A rule-based genetic algorithm for the scheduling of single-stage multi-product batch plants with parallel units

This paper presents a heuristic rule-based genetic algorithm (GA) for large-size single-stage multi-product scheduling problems (SMSP) in batch plants with parallel units. SMSP have been widely studied by the researchers. Most of them used mixed-integer linear programming (MILP) formulation to solve the problems. With the problem size increasing, the computational effort of MILP increases greatly. Therefore, it is very difficult for MILP to obtain acceptable solutions to large-size problems within reasonable time. To solve large-size problems, the preferred method in industry is the use of scheduling rules. However, due to the constraints in SMSP, the simple rule-based method may not guarantee the feasibility and quality of the solution. In this study, a random search based on heuristic rules was proposed first. Through exploring a set of random solutions, better feasible solutions can be achieved. To improve the quality of the random solutions, a genetic algorithm-based on heuristic rules has been proposed. The heuristic rules play a very important role in cutting down the solution space and reducing the search time. Through comparative study, the proposed method demonstrates promising performance in solving large-size SMSP.     

Optimal scheduling of continuous plants with energy constraints

This work addresses the scheduling of continuous single stage multiproduct plants with parallel units and shared storage tanks. Processing tasks are energy intensive and we consider time-dependent electricity pricing and availability together with multiple intermediate due dates, handled as hard constraints. A new discrete-time aggregate formulation is proposed to rapidly plan the production levels. It is combined with a continuous-time model for detailed scheduling as the essential part of a rolling-horizon algorithm. Their computational performance is compared to traditional discrete and continuous-time full-space formulations with all models relying on the Resource-Task Network (RTN) process representation. The results show that the new models and algorithm can generate global optimal schedules much more efficiently than their counterparts in problems involving unlimited power availability. Under restricted power, the aggregate model underestimates the electricity cost, which may cause the rolling-horizon approach to converge to a suboptimal solution, becoming the discrete-time model a better approach.     

A CP formulation for scheduling multiproduct multistage batch plants

The short-term scheduling of multiproduct multistage batch plants is tackled in this paper by means of a constraint programming (CP) methodology. This approach, consisting of both a model and a search strategy, easily handles different features found in industrial environments: finite unit ready times, dissimilar parallel equipment at each stage, sequence-dependent changeovers, topology constraints, forbidden job-equipment assignments, order release times, as well as renewable resources limitations. It can also address various interstage storage and operational policies: UIS, NIS/ZW, NIS/UW, and mixed ones. Besides, it introduces two simple and efficient search methodologies based on domain knowledge, whose great impact on the computational performance is shown. The approach was extensively tested by means of several examples having various difficulty degrees. It rendered good computational results for a variety of interstage storage policies and objective functions. Moreover, this work shows that the default depth-first search strategy does not perform well for scheduling problems.     

Genetic algorithm for large-size multi-stage batch plant scheduling

This paper presents a heuristic approach based on genetic algorithm (GA) for solving large-size multi-stage multi-product scheduling problem (MMSP) in batch plant. The proposed approach is suitable for different scheduling objectives, such as total process time, total flow time, etc. In the algorithm, solutions to the problem are represented by chromosomes that will be evolved by GA. A chromosome consists of order sequences corresponding to the processing stages. These order sequences are then assigned to processing units according to assignment strategies such as forward or backward assignment, active scheduling technique or similar technique, and some heuristic rules. All these measures greatly reduce unnecessary search space and increase the search speed. In addition, a penalty method for handling the constraints in the problem, e.g., the forbidden changeovers, is adopted, which avoids the infeasibility during the GA search and further greatly increases the search speed.     

Three-scale integrated optimization model of furnace simulation,cyclic scheduling,and supply chain of ethylene plants

In order to explore the potential of profit margin improvement, a novel three-scale integrated optimization model of furnace simulation, cyclic scheduling, and supply chain of ethylene plants is proposed and evaluated. A decoupling strategy is proposed for the solution of the three-scale model, which uses our previously proposed reactor scale model for operation optimization and then transfers the obtained results as a parameter table in the joint MILP optimization of plant-supply chain scale for cyclic scheduling. This optimization framework simplifies the fundamental mixed-integer nonlinear programming (MINLP) into several sub-models, and improves the interpretability and extendibility. In the evaluation of an industrial case, a profit increase at a percentage of 3.25% is attained in optimization compared to the practical operations. Further sensitivity analysis is carried out for strategy evolving study when price policy, supply chain, and production requirement parameters are varied. These results could provide useful suggestions for petrochemical enterprises on thermal cracking production.     

Heat integration of intermittently available continuous streams in multipurpose batch plants

Presented in this paper is a mathematical technique for simultaneous heat integration and process scheduling in multipurpose batch plants. Taking advantage of the intermittent continuous behavior of process streams during transfer from one processing unit to another, as determined by the recipe, the presented formulation aims to maximize the coincidence of availability of hot and cold stream pairs with feasible temperature driving forces, while taking into consideration process scheduling constraints. Contrary to similar contributions in published literature, time is treated as one of the key optimization variables instead of a parameter fixed a priori. Heat integration during stream transfer has the added benefit of shortened processing time, which invariably improves throughput, as more batches are likely to be processed within a given time horizon, compared to conventional heating and cooling in situ. Application of the proposed model to a case study shows improvements of more than 30% in energy savings and up to 15% in product output.     

