Efficient multi-product multi-BOM batch scheduling for a petrochemical blending plant with a shared pipeline network

We present an effective scheduling heuristic for realistic production planning in a petrochemical blending plant. The considered model takes into account orders spanning a multi-product portfolio with multiple bills of materials per product, that need to be scheduled on shared production facilities including a complex pipeline network. Capacity constraints, intermediate storage restrictions, due dates, and the dedication of resources to specific product families have to be respected. The primary objective of the heuristic is to minimize the total order tardiness. Secondary objectives include the minimization of pipeline cleaning operations, the minimization of lead times, and the balanced utilization of filling units.The developed algorithm is based on a dynamic prioritization-based greedy search that schedules the orders sequentially. The proposed method can schedule short to mid-term operations and evaluate different plant configurations or production policies on a tactical level. We demonstrate its performance on various real-world inspired scenarios for different scheduling strategies.Our heuristic was used during the construction phase of a new blending plant and was instrumental in the optimal design of the plant.     

Integrated production planning and scheduling using a decomposition framework

To ensure the consistency between planning and scheduling decisions, the integrated planning and scheduling problem should be addressed. Following the natural hierarchy of decision making, integrated planning and scheduling problem can be formulated as bilevel optimization problem with a single planning problem (upper level) and multiple scheduling subproblems (lower level). Equivalence between the proposed bilevel model and a single level formulation is proved considering the special structure of the problem. However, the resulting model is still computationally intractable because of the integrality restrictions and large size of the model. Thus a decomposition based solution algorithm is proposed in this paper. In the proposed method, the production feasibility requirement is modeled through penalty terms on the objective function of the scheduling subproblems, which is further proportional to the amount of unreachable production targets. To address the nonconvexity of the production cost function of the scheduling subproblems, a convex polyhedral underestimation of the production cost function is developed to improve the solution accuracy. The proposed decomposition framework is illustrated through examples which prove the effectiveness of the method.     

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.     

Sequencing a generalized two-stage flowshop with finite intermediate storage

The scheduling of batch chemical facilities may be modeled as a generalized flowshop problem, for which the objective is to minimize the products' completion time. In particular, this paper examines the scheduling difficulties that arise if interstage storage is used within the production facility. A branch and bound solution procedure is presented which uses a simulation model to evaluate sequence compeltion times. An initial upper bound completion time is determined based on a heuristic scheduling rule.     

Optimal cyclic cleaning scheduling in heat exchanger networks under fouling

This work addresses the problem of cyclic cleaning scheduling in heat exchanger networks (HENs). A salient characteristic of this problem is that the performance of each heat exchanger decreases with time which can then be restored to its initial state by performing cleaning operations. Due to the cyclic nature of the schedule, some operations may span successive cycles (wrap-around) which should be taken into account in the mathematical models. A tight mixed integer linear programming (MILP) model is proposed minimising cleaning cost and energy requirements. A complex heat exchanger network example is presented to illustrate the applicability of the proposed model.     

Short-term scheduling and recipe optimization of blending processes

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

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     

Multi-objective modeling and optimization for scheduling of cracking furnace systems

Cracking furnace is the core device for ethylene production. In practice, multiple ethylene furnaces are usual y run in parallel. The scheduling of the entire cracking furnace system has great significance when multiple feeds are simultaneously processed in multiple cracking furnaces with the changing of operating cost and yield of product. In this paper, given the requirements of both profit and energy saving in actual production process, a multi-objective optimization model contains two objectives, maximizing the average benefits and minimizing the average coking amount was proposed. The model can be abstracted as a multi-objective mixed integer non-linear programming problem. Considering the mixed integer decision variables of this multi-objective problem, an improved hybrid encoding non-dominated sorting genetic algorithm with mixed discrete variables (MDNSGA-I ) is used to solve the Pareto optimal front of this model, the algorithm adopted crossover and muta-tion strategy with multi-operators, which overcomes the deficiency that normal genetic algorithm cannot handle the optimization problem with mixed variables. Finally, using an ethylene plant with multiple cracking furnaces as an example to illustrate the effectiveness of the scheduling results by comparing the optimization results of multi-objective and single objective model.     

Rigorous approach to scheduling of sterile drug product manufacturing

Optimizing the scheduling of liquid drug product manufacturing is paramount for pharmaceutical companies in their increasingly competitive environment and requires the modelling of industry-specific constraints. Such constraints include: (i) changing sequence-dependent setup times; (ii) maintaining a sterile production environment (e.g., through sterile holding times); (iii) periods with limited or no plant activity (e.g., no workforce during weekends); and (iv) demand timing (i.e., delivery deadline and release date constraints). In this work, an immediate precedence model is formulated to optimize the scheduling of liquid drug product manufacturing, considering the industry-specific constraints. The primary objective is to minimize the production makespan.Four case studies comprising up to 38 batches from a real multi-product facility illustrate the performance of the rigorous optimization approach. The makespan could be reduced by up to 7.9% compared to expert schedules.     

多因素不确定条件下的间歇生产调度优化

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

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.     

