models, including a relatively complex model for amine-based CO₂ capture. We thus verify that the generalization of the robust cutting-set algorithm allows for the facile identification of robust feasible designs for process systems of practical relevance.     

Optimizing inventory policies in process networks under uncertainty

We address the inventory planning problem in process networks under uncertainty through stochastic programming models. Inventory planning requires the formulation of multiperiod models to represent the time-varying conditions of industrial process, but multistage stochastic programming formulations are often too large to solve. We propose a policy-based approximation of the multistage stochastic model that avoids anticipativity by enforcing the same decision rule for all scenarios. The proposed formulation includes the logic that models inventory policies, and it is used to find the parameters that offer the best expected performance. We propose policies for inventory planning in process networks with arrangements of inventories in parallel and in series. We compare the inventory planning strategies obtained from the policy-based formulation and the analogous two-stage approximation of the multistage stochastic program. Sequential implementation of the planning strategies in receding horizon simulations shows the advantages of the policy-based model, despite the increase in computational complexity.     

Tactical capacity planning for semiconductor manufacturing: MILP models and scalable distributed parallel algorithms

A multiperiod stochastic mixed‐integer linear programming model is developed to address the tactical capacity planning of semiconductor manufacturing with considerations of complex routing of material flows, in‐process inventory, demand and capacity variability, multisite production, capacity utilization rate, and downside risk management. Both planning level decisions (i.e., capacity allocation and customer service level decisions) as well as operational level decisions (i.e., production, inventory, and shipment decisions) can be simultaneously determined based on the two proposed multiobjective optimization models. To address the huge number of scenarios needed to characterize the uncertainty and the large number of first‐stage integer variables in industrial scale applications, two novel scalable distributed parallel optimization algorithms are developed to mitigate the computational burden. The proposed mathematical models and algorithms are illustrated through two case studies from a major US semiconductor manufacturer. Results from these case studies provide key decision support for capacity expansion in semiconductor industry. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3930–3946, 2016     

Planning and scheduling of flexible process networks under uncertainty with stochastic inventory: MINLP models and algorithm

The tactical planning and scheduling of chemical process networks consisting of both dedicated and flexible processes under demand and supply uncertainty is addressed. To integrate the stochastic inventory control decisions with the production planning and scheduling, a mixed‐integer nonlinear programming (MINLP) model is proposed that captures the stochastic nature of the demand variations and supply delays using the guaranteed‐service approach. The model takes into account multiple tradeoffs and simultaneously determines the optimal selection of production schemes, purchase amounts of raw materials, sales of final products, production levels of processes, detailed cyclic production schedules for flexible processes, and working inventory and safety stock levels of all chemicals involved in the process network. To globally optimize the resulting nonconvex MINLP problems with modest computational times, the model properties are exploited and a tailored branch‐and‐refine algorithm based on the successive piecewise linear approximation is proposed. To handle the degeneracy of alternative optima in assignment configurations of production scheduling, three symmetry breaking cuts are further developed to accelerate the solution process. The application of the model and the performance of the proposed algorithm are illustrated through three examples with up to 25 chemicals and 16 processes including at most 8 production schemes for each flexible process. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1511–1532, 2013     

Multiechelon supply chain planning with sequence‐dependent changeovers and price elasticity of demand under uncertainty

An optimization framework is proposed for a multiechelon multiproduct process supply chain planning under demand uncertainty considering inventory deviation and price fluctuation. In this problem, the sequence‐dependent changeovers occur at the production plants, and price elasticity of demand is considered at the markets. Based on the classic formulation of travelling salesman problem (TSP), a mixed‐integer liner programming (MILP) is developed, whose objective function considers the profit, inventory deviations from the desired trajectories and price changes simultaneously. Model predictive control (MPC) approach is adopted to tackle the uncertain issues, as well as the inventory and price maintenance. The applicability of the proposed model and approach was illustrated by solving a supply chain example. Some issues, including length of the control horizon, price elasticity of demand, weights, inventory trajectories, and changeovers, are discussed based on the computational results. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

