A data‐driven multistage adaptive robust optimization framework for planning and scheduling under uncertainty

A novel data‐driven approach for optimization under uncertainty based on multistage adaptive robust optimization (ARO) and nonparametric kernel density M‐estimation is proposed. Different from conventional robust optimization methods, the proposed framework incorporates distributional information to avoid over‐conservatism. Robust kernel density estimation with Hampel loss function is employed to extract probability distributions from uncertainty data via a kernelized iteratively reweighted least squares algorithm. A data‐driven uncertainty set is proposed, where bounds of uncertain parameters are defined by quantile functions, to organically integrate the multistage ARO framework with uncertainty data. Based on this uncertainty set, we further develop an exact robust counterpart in its general form for solving the resulting data‐driven multistage ARO problem. To illustrate the applicability of the proposed framework, two typical applications in process operations are presented: The first one is on strategic planning of process networks, and the other one on short‐term scheduling of multipurpose batch processes. The proposed approach returns 23.9% higher net present value and 31.5% more profits than the conventional robust optimization method in planning and scheduling applications, respectively. © 2017 American Institute of Chemical Engineers AIChE J, 63: 4343–4369, 2017     

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.     

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.     

Adaptive model predictive inventory controller for multiproduct batch plant

An inventory control system was developed for multiproduct batch plants with an arbitrary number of batch processes and storage units. Customer orders are received by the plant at order intervals and in order quantities that are subject to random fluctuations. The objective of the plant operation is to minimize the total cost while maintaining inventory levels within the storage or warehouse capacity by adjusting the startup times, the quantities of raw material orders, and production batch sizes. An adaptive model predictive control algorithm was developed that uses a periodic square wave model to represent the flows of the material between the processes and the storage units. The boundedness of the control output and the convergence of the estimated parameters in implementations of the proposed algorithm were mathematically proven under the assumption that disturbances in the orders are bounded. The effectiveness of this approach was demonstrated by performing simulations. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1867–1880, 2015     

Modeling and Optimization for Short-term Scheduling of Multipurpose Batch Plants

In the past two decades, short-term scheduling of multipurpose batch plants has received significant attention. Most scheduling problems are modeled using either state-task-network or resource-task-network (RTN) process representation. In this paper, an improved mixed integer linear programming model for short-term scheduling of multipurpose batch plants under maximization of profit is proposed based on RTN representation and unit-specific events. To solve the model, a hybrid algorithm based on line-up competition algorithm and linear programming is presented. The proposed model and hybrid algorithm are applied to two benchmark examples in literature. The simulation results show that the proposed model and hybrid algorithm are effective for short-term scheduling of multipurpose batch plants.     

批处理过程优化调度研究综述--1.MILP调度方法的描述框架

综述化工批处理过程调度建模研究及其实际应用。计划／调度在企业生产管理中起着承上启下的作用，合理的计划调度不但能提高企业的服务水平、降低存储费用，而且还能提高企业的生产能力、加深对过程机制及关键数据的理解。整数规划方法应用于批处理过程计划调度，具有较好的适用性和扩展性，解的性质良好，在批处理过程调度研究得到广泛的应用。     

An integrated approach to computer-aided operation of batch chemical plants

The design and implementation of a computer-based system which integrates planning and plant control of batch chemical plants is presented. Such a system is required so that the full benefits of computer-aided operation, increased production, improved product quality and reduced operating costs may be realized. A functional analysis of the operational requirements of batch plants indicate that a hierarchical and distributed system is favoured. A new operational activity, batch management, is defined which provides the necessary integration by coordinating the activities of the planning and control levels. Batch management allows the control level activities to be driven by events at the planning level such as changes in product demands. It also provides a feedback path from the control level back up to the planning level so that the inherent variability of batch processes can be accounted for and overcome. This is achieved by dynamic, on-line rescheduling. A very general implementation of this design is described. The implementation is centred around a real-time database and permits the operation of a wide range of processes including multiproduct, multipurpose plants with both serial and parallel lines, intermediate storage, shared utilities, etc. To demonstrate its effectiveness, two applications are presented, one in conjunction with an on-line, real-time control system, and the other with an off-line discrete event simulator. The significant benefits achieved in terms of improved operation are discussed.     

