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     

A cost‐effective model for the gasoline blend optimization problem

Gasoline blending is a critical process with a significant impact on the total revenues of oil refineries. It consists of mixing several feedstocks coming from various upstream processes and small amounts of additives to make different blends with some specified quality properties. The major goal is to minimize operating costs by optimizing blend recipes, while meeting product demands on time and quality specifications. This work introduces a novel continuous‐time mixed‐integer linear programming (MILP) formulation based on floating time slots to simultaneously optimize blend recipes and the scheduling of blending and distribution operations. The model can handle non‐identical blenders, multipurpose product tanks, sequence‐dependent changeover costs, limited amounts of gasoline components, and multi‐period scenarios. Because it features an integrality gap close to zero, the proposed MILP approach is able to find optimal solutions at much lower computational cost than previous contributions when applied to large gasoline blend problems. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3002–3019, 2016     

Data‐driven mathematical modeling and global optimization framework for entire petrochemical planning operations

In this work we develop a novel modeling and global optimization‐based planning formulation, which predicts product yields and properties for all of the production units within a highly integrated refinery‐petrochemical complex. Distillation is modeled using swing‐cut theory, while data‐based nonlinear models are developed for other processing units. The parameters of the postulated models are globally optimized based on a large data set of daily production. Property indices in blending units are linearly additive and they are calculated on a weight or volume basis. Binary variables are introduced to denote unit and operation modes selection. The planning model is a large‐scale non‐convex mixed integer nonlinear optimization model, which is solved to ε‐global optimality. Computational results for multiple case studies indicate that we achieve a significant profit increase (37–65%) using the proposed data‐driven global optimization framework. Finally, a user‐friendly interface is presented which enables automated updating of demand, specification, and cost parameters. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3020–3040, 2016     

A novel adaptive surrogate modeling‐based algorithm for simultaneous optimization of sequential batch process scheduling and dynamic operations

A novel adaptive surrogate modeling‐based algorithm is proposed to solve the integrated scheduling and dynamic optimization problem for sequential batch processes. The integrated optimization problem is formulated as a large scale mixed‐integer nonlinear programming (MINLP) problem. To overcome the computational challenge of solving the integrated MINLP problem, an efficient solution algorithm based on the bilevel structure of the integrated problem is proposed. Because processing times and costs of each batch are the only linking variables between the scheduling and dynamic optimization problems, surrogate models based on piece‐wise linear functions are built for the dynamic optimization problems of each batch. These surrogate models are then updated adaptively, either by adding a new sampling point based on the solution of the previous iteration, or by doubling the upper bound of total processing time for the current surrogate model. The performance of the proposed method is demonstrated through the optimization of a multiproduct sequential batch process with seven units and up to five tasks. The results show that the proposed algorithm leads to a 31% higher profit than the sequential method. The proposed method also outperforms the full space simultaneous method by reducing the computational time by more than four orders of magnitude and returning a 9.59% higher profit. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4191–4209, 2015     

Continuous‐time modeling and global optimization approach for scheduling of crude oil operations

Scheduling of crude oil operations is a critical and complicated component of overall refinery operations, because crude oil costs account for about 80% of the refinery turnover. Moreover, blending with less expensive crudes can significantly increase profit margins. The mathematical modeling of blending different crudes in storage tanks results in many bilinear terms, which transforms the problem into a challenging, nonconvex, and mixed‐integer nonlinear programming (MINLP) optimization model. Two primary contributions have been made. First, the authors developed a novel unit‐specific event‐based continuous‐time MINLP formulation for this problem. Then they incorporated realistic operational features such as single buoy mooring (SBM), multiple jetties, multiparcel vessels, single‐parcel vessels, crude blending, brine settling, crude segregation, and multiple tanks feeding one crude distillation unit at one time and vice versa. In addition, 15 important volume‐based or weight‐based crude property indices are also considered. Second, they exploited recent advances in piecewise‐linear underestimation of bilinear terms within a branch‐and‐bound algorithm to globally optimize the MINLP problem. It is shown that the continuous‐time model results in substantially fewer bilinear terms. Several examples taken from the work of Li et al. are used to illustrate that (1) better solutions are obtained and (2) ε‐global optimality can be attained using the proposed branch‐and‐bound global optimization algorithm with piecewise‐linear underestimations of the bilinear terms. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Short‐term scheduling of a large‐scale oil‐refinery operations: Incorporating logistics details

