Parallel Batch Processing Machines Research Articles

A clustering-aided multi-agent deep reinforcement learning for multi-objective parallel batch processing machines scheduling in semiconductor manufacturing

Batch processing machines are often the bottleneck in semiconductor manufacturing and their scheduling plays a key role in production management. Pioneer researches on multi-objective batch machines scheduling mainly focus on evolutionary algorithms, failing to meet the online scheduling demand. To deal with the challenges confronted by incompatible job families, dynamic job arrivals, capacitated machines and multiple objectives, we propose a clustering-aided multi-agent deep reinforcement learning approach (CA-MADRL) for the scheduling problem. Specifically, to achieve diverse nondominated solutions, an offline multi-objective scheduling algorithm named Multi-Subpopulation fast elitist Non-Dominated Sorting Genetic Algorithm (MS-NSGA-II) is firstly developed to obtain the Pareto Fronts, and a clustering algorithm based on cosine distance is employed to analyze the distribution of Pareto frontier solution, which would be used to guide reward functions design in multi-agent deep reinforcement learning. To realize multi-objective optimization, several reinforcement learning base models are trained for different optimization directions, each of which composed of batch forming agent and batch scheduling agent. To alleviate time complexity of model training, a parameter sharing strategy is introduced between different reinforcement learning base model. By validating the proposed approach with 16 instances designed based on actual production data from a semiconductor manufacturing company, it has been demonstrated that the approach not only meets the high-frequency scheduling requirements of manufacturing systems for parallel batch processing machines but also effectively reduces the total job tardiness and machine energy consumption.

Scheduling parallel batch processing machines: A case study in the semiconductor industry

This paper presents a mathematical programming-based solution approach for the scheduling problem of batch-processing parallel machines with eligibility constraints. A case study has been presented in the semiconductor industry, where the ovens are scheduled for the underfill cure operation of products. The case includes constraints, such as oven-product eligibility restrictions, loading constraints for the batching of products for ovens, daily production requirements, and oven capacity constraints. In this study, we also assess the difference between creating batches of a single product type or different product types to be allocated to the ovens. The case study results have shown that the proposed models, in comparison to the current situation, increase the occupancy rate of ovens. The execution of the models aids the company in gaining visibility on the scheduling of ovens and successfully managing the production plan and order commitment. The proposed models have been effective and supportive of the semiconductor company.

Parallel batch processing machines scheduling for SLM additive manufacturing in cloud manufacturing

For the scheduling problem of parallel batch processing machines for Selective Laser Melting (SLM) additive manufacturing in cloud manufacturing environments, an Improved Discrete Artificial Bee Colony algorithm(IABC) is proposed by considering the service time of the product as well as introducing the mathematical model of the problem. Firstly, a population initialization strategy is introduced to improve the quality of initial solutions and accelerate the convergence of the population.Secondly, through three neighborhood search operators, the transition from the original nectar source to the new nectar source is achieved for employed bees and following bees. Furthermore, a local search strategy and a modified abandonment pattern are proposed to increase population diversity and prevent the algorithm from falling into local optima.Finally, the performance of the algorithm is analyzed, and the IABC algorithm was applied to 36 examples. The effectiveness and advantages of IABC in solving the studied problem are verified through a large number of simulation experiments.

An adaptive shuffled frog-leaping algorithm for parallel batch processing machines scheduling with machine eligibility in fabric dyeing process

Fabric dyeing is an important production process in clothing industry and consists of some batch processing machines (BPM). In this study, parallel BPM scheduling problem with machine eligibility in fabric dyeing process is considered and an adaptive shuffled frog-leaping algorithm (ASFLA) is presented to minimise makespan and total tardiness simultaneously. A heuristic is used to produce initial population. Evolution quality of population on the last generation is used to implement adaptive population division and adaptive search process in each memeplex on the current generation. Search process of each memeplex is divided into some segments and search operators are dynamically adjusted after each segment is done. Adaptive elimination is performed on the worst memeplex. Extensive experiments are conducted to test the performance of ASFLA and the computational results demonstrate that new strategies of ASFLA are effective and ASFLA has promising advantages on the considered problem.