Dynamic hybrid simulation of batch processes driven by a scheduling module

Simulation is now a CAPE tool widely used by practicing engineers for process design and control. In particular, it allows various offline analyses to improve system performance such as productivity, energy efficiency, waste reduction, etc. In this framework, we have developed the dynamic hybrid simulation environment PrODHyS whose particularity is to provide general and reusable object-oriented components dedicated to the modeling of devices and operations found in chemical processes. Unlike continuous processes, the dynamic simulation of batch processes requires the execution of control recipes to achieve a set of production orders. For these reasons, PrODHyS is coupled to a scheduling module (ProSched) based on a MILP mathematical model in order to initialize various operational parameters and to ensure a proper completion of the simulation. This paper focuses on the procedure used to generate the simulation model corresponding to the realization of a scenario described through a particular scheduling.     

An approximate mathematical framework for resource-constrained multistage batch scheduling

A rigorous representation of the multistage batch scheduling problem is often useless to even provide a good feasible schedule for many real-world industrial facilities. In order to derive a much simpler scheduling methodology, some usual features of multistage batch plants should be exploited. A common observation in industry is that multistage processing structures usually present a bottleneck stage (BS) controlling the plant output level. Therefore, the quality of the production schedule heavily depends on the proper allocation and sequencing of the tasks performed at the stage BS. Every other part of the processing sequence should be properly aligned with the selected timetable for the bottleneck tasks. A closely related concept with an empirical basis is the usual existence of a common batch sequencing pattern along the entire processing structure that leads to define the constant-batch-ordering rule (CBOR). According to this rule, a single sequencing variable is sufficient to establish the relative ordering of two batches at every processing stage in which both have been allocated to the same resource item. This work introduces a CBOR-based global precedence formulation for the scheduling of order-driven multistage batch facilities. The proposed MILP approximate problem representation is able to handle sequence-dependent changeovers, delivery due dates and limited manufacturing resources other than equipment units. Optimal or near-optimal solutions to several large-scale examples were found at very competitive CPU times.     

Integrated process design,scheduling, and model predictive control of batch processes with closed-loop implementation

Simultaneous evaluation of multiple time scale decisions has been regarded as a promising avenue to increase the process efficiency and profitability through leveraging their synergistic interactions. Feasibility of such an integral approach is essential to establish a guarantee for operability of the derived decisions. In this study, we present a modeling methodology to integrate process design, scheduling, and advanced control decisions with a single mixed-integer dynamic optimization (MIDO) formulation while providing certificates of operability for the closed-loop implementation. We use multi-parametric programming to derive explicit expressions for the model predictive control strategy, which is embedded into the MIDO using the base-2 numeral system that enhances the computational tractability of the integrated problem by exponentially reducing the required number of binary variables. Moreover, we apply the State Equipment Network representation within the MIDO to systematically evaluate the scheduling decisions. The proposed framework is illustrated with two batch processes with different complexities.     

Petri-net based scheduling strategy for semiconductor manufacturing processes

Semiconductor manufacturing is a highly automated and capital-intensive industrial process. The operating cost of a wafer processing plant is in general closely related to the design and management of its process flows. Traditionally, the task of production scheduling is performed manually on the basis of past experiences. There are thus real incentives to develop a systematic approach to construct a mathematical programming model in order to reduce the chance of human errors and to ensure operational efficiency in implementing the resulting schedules. To this end, the Petri nets are adopted in this work to accurately model the semiconductor manufacturing activities. The token movements in a Petri net are represented with the well-established scheduling model for batch chemical processes, and the optimal schedule of the given semiconductor process can then be determined accordingly. The feasibility and effectiveness of this scheduling strategy is demonstrated in the present paper with three examples, i.e., the final test process, the re-entrant flow process, and the photolithography-etching process.     

