Data-driven distributionally robust optimization of shale gas supply chains under uncertainty

This article aims to leverage the big data in shale gas industry for better decision making in optimal design and operations of shale gas supply chains under uncertainty. We propose a two-stage distributionally robust optimization model, where uncertainties associated with both the upstream shale well estimated ultimate recovery and downstream market demand are simultaneously considered. In this model, decisions are classified into first-stage design decisions, which are related to drilling schedule, pipeline installment, and processing plant construction, as well as second-stage operational decisions associated with shale gas production, processing, transportation, and distribution. A data-driven approach is applied to construct the ambiguity set based on principal component analysis and first-order deviation functions. By taking advantage of affine decision rules, a tractable mixed-integer linear programming formulation can be obtained. The applicability of the proposed modeling framework is demonstrated through a small-scale illustrative example and a case study of Marcellus shale gas supply chain. Comparisons with alternative optimization models, including the deterministic and stochastic programming counterparts, are investigated as well. © 2018 American Institute of Chemical Engineers AIChE J, 65: 947–963, 2019     

Multi‐stage adjustable robust optimization for process scheduling under uncertainty

Variations in parameters such as processing times, yields, and availability of materials and utilities can have a detrimental effect in the optimality and/or feasibility of an otherwise “optimal” production schedule. In this article, we propose a multi‐stage adjustable robust optimization approach to alleviate the risk from such operational uncertainties during scheduling decisions. We derive a novel robust counterpart of a deterministic scheduling model, and we show how to obey the observability and non‐anticipativity restrictions that are necessary for the resulting solution policy to be implementable in practice. We also develop decision‐dependent uncertainty sets to model the endogenous uncertainty that is inherently present in process scheduling applications. A computational study reveals that, given a chosen level of robustness, adjusting decisions to past parameter realizations leads to significant improvements, both in terms of worst‐case objective as well as objective in expectation, compared to the traditional robust scheduling approaches. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1646–1667, 2016     

Supply chain management using an optimization driven simulation approach

In this work, we propose a hybrid simulation‐based optimization framework to solve the supply chain management problem. The hybrid approach combines a mathematical programming model with an agent‐based simulation model and uses them in an iterative framework. The optimization model is used to guide the decisions toward an optimal allocation of resources given the realistic supply chain representation given by the simulation. Thus, the proposed approach provides a more realistic solution compared to a stand‐alone optimization model, often a simplified representation of the actual system, by making use of the simulation model, which captures the detailed dynamic behavior of the system. A multiobjective problem has been formulated by taking into consideration the environmental impact of supply chain operations. The proposed framework has been applied to small‐scale case studies to study the effectiveness of the approach for such problems. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4612–4626, 2013     

Scheduling of crude oil operations under demand uncertainty: A robust optimization framework coupled with global optimization

Scheduling of crude oil operations is an important component of overall refinery operations, because crude oil costs account for about 80% of the refinery turnover. The mathematical modeling of blending different crudes in storage tanks results in many bilinear terms, which transform the problem into a challenging, nonconvex, mixed‐integer nonlinear programming (MINLP) optimization model. In practice, uncertainties are unavoidable and include demand fluctuations, ship arrival delays, equipment malfunction, and tank unavailability. In the presence of these uncertainties, an optimal schedule generated using nominal parameter values may often be suboptimal or even become infeasible. In this article, the robust optimization framework proposed by Lin et al. and Janak et al. is extended to develop a deterministic robust counterpart optimization model for demand uncertainty. The recently proposed branch and bound global optimization algorithm with piecewise‐linear underestimation of bilinear terms by Li et al. is also extended to solve the nonconvex MINLP deterministic robust counterpart optimization model and generate robust schedules. Two examples are used to illustrate the capability of the proposed robust optimization approach, and the extended branch and bound global optimization algorithm for demand uncertainty. The computational results demonstrate that the obtained schedules are robust in the presence of demand uncertainty. © 2011 American Institute of Chemical Engineers AIChE J, 58: 2373–2396, 2012     

