Assembly Job Shop Scheduling Problem Research Articles

Matheuristic and learning-oriented multi-objective artificial bee colony algorithm for energy-aware flexible assembly job shop scheduling problem

With the increase of mass customization, flexible job shop scheduling problem considering assembly stage has widely existed in many manufacturing industries, such as die-casting mould factories. This problem is to find a reasonable machine assignment and operation sequence both in fabrication and assembly stages and simultaneously maximize production efficiency. In reality, energy shortages and environmental pollution have given an impetus to the development of energy-aware production scheduling problems. In this study, we address an energy-aware flexible assembly job shop scheduling problem (EFAJSP) with the objectives of minimizing flow time and energy consumption and first develop a mixed-integer linear programming (MILP) model to solve EFAJSP problem. Then, the model-specific characteristics are extracted and applied to a matheuristic decoding method for exploring the Pareto optimal solution. Due to the complexity of EFAJSP problem, a matheuristic and learning-oriented multi-objective artificial bee colony algorithm (MLABC), which combines the advantages of mathematical programming, reinforcement learning and meta-heuristic algorithm, is proposed. In addition, an initialization, destruction/construction operator and population update operator are proposed and work together to improve the exploration and exploitation performance of the proposed MLABC. Finally, numerical experimental results demonstrate the effectiveness of the proposed MILP model and the superiority of the MLABC over other algorithms in the literature.

A matheuristic-based multi-objective evolutionary algorithm for flexible assembly jobs shop scheduling problem in cellular manufacture

The flexible assembly job shop scheduling problem (FAJSP) and its extensions have received increased attention. However, multi-objective FAJSP in cellular manufacture (FAJSP-CM), a real-world extension of FAJSP with important applications in the mass customization of complex products, is barely considered in most previous studies. Hence, this study first addresses the multi-objective FAJSP-CM problem via a mixed-integer linear programming model (MILP). Then, a matheuristic-based multi-objective evolutionary algorithm (MMOEA), with a matheuristic decoding method, knowledge-guided initialization and learning-based local intensification method, is presented to efficiently tackle the FAJSP-CM problem in polynomial-time. The matheuristic decoding method, which hybrids a decomposition linear programming model (D-LP) that can quickly and optimally allocate the execution times of all operations, to search for the optimal solution in a specific space. The knowledge-guided initialization is extended to get a high-quality and great-diversity initial population for accelerated convergence. Meanwhile, the learning-based local intensification method is developed to adaptively coordinate five problem-specific local search operators to enhance the exploitation ability of the MMOEA algorithm. Finally, comprehensive experiments based on 720 instances are conducted to evaluate the proposed MILP model and MMOEA algorithm. The results of the first experiments illustrate the MILP model can obtain the Pareto solutions of small-scale instances. The remaining experiments demonstrate that the proposed MMOEA algorithm outperforms its competitors by 0.21 and 0.72 in hypervolume ratio and coverage indictors, along with approximately a 25 % improvement in success rate.

A modified memetic algorithm with multi-operation precise joint movement neighbourhood structure for the assembly job shop scheduling problem

This paper presents an adaptive memetic algorithm based on a new neighbourhood structure (AMA) for solving the assembly job shop scheduling problem, with the aim of minimising the maximum completion time (makespan). To utilise the knowledge of problem, a theoretical analysis is conducted to explore the criteria for feasible and effective movement of operations under assembly constraints, and a multi-operation precise joint movement neighbourhood structure is proposed accordingly. In the AMA, to ensure the feasibility of solutions during the evolution process, a feasible encoding mechanism based on the constraint degree of operations is designed, a greedy active decoding method as well as feasible crossover operation based on independent operation chains are designed specifically for this encoding method. To avoid premature convergence of the population, a population update operator with diversity adaptive control is proposed. Finally, by comparing the results with five state-of-the-art algorithms, the superiority of AMA in terms of solution quality and stability is verified, particularly with the update of known optimal solutions for 11 instances.