Refineries are increasingly concerned with improving the scheduling of their operations to achieve better economic performances by minimizing quality, quantity, and logistics give away. In this article, we present a comprehensive integrated optimization model based on continuous‐time formulation for the scheduling problem of production units and end‐product blending problem. The model incorporates quantity, quality, and logistics decisions related to real‐life refinery operations. These involve minimum run‐length requirements, fill‐draw‐delay, one‐flow out of blender, sequence‐dependent switchovers, maximum heel quantity, and downgrading of better quality product to lower quality. The logistics giveaways in our work are associated with obtaining a feasible solution while minimizing violations of sequence‐dependent switchovers and maximum heel quantity restrictions. A set of valid inequalities are proposed that improves the computational performance of the model significantly. The formulation is used to address realistic case studies where feasible solutions are obtained in reasonable computational time. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Optimal supply chain design and operations under multi‐scale uncertainties: Nested stochastic robust optimization modeling framework and solution algorithm

Although strategic and operational uncertainties differ in their significance of impact, a “one‐size‐fits‐all” approach has been typically used to tackle all types of uncertainty in the optimal design and operations of supply chains. In this work, we propose a stochastic robust optimization model that handles multi‐scale uncertainties in a holistic framework, aiming to optimize the expected economic performance while ensuring the robustness of operations. Stochastic programming and robust optimization approaches are integrated in a nested manner to reflect the decision maker's different levels of conservativeness toward strategic and operational uncertainties. The resulting multi‐level mixed‐integer linear programming model is solved by a decomposition‐based column‐and‐constraint generation algorithm. To illustrate the application, a county‐level case study on optimal design and operations of a spatially‐explicit biofuel supply chain in Illinois is presented, which demonstrates the advantages and flexibility of the proposed modeling framework and efficiency of the solution algorithm. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3041–3055, 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     

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     

Multi‐period planning,design, and strategic models for long‐term,quality‐sensitive shale gas development

In this work we address the long‐term, quality‐sensitive shale gas development problem. This problem involves planning, design, and strategic decisions such as where, when, and how many shale gas wells to drill, where to lay out gathering pipelines, as well as which delivery agreements to arrange. Our objective is to use computational models to identify the most profitable shale gas development strategies. For this purpose we propose a large‐scale, nonconvex, mixed‐integer nonlinear programming model. We rely on generalized disjunctive programming to systematically derive the building blocks of this model. Based on a tailor‐designed solution strategy we identify near‐global solutions to the resulting large‐scale problems. Finally, we apply the proposed modeling framework to two case studies based on real data to quantify the value of optimization models for shale gas development. Our results suggest that the proposed models can increase upstream operators’ profitability by several million U.S. dollars. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2296–2323, 2016     

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     

New MINLP formulation for the multiperiod pooling problem

The modeling of blending tank operations in petroleum refineries for the most profitable production of liquid fuels in a context of time‐varying supply and demand is addressed. A new mixed‐integer nonlinear programming formulation is proposed that using individual flows and split fractions as key model variables leads to a different set of nonconvex bilinear terms compared with the original work of Kolodziej et al. These are better handled by decomposition algorithms that divide the problem into integer and nonlinear components as well as by commercial solvers. In fact, BARON and GloMIQO can solve to global optimality all problems resulting from the new formulation and test problems from the literature. A tailored global optimization algorithm working with a tight mixed‐integer linear relaxation from multiparametric disaggregation achieves a similar performance. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3728–3738, 2015     

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     

Covariance‐based hardware selection part IV: Solution using the generalized benders decomposition

Recently the covariance based hardware selection problem has been shown to be of the mixed integer convex programming (MICP) class. While such a formulation provides a route to global optimality, use of the branch and bound search procedure has limited application to fairly small systems. The particular bottleneck is that during each iteration of the branch and bound search, a fairly slow semi‐definite programming (SDP) problem must be solved to its global optimum. In this work, we illustrate that a simple reformulation of the MICP and subsequent application of the generalized Benders decomposition algorithm will result in massive reductions in computational effort. While the resulting algorithm must solve multiple mixed integer linear programs, this increase in computational effort is significantly outweighed by the reduction in the number of SDP problems that must be solved. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3628–3638, 2016     

Inventory pinch based,multiscale models for integrated planning and scheduling‐part I: Gasoline blend planning