Flexible job-shop scheduling problem with parallel batch machines based on an enhanced multi-population genetic algorithm

AbstractThe flexible job-shop scheduling problem (FJSP) with parallel batch processing machine (PBM) is one of those long-standing issues that needs cutting-edge approaches. It is a recent extension of standard flexible job shop scheduling problems. Despite their wide application and prevalence in practical production, it seems that current research on these types of combinatorial optimization problems remains limited and uninvestigated. More specifically, existing research mainly concentrates on the flow shop scenarios in parallel batch machines for job shop scheduling but few literature emphasis on the flexible job shop integration in these contexts. To directly address the above mentioned problems, this paper establishes an optimization model considering parallel batch processing machines, aiming to minimize the maximum completion time in operating and production environments. The proposed solution merges variable neighborhood search with multi-population genetic algorithms, conducting a neighborhood search on the elite population to reduce the likelihood of falling into local optima. Subsequently, its applicability was evaluated in computational experiments using real production scenarios from a partnering enterprise and extended datasets. The findings from the analyses indicate that the enhanced algorithm can decrease the objective value by as much as 15% compared to other standard algorithms. Importantly, the proposed approach effectively resolves flexible job shop scheduling problems involving parallel batch processing machines. The contribution of the research is providing substantial theoretical support for enterprise production scheduling.

An Energy-Efficient Unrelated Parallel Machine Scheduling Problem with Batch Processing and Time-of-Use Electricity Prices

The extensive consumption of energy in manufacturing has led to a large amount of greenhouse gas emissions that have caused an enormous effect on the environment. Therefore, investigating how to reduce energy consumption in manufacturing is of great significance to cleaner production. This paper considers an energy-conscious unrelated parallel batch processing machine scheduling problem under time-of-use (TOU) electricity prices. Under TOU, electricity prices vary for different periods of a day. This problem is grouping jobs into batches, assigning the batches to machines and allocating time to the batches so as to minimize the total electricity cost. A mixed-integer linear programming model and two groups of heuristics are proposed to solve this problem. The first group of heuristics first forms batches, assigns the batches to machines and finally allocates time to the batches, while the second group of heuristics first assigns jobs to machines, batches the jobs on each machine and finally allocates time to each batch. The computational results show that the SPT-FBLPT-P1 heuristic in the second group can provide high-quality solutions for large-scaled instances in a short time, in which the jobs are assigned to the machines based on the shortest processing time rule, the jobs on each machine are batched following the full-batch longest processing time algorithm, and the time is allocated to each batch following an integer programming approach. The MDEC-FBLPT-P1 heuristic that uses the minimum difference of the power consumption algorithm to assign the jobs also performed well.

A feedback-based artificial bee colony algorithm for energy-efficient flexible flow shop scheduling problem with batch processing machines

Energy-efficient flexible flow shop scheduling problem (EFFSP) and parallel batch processing machines (BPM) scheduling problem have been extensively studied; however, as the integration of EFFSP and parallel BPM scheduling problem, EFFSP with BPM is seldom investigated even though it often exists in many energy-intensive manufacturing processes such as casting and steelmaking. In this study, EFFSP with BPM at a middle stage in hot & cold casting process is considered, and a feedback-based artificial bee colony (FABC) algorithm is proposed to simultaneously minimize makespan, total tardiness, and total energy consumption. A new cooperation between two employed bee swarms and three search cases are implemented, which are employed bee phase and onlooker bee phase or employed bee phase and cooperation or employed bee phase. Feedback mechanism is established by evolution quality of employed bee swarms and adaptive threshold and used to dynamically determine which search case is executed on each generation. New scout phase and recombination operator are also applied. Extensive experiments are conducted and the computational results demonstrated that new strategies such as cooperation are effective and FABC has promising advantages in the considered EFFSP.