A discrete-time scheduling model for continuous power-intensive process networks with various power contracts

Increased volatility in electricity prices and new emerging demand side management opportunities call for efficient tools for the optimal operation of power-intensive processes. In this work, a general discrete-time model is proposed for the scheduling of power-intensive process networks with various power contracts. The proposed model consists of a network of processes represented by Convex Region Surrogate models that are incorporated in a mode-based scheduling formulation, for which a block contract model is considered that allows the modeling of a large variety of commonly used power contracts. The resulting mixed-integer linear programming model is applied to an illustrative example as well as to a real-world industrial test case. The results demonstrate the model's capability in representing the operational flexibility in a process network and different electricity pricing structures. Moreover, because of its computational efficiency, the model holds much promise for its use in a real industrial setting.     

Simultaneous synthesis of a heat exchanger network with multiple utilities using utility substages

Heat exchanger network synthesis (HENS) has progressed by using mathematical programming-based simultaneous methodology. Although various considerations such as non-isothermal mixing and bypass streams are applied to consider real world alternatives in modeling phase, many challenges are faced because of its properties within non-convex mixed-integer nonlinear programming (MINLP). We propose a modified superstructure, which contains a utility substage for use in considering multiple utilities in a simultaneous MINLP model. To improve model size and convergence, fixed utility locations according to temperature and series connections between utilities are suggested. The numbers of constraints, discrete, and continuous variables show that overall model size decreases compared with previous research. Thus, it is possible to expand the feasible search area for reaching the nearest global solution. The model's effectiveness and applications are exemplified by several literature problems, where it is used to deduce a network superior to that of any other reported methodology.     

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.     

Optimal design of batch mass exchange networks with multipurpose exchange units

A novel mathematical model for simultaneous optimization of batch mass exchange networks with multipurpose mass exchange units that can be shared by more than one match in different periods is presented in this work. It can be shown that both utility cost and capital investment can be reduced simultaneously with the use of multipurpose mass exchangers and mass storage tanks. Specifically, state-space superstructure that does not contain any structural simplification is proposed to capture the entire characteristics of the network configuration and a mixed-integer nonlinear optimization model is then formulated accordingly to generate the optimal batch operating policies and the corresponding flowsheet. Two examples are presented in this paper to demonstrate the validity and advantages of the proposed approach.     

Simultaneous synthesis of heat exchanger networks with pressure recovery: Optimal integration between heat and work

The optimal integration between heat and work may significantly reduce the energy demand and consequently the process cost. This article introduces a new mathematical model for the simultaneous synthesis of heat exchanger networks (HENs), in which the pressure levels of the process streams can be adjusted to enhance the heat integration. A superstructure is proposed for the HEN design with pressure recovery, developed via generalized disjunctive programming, and mixed‐integer nonlinear programming formulation. The process conditions (stream temperature and pressure) must be optimized. Furthermore, the approach allows for coupling of the turbines and compressors and selection of the turbines and valves to minimize the total annualized cost, which consists of the operational and capital expenses. The model is tested for its applicability in three case studies, including a cryogenic application. The results indicate that the energy integration reduces the quantity of utilities required, thus decreasing the overall cost. © 2013 American Institute of Chemical Engineers AIChE J, 60: 893–908, 2014     

An adjustable robust optimization approach to scheduling of continuous industrial processes providing interruptible load

To ensure the stability of the power grid, backup capacities are called upon when electricity supply does not meet demand due to unexpected changes in the grid. As part of the demand response efforts in recent years, large electricity consumers are encouraged by financial incentives to provide such operating reserve in the form of load reduction capacities (interruptible load). However, a major challenge lies in the uncertainty that one does not know in advance when load reduction will be requested. In this work, we develop a scheduling model for continuous industrial processes providing interruptible load. An adjustable robust optimization approach, which incorporates recourse decisions using linear decision rules, is applied to model the uncertainty. The proposed model is applied to an illustrative example as well as a real-world air separation case. The results show the benefits from selling interruptible load and the value of considering recourse in the decision-making.     

Novel genetic algorithm for short-term scheduling of sequence dependent changeovers in multiproduct polymer plants

Polymer plants generally operate to produce different grades of product from the same reactor. Such systems commonly require short-term scheduling to meet market demand. One important requirement in continuous-time scheduling of such systems is to satisfy a variety of constraints, including identifying feasible sequences of the predecessor and successor jobs to effectively handle changeovers. In this study, a new genetic algorithm (GA) is proposed to solve such job sequencing problems. The proposed GA uses real-coded chromosome to represent job orders and their sequences in the schedule. The novelty is that the representation ensures that all constraints are satisfied a priori, except the sequence constraint which is handled by penalizing violations. Three important problems relevant to polymer industry are solved to obtain optimal schedules. The first deals with the sequencing constraint between individual product orders, the second with sequencing constraint between groups of product orders, while the third incorporates batching with scheduling.     