A two‐level algorithm to compute blend plans that have much smaller number of different recipes, much shorter execution times, and the same cost as the corresponding multiperiod mixed‐integer nonlinear programming is introduced. These plans become a starting point for computation of approximate schedules, which minimize total number of switches in blenders and swing tanks. The algorithm uses inventory pinch points to delineate time periods where optimal blend recipes are likely constant. At the first level, nonlinear blend models are optimized via nonlinear programming. The second level uses fixed recipes (from the first level) in a multiperiod mixed‐integer linear programming to determine optimal production plan followed by an approximate schedule. Approximate schedules computed by the multiperiod inventory pinch algorithm in most of the case studies are slightly better than those computed by global optimizers (ANTIGONE, GloMIQO) while requiring significantly shorter execution times. Such schedules provide constraints for subsequent detailed scheduling in Part II. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2158–2178, 2014     

汽油调合调度优化

采用连续时间建模方法,建立了一种新的汽油非线性调合和调度集成优化的混合整数非线性规划（MINLP）模型,克服了当前在油品调合调度中采用线性调合模型或者将非线性调合过程和调度分开优化的缺陷。针对建立MINLP模型的特点,将原MINLP问题转化为求解一系列的混合整数线性规划（MILP）模型,避免了直接求解MINLP模型的复杂性。最后以某大型炼油企业为例,验证了模型和算法的实用性。     

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     

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     

New approach for scheduling crude oil operations

Scheduling of crude oil operations is crucial to petroleum refining, which includes determining the times and sequences of crude oil unloading, blending, and CDU feeding. In the last decades, many approaches have been proposed for solving this problem, but they either suffered from composition discrepancy [Lee et al. 1996. Mixed-integer linear programming model for refinery short-term scheduling of crude oil unloading with inventory management. Industrial and Engineering Chemistry Research 35, 1630-1641; Jia et al., 2003. Refinery short-term scheduling using continuous time formulation: crude-oil operations. Industrial and Engineering Chemistry Research 42, 3085-3097; Jia and Ierapetritou, 2004. Efficient short-term scheduling of refinery operations based on a continuous time formulation. Computer and Chemical Engineering 28, 1001-1019] or led to infeasible solutions for some cases [Reddy et al., 2004a. Novel solution approach for optimizing crude oil operations. A.I.Ch.E. Journal 50(6), 1177-1197; 2004b. A new continuous-time formulation for scheduling crude oil operations. Chemical Engineering Science 59, 1325-1341]. In this paper, coastal and marine-access refineries with simplified workflow are considered. Unlike existing approaches, the new approach can avoid composition discrepancy without using iterative algorithm and find better solution effectively. In this approach, a new mixed integer non-linear programming (MINLP) formulation is set up for crude oil scheduling firstly, and then some heuristic rules collected from expert experience are proposed to linearize bilinear terms and prefix some binary variables in the MINLP model. Thus, crude oil scheduling can be expressed as a complete mixed integer linear programming (MILP) model with fewer binary variables. To illustrate the advantage of the new approach, four typical examples are solved with three models. The new model is compared with the most effective models (RKS(a) and RKS(b) models) presented by Reddy et al. [2004a. Novel solution approach for optimizing crude oil operations. A.I.Ch.E. Journal 50(6), 1177-1197; 2004b. A new continuous-time formulation for scheduling crude oil operations. Chemical Engineering Science 59, 1325-1341], which proves that the new approach is valid and feasible in most small-size and medium-size problems.     

A data‐driven rolling‐horizon online scheduling model for diesel production of a real‐world refinery

A rolling‐horizon optimal control strategy is developed to solve the online scheduling problem for a real‐world refinery diesel production based on a data‐driven model. A mixed‐integer nonlinear programming (MINLP) scheduling model considering the implementation of nonlinear blending quality relations and quantity conservation principles is developed. The data variations which drive the MINLP model come from different sources of certain and uncertain events. The scheduling time horizon is divided into equivalent discrete time intervals, which describe regular production and continuous time intervals which represent the beginning and ending time of expected and unexpected events that are not restricted to the boundaries of discrete time intervals. This rolling‐horizon optimal control strategy ensures the dimension of the diesel online scheduling model can be accepted in industry use. LINGO is selected to be the solution software. Finally, the daily diesel scheduling scheme of one entire month for a real‐world refinery is effectively solved. © 2012 American Institute of Chemical Engineers AIChE J, 59: 1160–1174, 2013