A Metaheuristic Framework for Energy-Intensive Industries With Batch Processing Machines

Batch processing machines, which operate multiple jobs at a time, are commonly used in energy-intensive industries. A significant amount of energy can be saved in such industries using production scheduling as an approach to enhance efficiency. This study deals with an energy-aware scheduling problem for parallel batch processing machines with incompatible families and job release times. In such an environment, a machine may need to wait until all the jobs in the next batch become ready. During waiting time, a machine can be switched <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">off</small> or kept <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">on</small> standby for more energy-efficient scheduling. We first present a mixed-integer linear programming (MILP) model to solve the problem. However, the presented MILP model can only solve small problem instances. We therefore propose an energy-efficient tabu search (ETS) algorithm for solving larger problem instances. The proposed solution framework incorporates multiple neighborhood methods for efficient exploration of the search space. An energy-related heuristic is also integrated into the ETS for minimizing energy consumption during the waiting time. The performance of our proposed ETS algorithm is validated by comparing it with CPLEX for small problem instances and with two other heuristic algorithms for larger problem instances. The contribution of different components in ETS is also established in our experimental studies. The proposed solution framework is expected to bring many benefits in energy-intensive industries both economically and environmentally.

Unrelated parallel batch processing machine scheduling with time requirements and two-dimensional packing constraints

In various complex manufacturing systems such as wafer fabrication, ceramic processes, and additive manufacturing, a single machine often performs multiple distinct jobs simultaneously, requiring non-overlapping positions in the 2D-plane. As the demand for manufacturing with two-dimensional (2D) packing constraints continues to rise, there is an urgent need to address the integrated scheduling of batch processing machines (BPMs) and 2D packing. However, only a limited number of studies have explored BPM scheduling problems with 2D packing constraints. In this study, we focus on the scheduling of unrelated parallel BPMs to process jobs with non-identical sizes, unequal release dates, and due dates. To model the machine’s capacity, we move beyond the traditional one-dimensional knapsack approach and consider it as a 2D rectangle, taking into account the 2D packing constraints. It is crucial to ensure that no overlapping or stacking occurs within the machine’s capacity under these constraints. To address this problem, we propose a mixed integer linear programming model as the initial approach. Additionally, we develop an adaptive large neighborhood search (ALNS) heuristic specifically designed for handling large instances. The ALNS incorporates eleven removal operators and seven insertion operators, offering a comprehensive exploration and improvement of solutions. To tackle the packing procedure, we adopt two distinct packing patterns, namely Skyline and Open Space. These patterns play a significant role in optimizing the packing of jobs within the machine’s capacity. Furthermore, we conduct extensive computational experiments, generating 48 categories of instances with varying job attributes. These experiments serve to compare the performance of the two packing patterns and validate the effectiveness of our ALNS approach. In conclusion, our research addresses the critical gap in BPM scheduling problems with 2D packing constraints. By introducing a mixed integer linear programming model and developing the ALNS heuristic with diverse operators, coupled with the adoption of different packing patterns, we present a comprehensive approach to tackle this complex problem. Computational experiments are conducted to compare packing patterns and verify the performance of our ALNS method.

Parallel Batch Processing Machine Scheduling Under Two-Dimensional Bin-Packing Constraints

The parallel batch processing machine scheduling problem with two-dimensional bin packing constraints (PBS-2D) has appeared in many industrial environments, but the research on this problem is still not sufficient. In this article, we use the 2-D rectangular packing constraints to describe the spatial geometric layout of jobs more accurately, and propose a mixed integer linear programming (MILP) model to minimize the makespan of PBS-2D. According to the in-depth analysis of the problem properties, PBS-2D is separated into three subproblems, which are job-machine assignment, 2-D job placement, and job sequence optimization. An improved biased random key genetic algorithm (OBRKGA) is proposed to solve job-machine assignment and job sequence optimization. This algorithm generates the initial population based on the idea of orthogonal experimental design, so that the whole solution space can be scanned evenly when generating the initial solution, making the algorithm be more likely to find better solutions for subsequent evolution. At the same time, a bin packing algorithm based on best fit is designed to handle 2-D job placement problem. Finally, the algorithms are tested on a large number of randomly generated instances, the results show that OBRKGA outperformed the original BRKGA, the classical moth-flame optimization algorithm, particle swarm optimization algorithm, gravity search algorithm, and MILP.