空分短期停车时间阈值对氧气生产调度的影响

针对钢铁企业高炉休风场景下的氧气生产调度问题,提出以空分短期计划性停车为主要手段的调度策略,并基于MILP方法建立了氧气系统的优化调度模型。调度模型的优化目标为整个规划周期内氧气高压管网的综合压力最小化。模型包含了空分和部分氧气压缩机短期停车再启动操作的约束条件,并结合实际情况考虑了前述设备的停车时间阈值和运行时间阈值。以国内某大型钢铁企业为实际案例,验证了调度模型的合理性与可行性,然后基于模型计算分析了空分停车时间阈值对调度目标的影响规律。分析结果表明,减小空分停车时间阈值有利于获得更优的调度目标,但空分停车时间阈值对优化目标的影响规律具有阶跃特性,而非简单的比例关系。     

Ordonnancement à court-terme d'un atelier discontinu de chimie fine

The objective of this paper is to use production engineering concepts to solve scheduling problems encountered in chemical engineering. The studied case is the multipurpose (or job-shop) chemical batch plant involving the most complex specific constraints which can be found practically: various products to be manufactured, different synthesis sequences, presence of intermediate products, various storage policies, mass balances, utilities, effluent limitation,… The development of a discrete-event simulation model of a fine chemistry plant is proposed in this paper. Use of the model and simulation results are then analyzed. Attention is focused on applications which seem interesting from a production management viewpoint but also from chemical engineering concepts (plant design, effluent treatment, stability et storage of reaction intermediates…).     

Rule-based scheduling of multi-stage multi-product batch plants with parallel units

A novel rule-based model for multi-stage multi-product scheduling problem (MMSP) in batch plants with parallel units is proposed. The scheduling problem is decomposed into two sub-problems of order assignment and order sequencing. Firstly, hierarchical scheduling strategy is presented for solving the former sub-problem, where the multi-stage multi-product batch process is divided into multiple sequentially connected single process stages, and then the production of orders are arranged in each single stage by using forward order assignment strategy and backward order assignment strategy respectively according to the feature of scheduling objective. Line-up competition algorithm (LCA) is presented to find out optimal order sequence and order assignment rule, which can minimize total flow time or maximize total weighted process time. Computational results show that the proposed approach can obtain better solutions than those of the literature for all scheduling problems with more than 10 orders. Moreover, with the problem size increasing, the solutions obtained by the proposed approach are improved remarkably. The proposed approach has the potential to solve large size MMSP.     

Optimal planning and scheduling of batch plants with operational uncertainties: An industrial application to Baker's yeast production

In this work, the mixed integer linear programming (MILP) model developed in Orçun et. al 1996 for optimal planning and scheduling of batch process plants under uncertain operating conditions is further improved to deal also with discrete probability functions. Furthermore, the logic behind integrating the processing uncertainties within the MILP model is implemented on the variations in the production volumes that can be faced in some batch processes such as Baker's yeast production. The modified model is tested on Baker's yeast production plant data to illustrate the effect of uncertainties on the production planning and scheduling. The results show that the plant production will be improved by 20% when the optimal production planning and scheduling is utilized by fine tuning the degree of risk the management can resist. An example on how a process design engineer may utilize such an MILP model for optimal planning and scheduling of batch process plant and identify plant problems, such as the bottleneck operations, is also included. A simulation type analysis on how to improve the processing site, i.e. the effect of introducing an extra operator to the bottleneck operation, is also demonstrated in this work using the available plant data.     

A projection‐based method for production planning of multiproduct facilities

An algorithm is presented for identifying the projection of a scheduling model's feasible region onto the space of production targets. The projected feasible region is expressed using one of two mixed‐integer programming formulations, which can be readily used to address integrated production planning and scheduling problems that were previously intractable. Production planning is solved in combination with a surrogate model representing the region of feasible production amounts to provide optimum production targets, while a detailed scheduling is solved in a rolling‐horizon manner to define feasible schedules for meeting these targets. The proposed framework provides solutions of higher quality and yields tighter bounds than previously proposed approaches. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

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     

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

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

Optimum cleaning cycles for heat transfer equipment undergoing fouling and ageing

Complete elimination of fouling in heat transfer equipment is rarely achieved in practice, so cleaning of fouled units is a regular task in the process industries. Algorithms for scheduling cleaning have, to date, minimized the net losses due to fouling by focusing on when and which units to clean. In contrast, this paper focuses on when and how to clean a unit, when more than one cleaning method is available.The model formulation is approached by idealizing a foulant deposit as consisting of two layers, soft (fresh) and hard (aged). The hard material is formed through the ageing of the soft material. Hard deposits are more difficult to remove and require time- and cost-intensive cleaning methods (such as mechanical cleaning). Soft deposits are removed through less time- and cost-intensive methods such as chemical cleaning by recirculation of solvents. The hard deposit usually consists of more thermally conductive material and hence, for a given thickness, has a lower thermal resistance compared to the soft deposit.This work introduces a new methodology to identify optimum cleaning cycles (OCCs) under the presence of both soft and hard deposit, when two cleaning methods (solvent and mechanical cleaning) are available. The analysis of OCCs is extended and a new concept called the ‘cleaning supercycle’ is elaborated, which can be related to the optimal time between plant shutdowns.     

Batch selection,assignment and sequencing in multi-stage multi-product processes

The scheduling of multi-product, multi-stage batch processes is industrially important because it allows us to utilize resources that are shared among competing products in an optimal manner. Previously proposed methods consider problems where the number and size of batches is known a priori. In many instances, however, the selection and sizing (batching) of batches is or should be an optimization decision. To address this class of problems we develop a novel mixed-integer linear programming (MILP) formulation that involves three levels of discrete decisions: selection of batches, assignment of batches to units and sequencing of batches in each unit. Continuous decision variables include sizing and timing of batches. We consider various objective functions: minimization of makespan, earliness, lateness and production cost, as well as maximization of profit, an objective not addressed by previous multi-stage scheduling methods. To enhance the solution of the proposed MILP model we propose symmetry breaking constraints, develop a preprocessing algorithm for the generation of constraints that reduce the number of feasible solutions, and fix sequencing variables based upon time window information. The model enables the optimization of batch selection, assignment and sequencing decisions simultaneously and is shown to yield solutions that are better than those obtained by existing sequential optimization methods.