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.     

Simultaneous regular and non-regular production scheduling of multipurpose batch plants: A real chemical–pharmaceutical case study

Regular and non-regular production can often be found in multipurpose batch plants, requiring two distinct operating strategies: campaign and short-term production. This paper proposes a solution approach for simultaneous scheduling of campaign and short-term products in multipurpose batch plants. Regular products follow a cyclic schedule and must cover several product deliveries during the scheduling horizon, while non-regular products have a non-cyclic schedule. The proposed approach explores the Resource-Task Network (RTN) discrete-time formulation. Moreover, a rolling horizon approach, and reformulation and branching strategies have been applied to deal with the computational complexity of the scheduling problem. Real case instances of a chemical–pharmaceutical industry are solved, showing the applicability of the solution approach.     

多目的间歇过程短期排程的柔性研究

本文建立了一个多目的间歇过程短期排程柔性的模型，并开发了一个实用的计算程序求解此ＭＩＮＬＰ模型。通过例证研究说明，应用此模型进行短期排程可实现快速有效的间歇化工厂生产管理。     

Multiobjective evolutionary optimization of batch process scheduling under environmental and economic concerns

The simultaneous consideration of economic and environmental objectives in batch production scheduling is today a subject of major concern. However, it constitutes a complex problem whose solution necessarily entails production trade‐offs. Unfortunately, a rigorous multiobjective optimization approach to solve this kind of problem often implies high computational effort and time, which seriously undermine its applicability to day‐to‐day operation in industrial practice. Hence, this work presents a hybrid optimization strategy based on rigorous local search and genetic algorithm to efficiently deal with industrial scale batch scheduling problems. Thus, a deeper insight into the combined environmental and economic issues when considering the trade‐offs of adopting a particular schedule is provided. The proposed methodology is applied to a case study concerning a multiproduct acrylic fiber production plant, where product changeovers influence the problem results. The proposed strategy stands for a marked improvement in effectively incorporating multiobjective optimization in short‐term plant operation. © 2012 American Institute of Chemical Engineers AIChE J, 59: 429–444, 2013     

An MILP continuous-time approach to short-term scheduling of resource-constrained multistage flowshop batch facilities

This work presents a new MILP mathematical formulation for the resource-constrained short-term scheduling of flowshop batch facilities with a known topology and limited supplies of discrete resources. The processing structure is composed of multiple stages arranged in series and several units working in parallel at each one. All production orders consist of a single batch and follow the same processing sequence throughout the plant. The proposed MILP approach is based on a continuous time domain representation that relies on the notion of order predecessor and accounts for sequence-dependent setup times. Assignment and sequencing decisions are independently handled through separate sets of binary variables. A proper formulation of the sequencing constraints provides a substantial saving in sequencing variables and constraints. By postulating a pair of conditions for the simultaneous execution of processing tasks, rather simple resource constraints requiring a few extra binary variables are derived. The proposed MILP scheduling approach shows a remarkable computational efficiency when applied to real-world problems.     

A tighter continuous time formulation for the cyclic scheduling of a mixed plant

In this paper, based on the cyclic scheduling formulation of Schilling and Pantelides [Schilling, G., & Pantelides, C. (1999). Optimal periodic scheduling of multipurpose plants. Computers& Chemical Engineering, 23, 635–655], we propose a continuous time mixed integer linear programming (MILP) formulation for the cyclic scheduling of a mixed plant, i.e. a plant composed of batch and continuous tasks. The cycle duration is a variable of the model and the objective is to maximize productivity. By using strengthening techniques and the analysis of small polytopes related to the problem formulation, we strengthen the initial formulation by tightening some initial constraints and by adding valid inequalities. We show that this strengthened formulation is able to solve moderate size problems quicker than the initial one. However, for real size cases, it remains difficult to obtain the optimal solution of the scheduling problem quickly. Therefore, we introduce MILP-based heuristic methods in order to solve these larger instances, and show that they can provide good feasible solutions quickly.     

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.     

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…).     

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