Unrelated parallel batch processing machine scheduling for production systems under carbon reduction policies: NSGA-II and MOGWO metaheuristics

Unrelated parallel batch processing machine scheduling for production systems under carbon reduction policies: NSGA-II and MOGWO metaheuristics

Approximation algorithms for scheduling single batch machine with incompatible deteriorating jobs

Motivated by the soaking process under separate heating mode in iron and steel enterprises, we study the parallel batch machine scheduling problem with incompatible deteriorating jobs. The objective is to minimize makespan. A soaking furnace can be seen as a parallel batch processing machine. In order to avoid the thermal stress caused by excessive temperature difference, initial temperature is needed for the ingot before processing. With the increasing of waiting time, the ingot temperature decreases and the soaking time increases. This property is called deterioration. Setup time is needed between incompatible jobs. We show that if jobs have the same sizes, an optimal solution can be found withinO(nlogn) time. If jobs have identical processing times, the problem is proved to be NP-hard in the strong sense. We propose an approximate algorithm whose absolute and asymptotic worst-case ratios are less than 2 and 11/9, respectively. When the jobs have arbitrary sizes and arbitrary processing times, the model is also NP-hard in the strong sense. An approximate algorithm with an absolute and asymptotic worst-case ratio less than 2 is proposed. The time complexity isO(nlogn).

A tabu-based adaptive large neighborhood search for scheduling unrelated parallel batch processing machines with non-identical job sizes and dynamic job arrivals

A tabu-based adaptive large neighborhood search for scheduling unrelated parallel batch processing machines with non-identical job sizes and dynamic job arrivals

A Hybrid Large Neighborhood Search Method for Minimizing Makespan on Unrelated Parallel Batch Processing Machines with Incompatible Job Families

This paper studies a scheduling problem with non-identical job sizes, arbitrary job ready times, and incompatible family constraints for unrelated parallel batch processing machines, where the batches are limited to the jobs from the same family. The scheduling objective is to minimize the maximum completion time (makespan). The problem is important and has wide applications in the semiconductor manufacturing industries. This study proposes a mixed integer programming (MIP) model, which can be efficiently and optimally solved by commercial solvers for small-scale instances. Since the problem is known to be NP-hard, a hybrid large neighborhood search (HLNS) combined with tabu strategy and local search is proposed to solve large-scale problems, and a lower bound is proposed to evaluate the effectiveness of the proposed algorithm. The proposed algorithm is evaluated on numerous compatible benchmark instances and newly generated incompatible instances. The results of computational experiments indicate that the HLNS outperforms the commercial solver and the lower bound for incompatible problems, while for compatible problems, the HLNS outperforms the existing algorithm. Meanwhile, the comparison results indicate the effectiveness of the tabu and local search strategies.

Minimizing total completion time on non-identical parallel batch machines with arbitrary release times using ant colony optimization

This paper considers the problem of scheduling a group of jobs with arbitrary release times, non-identical sizes, and different processing times on non-identical parallel batch processing machines to minimize the total completion time. A mixed-integer programming (MIP) model is firstly constructed in this paper to solve this problem. Then since the studied problem is strongly NP-hard, a modified elite ant system algorithm with the local search (MEASL) is also proposed to solve it, which is compared with several meta-heuristic algorithms and the commercial optimization solver (Gurobi) through extensive simulation experiments. Finally, the experimental results verify the effectiveness of the proposed algorithm.

A Self-Adaptive Multiobjective Differential Evolution Algorithm for the Unrelated Parallel Batch Processing Machine Scheduling Problem

In this paper, the unrelated parallel batch processing machine (UPBPM) scheduling problem is addressed to minimize the total energy consumption (TEC) and makespan. Firstly, a mixed-integer line programming model (MILP) of the UPBPM scheduling problem is presented. Secondly, a self-adaptive multiobjective differential evolution (AMODE) algorithm is put forward. Since the parameter value can affect the performance of the algorithm greatly, an adaptive parameter control method is proposed according to the convergence index of the individual and the evolution degree of the population to improve the exploitation and exploration ability of the algorithm. Meanwhile, an adaptive mutation strategy is proposed to improve the algorithm’s convergence and the solutions’ diversity. Finally, to verify the effectiveness of the algorithm, comparative experiments are carried out on 20 instances with 5 different scales. Numerical comparisons indicate that the proposed method can achieve high comprehensive performance.

