Integrated gasoline blending and order delivery operations: Part I. short‐term scheduling and global optimization for single and multi‐period operations

Gasoline is one of the most valuable products in an oil refinery and can account for as much as 60–70% of total profit. Optimal integrated scheduling of gasoline blending and order delivery operations can significantly increase profit by avoiding ship demurrage, improving customer satisfaction, minimizing quality give‐aways, reducing costly transitions and slop generation, exploiting low‐quality cuts, and reducing inventory costs. In this article, we first introduce a new unit‐specific event‐based continuous‐time formulation for the integrated treatment of recipes, blending, and scheduling of gasoline blending and order delivery operations. Many operational features are included such as nonidentical parallel blenders, constant blending rate, minimum blend length and amount, blender transition times, multipurpose product tanks, changeovers, and piecewise constant profiles for blend component qualities and feed rates. To address the nonconvexities arising from forcing constant blending rates during a run, we propose a hybrid global optimization approach incorporating a schedule adjustment procedure, iteratively via a mixed‐integer programming and nonlinear programming scheme, and a rigorous deterministic global optimization approach. The computational results demonstrate that our proposed formulation does improve the mixed‐integer linear programming relaxation of Li and Karimi, Ind. Eng. Chem. Res., 2011, 50, 9156–9174. All examples are solved to be 1%‐global optimality with modest computational effort. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2043–2070, 2016     

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     

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     

Source-based discrete and continuous-time formulations for the crude oil pooling problem

The optimization of crude oil operations in refineries is a challenging scheduling problem due to the need to model tanks of varying composition with nonconvex bilinear terms, and complicating logistic constraints. Following recent work for multiperiod pooling problems of refined petroleum products, a source-based mixed-integer nonlinear programming formulation is proposed for discrete and continuous representations of time. Logistic constraints are modeled through Generalized Disjunctive Programming while a specialized algorithm featuring relaxations from multiparametric disaggregation handles the bilinear terms. Results over a set of test problems from the literature show that the discrete-time approach finds better solutions when minimizing cost (avoids source of bilinear terms). In contrast, solution quality is slightly better for the continuous-time formulation when maximizing gross margin. The results also show that the specialized global optimization algorithm can lead to lower optimality gaps for fixed CPU, but overall, the performance of commercial solvers BARON and GloMIQO are better.     

A new continuous-time formulation for scheduling crude oil operations

In today's competitive business climate characterized by uncertain oil markets, responding effectively and speedily to market forces, while maintaining reliable operations, is crucial to a refinery's bottom line. Optimal crude oil scheduling enables cost reduction by using cheaper crudes intelligently, minimizing crude changeovers, and avoiding ship demurrage. So far, only discrete-time formulations have stood up to the challenge of this important, nonlinear problem. A continuous-time formulation would portend numerous advantages, however, existing work in this area has just begun to scratch the surface. In this paper, we present the first complete continuous-time mixed integer linear programming (MILP) formulation for the short-term scheduling of operations in a refinery that receives crude from very large crude carriers via a high-volume single buoy mooring pipeline. This novel formulation accounts for real-world operational practices. We use an iterative algorithm to eliminate the crude composition discrepancy that has proven to be the Achilles heel for existing formulations. While it does not guarantee global optimality, the algorithm needs only MILP solutions and obtains excellent maximum-profit schedules for industrial problems with up to 7 days of scheduling horizon. We also report the first comparison of discrete- vs. continuous-time formulations for this complex problem.     

单机多产品注塑过程的节能调度方法

为减小单机多产品注塑过程的生产总能耗,提出一种基于旅行商算法(TSP)和遗传算法(GA)的节能调度方法。研究了注塑生产总能耗的3个重要组成:产品切换能耗、过渡调整能耗和稳定生产能耗,建立了产品切换过渡的能耗模型。以单产平稳模态为节点、过渡模态为支路,建立了单机多产品过程生产总能耗的有向图模型,将单机多产品能耗优化问题转化为经典的TSP问题。采用基于遗传算法的多目标逐层优化与TSP路径寻优思想,搜索各个单产平稳生产下的最优操作参数以及多产品的最优生产顺序,以期降低生产总能耗。该方法可提高生产效率,降低生产能耗。应用研究结果验证了方法的可行性和有效性。     

Scheduling Model for a Multi‐Product Batch Plant Using a Pre‐Ordering Approach

A scheduling model for a multi‐product, multistage batch plant with parallel units is presented. The objective is to maximize the weighted completion times of orders in every processing stage while imposing a penalty on the slower orders. The proposed model uses the continuous‐time representation mode and describes the allocations of tasks, units and stages by a set of binary variables. In order to reduce the model size and provide a more effective solution to the model, a pre‐ordering approach that sorts the processing sequence of orders is developed. The pre‐ordering approach identifies the infeasible assignments through which the number of binary variables is significantly reduced. Illustrative examples are provided to show that the size of the proposed model is small, and therefore, needs much less computational effort in comparison with the existing models in the literature.     