A new Lagrangian decomposition approach applied to the integration of refinery planning and crude-oil scheduling

The aim of this paper is to introduce a methodology to solve a large-scale mixed-integer nonlinear program (MINLP) integrating the two main optimization problems appearing in the oil refining industry: refinery planning and crude-oil operations scheduling. The proposed approach consists of using Lagrangian decomposition to efficiently integrate both problems. The main advantage of this technique is to solve each problem separately. A new hybrid dual problem is introduced to update the Lagrange multipliers. It uses the classical concepts of cutting planes, subgradient, and boxstep. The proposed approach is compared to a basic sequential approach and to standard MINLP solvers. The results obtained on a case study and a larger refinery problem show that the new Lagrangian decomposition algorithm is more robust than the other approaches and produces better solutions in reasonable times.     

Novel continuous-time formulations for scheduling multi-stage batch plants with identical parallel units

Scheduling production optimally in multi-stage multi-product plants is a very difficult problem that has received limited attention. While the case of non-identical parallel units has been addressed, the case of identical parallel units is equally worthy of attention, as many plants are or can be approximated as such. In this paper, we construct and compare several novel MILP formulations for the latter. In contrast to the existing work, we increase solution efficiency by considering each stage as a block of multiple identical units, thereby eliminating numerous binary variables for assigning batches to specific units. Interestingly, a novel formulation using an adjacent pair-wise sequencing approach proves superior to slot-based formulations. Furthermore, we develop heuristic variations of our proposed formulations to address moderate-size problems. A novel heuristic strategy inspired from list scheduling algorithms seems to be efficient for moderate-size problems and scales well with problem size.     

Computational strategies for large-scale MILP transshipment models for heat exchanger network synthesis

Determining the minimum number of units is an important step in heat exchanger network synthesis (HENS). The MILP transshipment model (Papoulias and Grossmann, 1983) and transportation model (Cerda and Westerberg, 1983) were developed for this purpose. However, they are computationally expensive when solving for large-scale problems. Several approaches are studied in this paper to enable the fast solution of large-scale MILP transshipment models. Model reformulation techniques are developed for tighter formulations with reduced LP relaxation gaps. Solution strategies are also proposed for improving the efficiency of the branch and bound method. Both approaches aim at finding the exact global optimal solution with reduced solution times. Several approximation approaches are also developed for finding good approximate solutions in relatively short times. Case study results show that the MILP transshipment model can be solved for relatively large-scale problems in reasonable times by applying the approaches proposed in this paper.     

考虑能耗影响的多产品间歇化工过程优化排序

提出一种用于间歇生产的多产品化工厂排序的多目标优化的混合整数非线性规划(MINLP)模型,其目标函数同时考虑了总生产时间最短和能耗最小的影响,定义了关于过程能耗的影响因子及决策因子,用以对总生产时间和能耗的影响进行权衡。采用改进的模拟退火算法(SA)对具有不同决策因子和能耗影响因子情况下的算例进行了求解,结果表明,该模型能够较好地反映能耗因素在多产品厂排序问题中的影响,使排序结果达到生产时间和能耗影响的综合最优。     

基于特定单元事件点的改进间歇生产调度模型

建立有效的间歇调度模型一直是生产调度问题调度研究的热点,而连续时间模型是优化短期间歇生产调度问题的有效工具。基于特定单元事件点的概念,建立一种改进的间歇调度连续时间混合整数线性规划(MILP)模型。该调度模型引入了新变量,使模型处理物料在不同设备间的传输过程更加灵活。结果表明,提出的改进模型只需要较少的事件点,就可以快速有效处理无限中间存储(UIS)间歇调度问题。     

Simultaneous synthesis of sub and above-ambient heat exchanger networks including expansion process based on an enhanced superstructure model

Synthesis of heat exchanger networks including expansion process is a complex task due to the involvement of both heat and work. A stream that expands through expanders can produce work and cold load, while expansion through valves barely affects heat integration. In addition, expansion through expanders at higher temperature produces more work, but consumes more hot utility. Therefore, there is a need to weigh work production and heat consumption. To this end, an enhanced stage-wise superstructure is proposed that involves synchronous optimization of expander/valve placement and heat integration for each pressure-change sub-stream in stages. A mixed-integer nonlinear programming (MINLP) model is established for synthesizing sub and aboveambient heat exchanger networks with multi-stream expansion, which explicitly considers the optimized selection of end-heaters and end-coolers to adjust temperature requirement. Our proposed method can commendably achieve the optimal selection of expanders and valves in a bid for minimizing exergy consumption and total annual cost. Four example studies are conducted with two distinct objective function (minimization of exergy consumption and total annual cost, respectively) to illustrate the feasibility and efficacy of the proposed method.     

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.