A bi-objective evolutionary algorithm for minimizing maximum lateness and total pollution cost on non-identical parallel batch processing machines

The concept of sustainable development, which strives to protect the environment while developing economic and industrial sectors, has received widespread attention. This paper takes the fabric dyeing process in the textile industry as an example to study the problem of minimizing the total pollution cost and the maximum lateness on non-identical parallel batch processing machines with different unit pollution costs. This paper analyzes the characteristics of the batch scheduling problem and proposes a method of constructively generating the initial solutions based on these characteristics. Meanwhile, An environment selection based on hierarchical clustering is proposed. This paper develops an NSGA-CC algorithm combining the above two methods in the NSGA-II framework to solve this bi-objective problem. Through extensive simulation experiments, NSGA-CC is compared with several latest algorithms, and then the experimental results show that the proposed algorithm outperforms compared algorithms.

Discrete particle swarm algorithm with Q-Learning for solving flexible job shop scheduling problem with parallel batch processing machine

For the flexible job shop scheduling problem with parallel batch processing machines (FJSP-PBPM), the mathematical model of the problem is defined, and an improved enhanced discrete particle swarm algorithm is proposed to solve this problem. In terms of global search, an improved discrete particle swarm algorithm is adopted, and effective particle velocity and position update formulas are designed; in the local search, in order to speed up the convergence speed and avoid local convergence, it is integrated into the q-learning method in reinforcement learning. The state space, action space, reward function, and Q-table update methods that meet the scheduling problem are designed, and the proposed hybrid algorithm achieves an effective balance between global search and local search capabilities. At the same time, according to the characteristics of FJSP-PBPM, effective process sequence scheduling rules and batch machine selection rules are designed respectively to improve the search ability of the algorithm. Through the standard FJSP benchmark problem and the production data of a transformer manufacturer that meets the characteristics of the FJSP-PBPM problem, the validity and feasibility of the proposed algorithm are verified.

Parallel batch processing machines scheduling in cloud manufacturing for minimizing total service completion time

This paper considers the integrated scheduling problem of production and delivery on parallel batch processing machines with non-identical capacities in different locations in cloud manufacturing. It is assumed that the jobs have arbitrary release times, different job sizes, unequal processing times, and unique information of customers submitting jobs. The service completion time of a job is the sum of the production completion time and the delivery duration. The objective of the studied problem is to minimize the total service completion time. A mixed-integer programming (MIP) model is presented to solve this problem. Since the problem is NP-hard, an efficient heuristic algorithm and an improved particle swarm optimization algorithm are proposed. The two proposed algorithms are compared with several state-of-the-art algorithms and the commercial optimization solver (Gurobi) through extensive experiments, verifying the effectiveness of the proposed algorithms.

A bi-objective evolutionary algorithm scheduled on uniform parallel batch processing machines

This paper addresses the problem of minimizing the maximum lateness and the total pollution emission costs by scheduling a group of jobs with different processing times, sizes, release times, and due dates on uniform parallel batch processing machines with non-identical machine capacities and different unit pollution emission costs. We develop a discrete bi-objective evolutionary algorithm C-NSGA-A to solve this problem. On the one hand, we present a method of constructively generating an individual with the first job selection to produce an initial population for improving the convergence of individuals. On the other hand, we propose an angle-based environmental selection strategy to choose individuals to maintain the diversity of individuals. Through extensive simulation experiments, C-NSGA-A is compared with several state-of-the-art algorithms, and experimental results show that the proposed algorithm performs better than those algorithms. Moreover, the proposed algorithm has more obvious advantages on instances with a larger number of jobs.