考虑需求不确定性的化工生产计划与调度集成

生产计划与调度是化工供应链优化中两个重要的决策问题。为了提高生产决策的效率,不仅要对计划与调度进行集成,而且要考虑不确定性的影响。对于多周期生产计划与调度问题,首先在每个生产周期内,分别建立计划与调度的确定性模型,通过产量关联对二者进行集成。然后考虑需求不确定性,使用有限数量的场景表达决策变量,建立二阶段随机规划模型。最后运用滚动时域求解策略,使计划与调度结果在迭代过程中达到一致。实例结果表明,在考虑需求不确定性时,与传统方法相比,随机规划方法可以降低总费用,结合计划与调度的分层集成策略,实现了生产操作性和经济性的综合优化。     

Multisite supply planning for drug products under uncertainty

In the pharmaceutical industry, the goal of a supply planner is to make efficient capacity allocation decisions that ensure an uninterrupted supply of drug products to patients and to maintain product inventory levels close to the target stock. This task can be challenging due to the limited availability of manufacturing assets, uncertainties in product demand, fluctuations in production yields, and unplanned site downtimes. It is not uncommon to observe uneven distribution of product inventories with some products carrying excess inventories, while other products may be close to a stockout. Maintaining high stock levels can have economic repercussions due to the risk of expiration of unused products (whereas products facing a stockout can adversely affect the treatment regimen of patients). The network complexity of pharmaceutical supply-chains coupled with regulatory constraints and siloed planning systems force supply planners to rely on manual (error-prone) decision-making processes. Such an approach results in suboptimal capacity allocation and inventory management decisions. In this work, we propose a stochastic optimization methodology for the production scheduling of multiple drug products in lyophilization units across multiple sites. The framework leverages information obtained from historical and forecast data to generate scenarios of uncertain parameters (e.g., yield, demand, and downtimes) that can realize in the future. The optimization model determines a product filling schedule that maintains product stock levels close to targets under diverse scenarios. We show that this approach helps in avoiding reactive scheduling and in maintaining a more robust production plan than deterministic procedures (which ignore uncertainty). Specifically, planning under a stochastic optimization approach reduces the number of scenarios under which backlogs are observed and also reduces the magnitude of the backlogs.     

Cooperative optimal power flow with flexible chemical process loads

Power systems operations involve dispatching generation capacity and ancillary services as required to sustain reliable functioning of the electric grid. The dispatch schedules are determined by solving power flow calculations that incorporate models of the network components in real time as the power grid conditions change. Electricity intensive chemical processes can potentially provide grid support services and a closer coordination between process and grid operations can be beneficial. This cooperation is hindered by the lack of suitable process models, which appropriately protect process information. We propose a means to model the grid-relevant dynamics of chemical processes, and a framework for embedding such models in optimal power flow calculations. We present an extensive case study concerning cooperative demand-response operation for an electricity-intensive chemical process, chlor-alkali production. The results indicate significant flexibility and economic benefits both at the utility and at the end-user levels.     

A Comparative Theoretical and Computational Study on Robust Counterpart Optimization: I. Robust Linear Optimization and Robust Mixed Integer Linear Optimization

Robust counterpart optimization techniques for linear optimization and mixed integer linear optimization problems are studied in this paper. Different uncertainty sets, including those studied in literature (i.e., interval set; combined interval and ellipsoidal set; combined interval and polyhedral set) and new ones (i.e., adjustable box; pure ellipsoidal; pure polyhedral; combined interval, ellipsoidal, and polyhedral set) are studied in this work and their geometric relationship is discussed. For uncertainty in the left hand side, right hand side, and objective function of the optimization problems, robust counterpart optimization formulations induced by those different uncertainty sets are derived. Numerical studies are performed to compare the solutions of the robust counterpart optimization models and applications in refinery production planning and batch process scheduling problem are presented.     