Robust optimization and stochastic programming approaches for medium-term production scheduling of a large-scale steelmaking continuous casting process under demand uncertainty

Scheduling of steelmaking-continuous casting (SCC) processes is of major importance in iron and steel operations since it is often a bottleneck in iron and steel production. In practice, uncertainties are unavoidable and include demand fluctuations, processing time uncertainty, and equipment malfunction. In the presence of these uncertainties, an optimal schedule generated using nominal parameter values may often be suboptimal or even become infeasible. In this paper, we introduce robust optimization and stochastic programming approaches for addressing demand uncertainty in steelmaking continuous casting operations. In the robust optimization framework, a deterministic robust counterpart optimization model is introduced to guarantee that the production schedule remains feasible for the varying demands. Also, a two-stage scenario based stochastic programming framework is investigated for the scheduling of steelmaking and continuous operations under demand uncertainty. To make the resulting stochastic programming problem computationally tractable, a scenario reduction method has been applied to reduce the number of scenarios to a small set of representative realizations. Results from both the robust optimization and stochastic programming methods demonstrate robustness under demand uncertainty and that the robust optimization-based solution is of comparable quality to the two-stage stochastic programming based solution.     

Process design and control optimization: A simultaneous approach by multi‐parametric programming

We present a framework for the application of design and control optimization via multi‐parametric programming through four case studies. We develop design dependent multi‐parametric model predictive controllers that are able to provide the optimal control actions as functions of the system state and the design of the process at hand, via our recently introduced PAROC framework (Pistikopoulos et al, Chem Eng Sci. 2015;136:115–138). The process and the design dependent explicit controllers undergo a mixed integer dynamic optimization (MIDO) step for the determination of the optimal design. The result of the MIDO is the optimal design of the process under optimal operation. We demonstrate the framework through case studies of a tank, a continuously stirred tank reactor, a binary distillation column and a residential cogeneration unit. © 2017 American Institute of Chemical Engineers AIChE J, 2017     

Multi‐Objective Optimization of Pseudo‐Dynamic Operation of Naphtha Pyrolysis by a Surrogate Model

A simple pseudo‐dynamic surrogate model is developed in the framework of the state space model with the feed‐forward neural network to replace the complex free radical pyrolysis model. The surrogate model is then applied to investigate the multi‐objective optimization of two key performance objectives with distinct contradiction: the mean yields of key products and the day mean profits. The ?‐constraint method is employed to solve the multi‐objective optimization problem, which provides a broad range of operation conditions depicting tradeoffs of both key objectives. The Pareto‐optimal frontier is successfully obtained and five selected cases on the frontier are discussed, suggesting that flexible operations can be performed based on industrial demands.     

Integrated crude selection and refinery optimization under uncertainty

Crude oil selection and procurement is the most important step in the refining process and impacts the profit margin of the refinery significantly. Due to uncertain quality of the crudes, conventional deterministic modeling and optimization methods are not suitable for refinery profitability enhancement. Therefore, a novel optimization scheme for crude oil procurement integrated with refinery operations in the face of uncertainties is presented. The decision process comprises two stages and is solved using a scenario‐based stochastic programming formulation. In Stage I, the optimal crude selections and purchase amounts are determined by maximizing the expected profit across all scenarios. In Stage II, the uncertainties are realized and optimal operations for the refinery are determined according to this realization. The resulting large‐scale mixed‐integer nonlinear programming formulation incorporates integer variables for crude selection and continuous variables for refinery operations, as well as bilinear terms for pooling processes. Nonconvex generalized Benders decomposition is used to solve this problem to obtain an global optimum efficiently. © 2015 American Institute of Chemical Engineers AIChE J, 62: 1038–1053, 2016     

Energy optimization of water supply system scheduling: Novel MINLP model and efficient global optimization algorithm

