A novel precedence-based and heuristic approach for short-term scheduling of multipurpose batch plants

Many continuous-time formulations have been proposed during the last decades for short-term scheduling of multipurpose batch plants. Although these models establish advantages over discrete-time representations, they are still inefficient in solving moderate-size problems, such as maximization of profit in long horizon, and minimization of makespan. Unlike existing literature, this paper presents a new precedence-based mixed integer linear programming (MILP) formulation for short-term scheduling of multipurpose batch plants. In the new model, multipurpose batch plants are described with a modified state-task network (STN) approach, and binary variables express the assignments and sequences of batch processing and storing. To eliminate the drawback of precedence-based formulations which commonly include large numbers of batches, an iterative procedure is developed to determine the appropriate number of batch that leads to global optimal solution. Moreover, four heuristic rules are proposed to selectively prefix some binary variables to 0 or 1, thereby reducing the overall number of binary variables significantly. To evaluate model performance, our model and the best models reported in the literature (S&K model and I&F model) are utilized to solve several benchmark examples. The result comparison shows that our model is more effective to find better solution for complex problems when using heuristic rules. Note that our approach not only can handle unlimited intermediate storage efficiently as well as the I&F model, but also can solve scheduling problems in limited intermediate storage more quickly than the S&K model.     

Continuous-time scheduling formulation for multipurpose batch plants

Short-term scheduling of batch processes is a complex combinatorial problem with remarkable impact on the total revenue of chemical plants. It consists of the optimal allocation of limited resources to tasks over time in order to manufacture final products following given batch recipes. This article addresses the short-term scheduling of multipurpose batch plants, using a mixed integer linear programming formulation based on the state-task network representation. It employs both single-grid and multi-grid continuous-time representations, derived from generalized disjunctive programming. In comparison to other multigrid scheduling models in the literature, the proposed multi-grid model uses no big-M constraints and leads to more compact mathematical models with strong linear relaxations, which often results in shorter computational times. The single-grid counterpart of the formulation is not as favorable, as it leads to weaker linear relaxations than the multi-grid approach and is not capable of handling changeover time constraints.     

Hybrid time slots sequencing model for a class of scheduling problems

This article presents a new model for the short‐term scheduling of multistage batch plants with a single unit per stage, mixed storage policies, and multiple shared resources for moving orders between stages. Automated wet‐etching stations for wafer fabrication in semiconductor plants provide the industrial context. The uncommon feature of the continuous‐time model is that it relies on time grids, as well as on global precedence sequencing variables, to find the optimal solution to the problem. Through the solution of a few test cases taken from the literature, we show that new model performs significantly better than a pure sequencing formulation and better than a closely related hybrid model with slightly different sequencing variables. We also propose a new efficient heuristic procedure for extending the range of problems that can effectively be solved, which essentially solves relaxed and constrained versions of the full‐space model. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

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.     

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.     

A new approach for scheduling of multipurpose batch processes with unlimited intermediate storage policy

The increasing demand of goods, the high competitiveness in the global marketplace as well as the need to minimize the ecological footprint lead multipurpose batch process industries to seek ways to maximize their productivity with a simultaneous reduction of raw materials and utility consumption and efficient use of processing units. Optimal scheduling of their processes can lead facilities towards this direction. Although a great number of mathematical models have been developed for such scheduling, they may still lead to large model sizes and computational time. In this work, we develop two novel mathematical models using the unit-specific event-based modelling approach in which consumption and production tasks related to the same states are allowed to take place at the same event points. The computational results demonstrate that both proposed mathematical models reduce the number of event points required. The proposed unit-specific event-based model is the most efficient since it both requires a smaller number of event points and significantly less computational time in most cases especially for those examples which are computationally expensive from existing models.     

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.     

A simpler better slot-based continuous-time formulation for short-term scheduling in multipurpose batch plants

Short-term scheduling of multipurpose batch plants is a challenging problem for which several formulations exist in the literature. In this paper, we present a new, simpler, more efficient, and potentially tighter, mixed integer linear programming (MILP) formulation using a continuous-time representation with synchronous slots and a novel idea of several balances (time, mass, resource, etc.). The model uses no big-M constraints, and is equally effective for both maximizing profit and minimizing makespan. Using extensive, rigorous numerical evaluations on a variety of test problems, we show that in contrast to the best model in the literature, our model does not decouple tasks and units, but still has fewer binary variables, constraints, and nonzeros, and is faster.     