Greedy algorithm for scheduling batch plants with sequence‐dependent changeovers

This article presents a new algorithm for scheduling multistage batch plants with a large number of orders and sequence‐dependent changeovers. Such problems are either intractable when solved with full‐space approaches or poor solutions result. We use decomposition on the entire set of orders and derive the complete schedule in several iterations, by inserting a couple of orders at a time. The key idea is to allow for partial rescheduling without altering the main decisions in terms of unit assignments and sequencing (linked to the binary variables) so that the combinatorial complexity is kept at a manageable level. The algorithm has been implemented for three alternative continuous‐time mixed integer linear programing models and tested through the solution of 10 example problems for different decomposition settings. The results show that an industrial‐size scheduling problem with 50 orders, 17 units distributed over six stages can effectively be solved in roughly 6 min of computational time. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

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     

An LSTM-based mixed-integer model predictive control for irrigation scheduling

The development of well-devised irrigation scheduling methods is desirable from the perspectives of plant quality and water conservation. Accordingly, in this article, a mixed-integer model predictive control system is proposed to address the daily irrigation scheduling problem. In this framework, a long short-term memory (LSTM) model of the soil–crop–atmosphere system is employed to evaluate the objective of ensuring optimal water uptake in crops while minimizing total water consumption and irrigation costs. To enhance the computational efficiency of the proposed method, a heuristic method involving the logistic sigmoid function is used to approximate the binary variable that arises in the mixed-integer formulation. Through computer simulations, the proposed scheduler is applied to homogeneous and spatially variable fields. The results of these simulation experiments reveal that the proposed method can prescribe optimal/near-optimal irrigation schedules that are typical of irrigation practice within practical computational budgets.     

Multi-product batch scheduling with intermediate due dates using priced timed automata models

In this contribution, we discuss an extension of the earlier work on scheduling using reachability analysis of timed automata (TA) models, specifically addressing the problem of tardiness minimization. In the TA-based approach the resources, recipes and additional timing constraints are modeled independently as sets of priced timed automata. The sets of individual automata are synchronized by means of synchronization labels and are composed by parallel composition to form a global automaton. The global automaton has an initial location where no operations have been started and at least one target location where all operations that are required to produce the demanded quantities of end-products within the specified due dates have been finished. A cost-optimal symbolic reachability analysis is performed on the composed automaton to derive schedules with the objective of minimizing tardiness. The model formulation is extended to include release dates of the raw materials and due dates of the production orders. The meeting of due dates is modeled by causing additional costs (e.g. penalties for late delivery and storage costs for early production). The modeling approach and the performance of the approach are tested for two different case studies and the results are compared with that of a MILP formulation solved using the standard solver CPLEX. The numerical experiments demonstrate, that the TA-based approach is competitive compared to standard commercial solvers and good feasible solutions are obtained with considerably reduced computational effort.     

Scheduling of displacement batch digesters using discrete time formulation

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

Optimal design of batch‐storage network considering ownership

This article develops a model of multi‐national supply chain activities, which incorporates currency storage units to manage currency flows associated with activities such as raw material procurement, processing, inventory control, transportation, and finished product sales. The core contribution of this model is that it facilitates the quantitative investigation of the influence of macroscopic economic factors such as ownership on supply chain operational decisions. The supply chain system is modeled as a batch‐storage network with recycle streams. The supply chain optimization problem is posed with the objective of minimizing the opportunity costs of annualized capital investments and currency/material inventories, while taking into account the benefit to stockholders in the numeraire currency. The major constraints on the optimization are that the material and currency storage units must not be depleted. A production and inventory analysis formulation (the periodic square wave model) provides useful expressions for the upper and lower bounds and for the average levels of the currency and material inventory holdings. The expressions for the Kuhn‐Tucker conditions of the optimization problem are reduced to a subproblem that allows development of analytical lot‐sizing equations. The lot sizes of procurement, production, transportation, and financial transactions can be determined in closed form once the average flow rates are known. The key result we obtain is that optimal value of the economic order quantity changes substantially with variation in ownership, thus showing quantitatively that ownership structure does impact plant operation. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2418–2425, 2018     

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.     