This article is concerned with global optimization of water supply system scheduling with pump operations to minimize total energy cost. The scheduling problem is first formulated as a non‐convex mixed‐integer nonlinear programming (MINLP) problem, accounting for flow rates in pipes, operation profiles of pumps, water levels of tanks, and customer demand. Binary variables denote on–off switch operations for pumps and flow directions in pipes, and nonlinear terms originate from characteristic functions for pumps and hydraulic functions for pipes. The proposed MINLP model is verified with EPANET, which is a leading software package for water distribution system modeling. We further develop a novel global optimization algorithm for solving the non‐convex MINLP problem. To demonstrate the applicability of the proposed model and the efficiency of the tailored global optimization algorithm, we present results of two case studies with up to 4 tanks, 5 pumps, 5 check valves, and 21 pipes. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4277–4296, 2016     

Optimization‐based support for process design under uncertainty: A case study

The use of two‐stage stochastic optimization for the support of the solution of process design problems in the early phase of process development where the different potential elements of the production process can only be described with significant uncertainty is discussed. The first stage variables are the design decisions which are fixed after the process has been built, while the second stage variables are the operational parameters which can be adapted to the realization of the uncertainties. The application of the approach to the design of a hydroformylation process in a thermomorphic solvent system is demonstrated. The proposed designs which are computed using the software framework FSOpt are analyzed and compared using different graphic representations which provide insight into what the most important design decisions are. Finally, the experience with the proposed formulation and solution techniques and point out where further advances are needed is reviewed. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3404–3419, 2016     

Operational strategy and planning for raw natural gas refining complexes: Process modeling and global optimization

Optimal operational strategy and planning of a raw natural gas refining complex (RNGRC) is very challenging since it involves highly nonlinear processes, complex thermodynamics, blending, and utility systems. In this article, we first propose a superstructure integrating a utility system for the RNGRC, involving multiple gas feedstocks, and different product specifications. Then, we develop a large‐scale nonconvex mixed‐integer nonlinear programming (MINLP) optimization model. The model incorporates rigorous process models for input and output relations based on fundamentals of thermodynamics and unit operations and accurate models for utility systems. To reduce the noncovex items in the proposed MINLP model, equivalent reformulation techniques are introduced. Finally, the reformulated nonconvex MINLP model is solved to global optimality using state of the art deterministic global optimization approaches. The computational results demonstrate that a significant profit increase is achieved using the proposed approach compared to that from the real operation. © 2016 American Institute of Chemical Engineers AIChE J, 63: 652–668, 2017     

Theoretical and computational comparison of continuous‐time process scheduling models for adjustable robust optimization

Coping with uncertainty in system parameters is a prominent hurdle when scheduling multi‐purpose batch plants. In this context, our previously introduced multi‐stage adjustable robust optimization (ARO) framework has been shown to obtain more profitable solutions, while maintaining the same level of immunity against risk, as compared to traditional robust optimization approaches. This paper investigates the amenability of existing deterministic continuous‐time scheduling models to serve as the basis of this ARO framework. A comprehensive computational study is conducted that compares the numerical tractability of various models across a suite of literature benchmark instances and a wide range of uncertainty sets. This study also provides, for the first time in the open literature, robust optimal solutions to process scheduling instances that involve uncertainty in production yields. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3055–3070, 2018     

Joint capacity planning and distribution network optimization of coal supply chains under uncertainty

A two‐stage stochastic integer programming model is developed to address the joint capacity planning and distribution network optimization of multiechelon coal supply chains (CSCs) under uncertainty. The proposed model not only introduces the uses of compound real options in sequential capacity planning, but also considers uncertainty induced by both risks and ambiguities. Both strategic decisions (i.e., facility locations and initial investment, service assignment across the entire CSC, and option holding status) and scenario‐based operational decisions (i.e., facility operations and capacity expansions, outsourcing policy, and transportation and inventory strategies) can be simultaneously determined using the model. By exploiting the nested decomposable structure of the model, we develop a new distributed parallel optimization algorithm based on nonconvex generalized Bender decomposition and Lagrangean relaxation to mitigate the computation resource limitation. One of the main CSCs in China is studied to demonstrate the applicability of the proposed model and the performance of the algorithm. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1246–1261, 2018     