Tightening methods for continuous‐time mixed‐integer programming models for chemical production scheduling

Important advances in modeling chemical production scheduling problems have been made in recent years, yet effective solution methods are still required. We use an algorithm that uses process network and customer demand information to formulate powerful valid inequalities that substantially improve the solution process. In particular, we extend the ideas recently developed for discrete‐time formulations to continuous‐time models and show that these tightening methods lead to a significant decrease in computational time, up to more than three orders of magnitude for some instances. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4461–4467, 2013     

Multistage adaptive optimization using hybrid scenario and decision rule formulation

Scenario-based stochastic programming and linear decision rule (LDR)-based robust optimization are prevalent methods for solving multistage adaptive optimization (MSAP) problems. In practical applications such as capacity expansion planning of chemical processes, often multiple sources of uncertainty affect the problem which introduces challenges to traditional stochastic optimization methods. While a large number of uncertain parameters exist in the problem, using scenario-based method results in very large problem size and the solution becomes computationally expensive. In addition, when the constraints include multiplication of uncertain parameters and adaptive variables, the constraints are not linear with respect to uncertain parameters when the LDR method is used. In order to address these challenges, we propose two different hybrid methods where scenario and decision rule methods are combined to solve the MSAP problem. The article demonstrates the computational performance of the proposed hybrid methods using two chemical process planning examples.     

Evaluating demand response opportunities for power systems resilience using MILP and MINLP Formulations

While peak shaving is commonly used to reduce power costs, chemical process facilities that can reduce power consumption on demand during emergencies (e.g., extreme weather events) bring additional value through improved resilience. For process facilities to effectively negotiate demand response (DR) contracts and make investment decisions regarding flexibility, they need to quantify their additional value to the grid. We present a grid-centric mixed-integer stochastic programming framework to determine the value of DR for improving grid resilience in place of capital investments that can be cost prohibitive for system operators. We formulate problems using both a linear approximation and a nonlinear alternating current power flow model. Our numerical results with both models demonstrate that DR can be used to reduce the capital investment necessary for resilience, increasing the value that chemical process facilities bring through DR. However, the linearized model often underestimates the amount of DR needed in our case studies. Published 2018. This article is a U.S. Government work and is in the public domain in the USA. AIChE J, 65: e16508, 2019     

A hybrid science-guided machine learning approach for modeling chemical processes: A review

This study presents a broad perspective of hybrid process modeling combining the scientific knowledge and data analytics in bioprocessing and chemical engineering with a science-guided machine learning (SGML) approach. We divide the approach into two major categories: ML complements science, and science complements ML. We review the literature relating to the hybrid SGML approach, and propose a systematic classification of hybrid SGML models. For applying ML to improve science-based models, we present expositions of direct serial and parallel hybrid modeling and their combinations, inverse modeling, reduced-order modeling, quantifying uncertainty in the process and even discovering governing equations of the process model. For applying scientific principles to improve ML models, we discuss the science-guided design, learning and refinement. For each subcategory, we identify its requirements, strengths, and limitations, together with their published and potential applications. We also present several examples to illustrate different hybrid SGML methodologies for modeling chemical processes.     

The effect of uncertainty on the optimal closed-loop supply chain planning under different partnerships structure