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

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

A robust mathematical formulation for multipurpose batch plants

Several scheduling techniques exist in literature based on continuous time representation. The models based on unit specific time points have shown better solution efficiency by reducing the number of time points and problem size. In this paper novel scheduling techniques based on unit specific time point continuous time representation are presented. The proposed models allow nonsimultaneous material transfer into a unit. Nonsimultaneous transfer refers to when a task requires more than one intermediate state it is possible for one state to be transferred and stored in a unit that is processing it for a while and wait for the other intermediates to come together to start the task. This approach gives a better schedule as compared to most published models. The developed MILP scheduling models are based on state sequence network representation that has proven to inherently result in smaller problems in terms of binary variables. The models require a smaller number of time points as compared to single-grid and multi-grid continuous time models. Consequently, they exhibit much better computational performance. Numerical evaluation using literature examples indicate in some of the complex examples that the proposed models give a better objective value as compared to other scheduling models. An added feature of the proposed models is their ability to exactly handle fixed intermediate storage operational philosophy, which has proven to be a subtle drawback in most published scheduling techniques.     

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     

新的多产品间歇生产调度的MILP模型

提出了一种新的多产品厂间歇调度问题的连续时间混合整数线性规划 (MILP)模型,该模型的整数变量体系不依赖于时间块(或者事件点)的概念,并且利用了变量物理概念上的对称互补性,使得与传统的建模方法相比不仅整数变量的数目减少了一半以上,而且建模思想、建模理论都有了新的改进.通过对一个算例的考察证实了新模型可以快速地求得全局最优解.     

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     

Integration of scheduling and control for batch processes using multi‐parametric model predictive control

Integration of scheduling and control results in Mixed Integer Nonlinear Programming (MINLP) which is computationally expensive. The online implementation of integrated scheduling and control requires repetitively solving the resulting MINLP at each time interval. (Zhuge and Ierapetritou, Ind Eng Chem Res. 2012;51:8550–8565) To address the online computation burden, we incorporare multi‐parametric Model Predictive Control (mp‐MPC) in the integration of scheduling and control. The proposed methodology involves the development of an integrated model using continuous‐time event‐point formulation for the scheduling level and the derived constraints from explicit MPC for the control level. Results of case studies of batch processes prove that the proposed approach guarantees efficient computation and thus facilitates the online implementation. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3169–3183, 2014     

MILP scheduling model for multipurpose batch processes considering various intermediate storage policies

MILP (Mixed Integer Linear Programming) scheduling models for non-sequential multipurpose batch processes are presented. Operation sequences of products have to be made in each unit differently by considering production route of each product under a given intermediate storage policy to reduce idle time of units and to raise the efficiency of the process. We represent the starting and finishing time of a task in each unit with two coordinates for a given storage policy. One is based on products, and the other is based on operation sequences. Then, using binary variables and logical constraints, we match the variables used in the two coordinates into one. We suggest MILP models considering sequence dependent setup times to guarantee the optimality of the solutions. Two examples are presented to show the effectiveness of the suggested models.     

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     

一种改进的顺序型多目的间歇工厂生产调度的MILP模型

分析了顺序型多目的工厂间歇生产的特点,建立了一种新的混合整数线性规划（MILP）模型.该模型以操作活动序列作为建模的依据,将整个间歇生产过程分解成若干个子系统.在对各子系统建模的基础上,实现了顺序型多目的工厂间歇调度的全局性优化.并通过算例验证了该模型求解结果的正确性和可行性.然后将新模型运用到更大规模的调度问题上,均求解出了有效的调度方案.     

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     

Sustainable scheduling of batch processes under economic and environmental criteria with MINLP models and algorithms

We address the bi-criterion optimization of batch scheduling problems with economic and environmental concerns. The economic objective is expressed in terms of productivity, which is the profit rate with respect to the makespan. The environmental objective is evaluated by means of environmental impact per functional unit based on the life cycle assessment methodology. The bi-criterion optimization model is solved with the ε-constraint method. Each instance is formulated as a mixed-integer linear fractional program (MILFP), which is a special class of non-convex mixed-integer nonlinear programs. In order to globally optimize the resulting MILFPs effectively, we employ the tailored reformulation-linearization method and Dinkelbach's algorithm. The optimal solutions lead to a Pareto frontier that reveals the tradeoff between productivity and environmental impact per functional unit. To illustrate the application, we present two case studies on the short-term scheduling of multiproduct and multipurpose batch plants.     

Efficient scheduling method of complex batch processes with general network structure via agent‐based modeling

A novel efficient agent‐based method for scheduling network batch processes in the process industry is proposed. The agent‐based model is based on the resource‐task network. To overcome the drawback of localized solutions found in conventional agent‐based methods, a new scheduling algorithm is proposed. The algorithm predicts the objective function value by simulating another cloned agent‐based model. Global information is obtained, and the solution quality is improved. The solution quality of this approach is validated by detailed comparisons with the mixed‐integer programming (MIP) methods. A solution close to the optimal one can be found by the agent‐based method with a much shorter computational time than the MIP methods. As a scheduling problem becomes increasingly complicated with increased scale, more specifications, and uncertainties, the advantages of the agent‐based method become more evident. The proposed method is applied to simulated industrial problems where the MIP methods require excessive computational resources. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2884–2906, 2013