The quality‐constrained scheduling problem in plastics compounding

Interest is increasing in plastic compounding plants that offer tailor‐made resins. Such plants produce a wide range of products in small quantities and with frequent changeovers. The underlying scheduling problem has been extensively researched; however, the concept of incorporating qualities of the finished product in the problem of plastics compounding has not been considered. We express product qualities as an additional problem constraint so that the production schedule ensures product quality. The additional constraint makes this mixed integer nonlinear program (MINLP) problem more difficult to solve. Several case studies are solved to illustrate the utility of the proposed approach. Experiments demonstrated that qualities of the finished product can be ensured a priori if the appropriate relations are developed and integrated in the optimisation model. As well, this paper provides insight into the economic aspects of the scheduling problem under consideration. Experiments showed that none of the cost components (operation, raw material, inventory, penalty or utilities) can alone play the role of the optimisation criterion. © 2012 Canadian Society for Chemical Engineering     

Dynamic models and fault diagnosis‐based triggers for closed‐loop scheduling

Establishing an explicit feedback connection between production management and process control decisions is a key requirement for more nimble and cost effective process operations in today's variable market conditions. Past research efforts focused on embedding dynamic process information in the production scheduling problem. In this article, we propose a novel framework for closing the scheduling loop, based on considering the process‐level events and disturbances that impact the implementation of scheduling decisions. We emphasize the role of a comprehensive fault detection, isolation and reconstruction mechanism as a trigger for rescheduling decisions and for reflecting the process capabilities altered by these events in the rescheduling problem formulation. Our framework is agnostic to the process type, and we present two (continuous process, sequential batch process) case studies to demonstrate its applicability. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1959–1973, 2017     

A multi-level simulation approach for the crude oil loading/unloading scheduling problem

An integrated approach for refinery production scheduling and unit operation optimization problems is presented. Each problem is at a different decision making layer and has an independent objective function and model. The objective function at the operational level is an on-line maximization of the difference between the product revenue and the energy and environmental costs of the main refinery units. It is modeled as an NLP and is constrained by ranges on the unit's operating condition as well as product quality constraints. The production scheduling layer is modeled as an MILP with the objective of minimizing the logistical costs of unloading the crude oil over a day-to-week time horizon. The objective function is a linear sum of the unloading, sea waiting, inventory, and setup costs. The nonlinear simulation model for the process units is used to find optimized refining costs and revenue for a blend of two crudes. Multiple linear regression of the individual crude oil flow rates within the crude oil percentage range allowed by the facility is then used to derive linear refining cost and revenue functions. Along with logistics costs, the refining costs or revenue are considered in the MILP scheduling objective function. Results show that this integrated approach can lead to a decrease of production and logistics costs or increased profit, provide a more intelligent crude schedule, and identify production level scheduling decisions which have a tradeoff benefit with the operational mode of the refinery.     

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     

An efficient MILP continuous-time formulation for short-term scheduling of multiproduct continuous facilities

This paper presents a new MILP mathematical formulation for the scheduling of resource-constrained multiproduct plants involving continuous processes. In such facilities, a sequence of continuous processing steps is usually carried out to produce a significant number of final products and required intermediates. In order to reduce equipment idle time due to unbalanced stage capacities, storage tanks are available for temporary inventory of intermediates. The problem goal is to maximize the plant economic output while satisfying specified minimum product requirements. The proposed approach relies on a continuous time domain representation that accounts for sequence-dependent changeover times and storage limitations without considering additional tasks. The MILP formulation was applied to a real-world manufacturing facility producing seven intermediates and fifteen final products. Compared with previous scheduling methodologies, the proposed approach yields a much simpler problem representation with a significant saving in 0–1 variables and sequencing constraints. Moreover, it provides a more realistic and profitable production schedule at lower computational cost.     

A pattern matching method for large‐scale multipurpose process scheduling

This article proposes a novel pattern matching method for the large‐scale multipurpose process scheduling with variable or constant processing times. For the commonly used mathematical programming models, large‐scale scheduling with long‐time horizons implies a large number of binary variables and time sequence constraints, which makes the models intractable. Hence, decomposition and cyclic scheduling are often applied to such scheduling. In this work, a long‐time horizon of scheduling is divided into two phases. Phase one is duplicated from a pattern schedule constructed according to the principle that crucial units work continuously, in parallel and/or with full load as possible, exclusive of time‐consuming optimization. Phase two involves a small‐size subproblem that can be optimized easily by a heuristic method. The computational effort of the proposed method does not increase with the problem size. The pattern schedule can be not only used for production/profit maximization but also for makespan estimation and minimization. © 2010 American Institute of Chemical Engineers AIChE J, 2011