In a global economy, the key to success is providing products around the world at the right time in the right quantity and quality, at a low cost. Efficient supply chains have an important role in guaranteeing this success. Optimized planning of such structures is required and uncertainties regarding product demands and prices, amongst other supply chain conditions, should also be considered. In this paper, we look into supply chain planning decisions that account for uncertainty on product portfolios demand and prices. A multi-period planning model is developed where the supply chain operational decisions on supply, production, transportation, and distribution at the actual period consider the uncertainty on products’ demand and prices. Different decision scenarios, involving the evaluation of the supply chain economical performance, are analyzed (e.g. global operating costs/profit realized) for different criteria on the importance of the partners within the global chain (i.e. partners’ structure). A Mixed Integer Linear Programming (MILP) formulation is formulated for each planning scenario and the optimal solution is reached using a standard Branch and Bound (B&B) procedure. The final results provide details on the supply chain partners production, transportation and inventory, at each planning period, while accounting for the importance of each partner in the global chain as well as demand/price uncertainties. The applicability of the developed formulation is illustrated through the solution of a real case-study involving an industrial chain in the pharmaceutical sector.     

Moving horizon closed‐loop production scheduling using dynamic process models

The economic circumstances that define the operation of chemical processes (e.g., product demand, feedstock and energy prices) are increasingly variable. To maximize profit, changes in production rate and product grade must be scheduled with increased frequency. To do so, process dynamics must be considered in production scheduling calculations, and schedules should be recomputed when updated economic information becomes available. In this article, this need is addressed by introducing a novel moving horizon closed‐loop scheduling approach. Process dynamics are represented explicitly in the scheduling calculation via low‐order models of the closed‐loop dynamics of scheduling‐relevant variables, and a feedback connection is built based on these variables using an observer structure to update model states. The feedback rescheduling mechanism consists of, (a) periodic schedule updates that reflect updated price and demand forecasts, and, (b) event‐driven updates that account for process and market disturbances. The theoretical developments are demonstrated on the model of an industrial‐scale air separation unit. © 2016 American Institute of Chemical Engineers AIChE J, 63: 639–651, 2017     

多元校正分光光度法快速测定COD

快速消解分光光度法测定水质化学需氧量是新颁布的环境行业标准,其校正模型采用单波长点测定数据的直线拟合回归分析,存在某些测定波长点计算COD的不确定性和与国标重铬酸盐法的相对偏差较大等问题.应用多元校正法改进回归模型,在高量程和低量程范围内的校正计算结果与GB法测定COD的相对误差为1.42%和4.03%,具有较好的一致性,解决了直线拟合回归不确定性的问题.     

A computationally efficient simulation-based optimization method with region-wise surrogate modeling for stochastic inventory management of supply chains with general network structures

Simulation-based optimization is widely used to improve the performance of an inventory system under uncertainty. However, the black-box function between the input and output, along with the expensive simulation to reproduce a real inventory system, introduces a huge challenge in optimizing these performances. We propose an efficient framework for reducing the total operation cost while satisfying the service level constraints. The performances of each inventory in the system are estimated by kriging models in a region-wise manner which greatly reduces the computational time during both sampling and optimization. The aggregated surrogate models are optimized by a trust-region framework where a model recalibration process is used to ensure the solution's validity. The proposed framework is able to solve general supply chain problems with the multi-sourcing capability, asynchronous ordering, uncertain demand and stochastic lead time. This framework is demonstrated by two case studies with up to 18 nodes with inventory holding capability in the network.     

Nonlinear scheduling with time-variable electricity prices using sensitivity-based truncations of wavelet transforms

We propose an algorithm for scheduling subject to time-variable electricity prices using nonlinear process models that enables long planning horizons with fine discretizations. The algorithm relies on a reduced-space formulation and enhances our previous work (Schäfer et al., Comput Chem Eng, 2020;132:106598) by a sensitivity-based refinement procedure. We therein expose the coefficients of the wavelet transform of the time series of independent process variables to the optimizer. The problem size is reduced by truncating the transform and iteratively adjusted using Lagrangian multipliers. We apply the algorithm to the scheduling of a multi-product air separation unit. The nonlinear power consumption characteristic is replaced by an artificial neural network trained on data from a rigorous model. We demonstrate that the proposed algorithm reduces the number of optimization variables by more than one order of magnitude, whilst furnishing feasible schedules with insignificant losses in objective values compared to solutions considering the full dimensionality.