Flexibility assessment and risk management in supply chains

Increased uncertainty in recent years has led the supply chains to incorporate measures to be more flexible in order to perform well in the face of the uncertain events. It has been shown that these measures improve the performance of supply chains by mitigating the risks associated with uncertainties. However, it is also important to assess the uncertainty under which a supply chain network can perform well and manage risk. Flexibility is defined in terms of the bounds of uncertain parameters within which supply chain operation is feasible. A hybrid simulation‐based optimization framework that uses two‐stage stochastic programming in a rolling horizon framework is proposed. The framework enables taking optimum planning decisions considering demand uncertainty while managing risk. The framework is used to study the trade‐offs between flexibility, economic performance, and risk associated with supply chain operation. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4166–4178, 2015     

Optimal design and operations of supply chain networks for water management in shale gas production: MILFP model and algorithms for the water‐energy nexus

The optimal design and operations of water supply chain networks for shale gas production is addressed. A mixed‐integer linear fractional programming (MILFP) model is developed with the objective to maximize profit per unit freshwater consumption, such that both economic performance and water‐use efficiency are optimized. The model simultaneously accounts for the design and operational decisions for freshwater source selection, multiple transportation modes, and water management options. Water management options include disposal, commercial centralized wastewater treatment, and onsite treatment (filtration, lime softening, thermal distillation). To globally optimize the resulting MILFP problem efficiently, three tailored solution algorithms are presented: a parametric approach, a reformulation‐linearization method, and a novel Branch‐and‐Bound and Charnes–Cooper transformation method. The proposed models and algorithms are illustrated through two case studies based on Marcellus shale play, in which onsite treatment shows its superiority in improving freshwater conservancy, maintaining a stable water flow, and reducing transportation burden. © 2014 American Institute of Chemical Engineers AIChE J, 61: 1184–1208, 2015     

Reference Trajectory Optimization Under Constrained Predictive Control

Chemical process systems often need to respond to frequently changing product demands. This motivates the determination of optimal transitions, subject to specification and operational constraints. However, direct implementation of optimal input trajectories would, in general, result in offset in the presence of disturbances and plant/model mismatch. This paper considers reference trajectory optimization of processes controlled by constrained model predictive control (MPC). Consideration of the closed‐loop dynamics of the MPC‐controlled process in the reference trajectory optimization results in a multi‐level optimization problem. A solution strategy is applied in which the MPC quadratic programming subproblems are replaced by their Karush‐Kuhn‐Tucker optimality conditions, resulting in a single‐level mathematical program with complementarity constraints (MPCC). The performance of the method is illustrated through application to two case studies, the second of which considers economically optimal grade transitions in a polymerization process.     

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     

Optimal processing network design under uncertainty for producing fuels and value‐added bioproducts from microalgae: Two‐stage adaptive robust mixed integer fractional programming model and computationally efficient solution algorithm

Fractional metrics, such as return on investment (ROI), are widely used for performance evaluation, but uncertainty in the real market may unfortunately diminish the results that are based on nominal parameters. This article addresses the optimal design of a large‐scale processing network for producing a variety of algae‐based fuels and value‐added bioproducts under uncertainty. We develop by far the most comprehensive processing network with 46,704 alternative processing pathways. Based on the superstructure, a two‐stage adaptive robust mixed integer fractional programming model is proposed to tackle the uncertainty and select the robust optimal processing pathway with the highest ROI. Since the proposed problem cannot be solved directly by any off‐the‐shelf solver, we develop an efficient tailored solution method that integrates a parametric algorithm with a column‐and‐constraint generation algorithm. The resulting robust optimal processing pathway selects biodiesel and poly‐3‐hydroxybutyrate as the final fuel and bioproduct, respectively. © 2016 American Institute of Chemical Engineers AIChE J, 63: 582–600, 2017     

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