A genetic algorithm with critical path-based variable neighborhood search for distributed assembly job shop scheduling problem

Production scheduling in distributed manufacturing systems has become an active research field, where large-sized complicated products, such as airplanes and ships, are taken as the primary focus. This paper investigates a distributed assembly job shop scheduling problem (DAJSP) which consists of two production phases. The first stage processes components in several job shops, and the second stage assembles the processed parts into final products. First, a mixed integer linear programming (MILP) model is established to describe the problem with minimizing maximum completion time and find optimal schedules for small-scale scenarios. Afterwards, a genetic algorithm with variable neighborhood search (GA-VNS) is proposed to address more complex instances, which adopts the genetic algorithm as the main framework and employs the variable neighborhood search for exploration. A problem-specific three-vector encoding scheme is designed to represent three decision-making processes of the DAJSP accordingly. To improve candidate solutions, a disjunctive graph model for DAJSP is formulated and three critical path-based neighborhood structures which directly perform on encoding vectors are designed. Numerical experiments are conducted on four groups of instances with different scales and the experimental results demonstrate the effectiveness of the proposed MILP model and GA-VNS. To sum up, the proposed GA-VNS shows the best performance on 30 instances out of 40 instances, while the superior stability has also been proved by statistical tests. In addition, two complicated DAJSP cases are abstracted from an enterprise for fabricating large complex components to further validate the GA-VNS.

A multi-agent resource bidding algorithm for order acceptance and assembly job shop scheduling

This study uses an agent-based approach with a combinatorial auction mechanism to solve the joint order acceptance and assembly job shop scheduling problem. A set of jobs is offered. Each job has a revenue, ready time, due date, deadline, and consists of a set of operations with precedence relationships. Jobs that deviate from their due dates incur earliness/tardiness penalties. An operation may require several units of capacity per time unit and a resource could have multiple units of capacity. The manufacturer can reject any job to satisfy the capacity constraints and maximise the overall profit. We develop a mathematical model for the problem, then use an agent-based approach to solve it. First, the relaxed problem is decomposed into a set of job-level subproblems. Each job is optimised individually without considering the capacity constraints. Profitable jobs at the individual level submit their optimal schedules as combinatorial bids to an auctioneer to acquire combinations of resource capacity-time units. Then, the auctioneer records the profit upper bound, resolves capacity conflicts to reach a feasible solution, records the profit lower bound, and updates the dual variables. Experimental results show that the proposed methodology can solve large-sized problems in reasonable CPU times.

Mathematical model and augmented simulated annealing algorithm for mixed-model assembly job shop scheduling problem with batch transfer

In the mixed-model assembly job-shops, all the components are transferred in batches from the processing stage to the assembly stage to reduce transportation costs and timely satisfy the assembly material requirements. However, batch transfer in such a workshop has not received due attention in the current literature. Thus, this work addresses the mixed-model assembly job-shop scheduling problem with batch transfer via a mathematical model and an augmented simulated annealing algorithm to minimize manufacturing and transportation costs. The mathematical model takes batch transfer constraints into account and constructs the temporal and spatial links among the processing, transfer, and assembly stages. Production sequencing knowledge and batch transfer knowledge are first extracted via gene expression programming algorithm and clustering method and then implanted into the algorithmic operators in the form of rules and strategies to directly identify the promising solution space. Besides, eleven neighborhood structures including the critical component-based and batch-based ones, are designed to enhance the exploitation ability. A restart mechanism considering crossover and tempering helps to get out of local optima. Experimental results indicate that by adopting the extracted knowledge, problem-specific neighborhood structures, and restart mechanism, the proposed algorithm significantly outperforms other comparison algorithms in fixing the studied problem.

Mathematical model and adaptive simulated annealing algorithm for mixed-model assembly job-shop scheduling with lot streaming

Mixed-model assembly and lot streaming are two key technologies to improve efficiency and reduce setups in a multi-variety and small-batch discrete manufacturing environment. Yet few studies consider the two technologies in assembly job-shop scheduling problems. Thus, this paper investigates the mixed-model assembly job-shop scheduling problem with lot streaming, which contains two closely coordinated stages with differentiated production lot size: the processing stage with lot streaming and the mixed-model assembly stage with single-piece flow. To tackle this problem, a mathematical model including new constraints i.e. production sequence constraints within/among sublots, sequence-dependent setup constraints between sublots and mixed-model assembly constraints, is developed to establish the temporal and spatial links between the processing and assembly stages. Besides, an adaptive simulated annealing algorithm is proposed. In this algorithm, a sublot sequence rule considering sublot and assembly features is discovered via gene expression programming to promote the performance of initial solutions; a Q-learning-based temperature control mechanism is designed to adaptively adjust the acceptance probability of inferior solutions and accordingly avoid local optima; an adaptive selection mechanism of neighborhood operators is designed to increase the chance of finding potential solutions; an adaptive adjustment mechanism of neighborhood size is put forward to balance computing resources and the coverage of neighborhood space. Experimental results show that both the discovered rule and the adaptive mechanisms are effective, and the developed algorithm is more adapt to fix the studied problem than other state-of-the-art algorithms.

A teaching-learning-based optimization with feedback for L-R fuzzy flexible assembly job shop scheduling problem with batch splitting

A teaching-learning-based optimization with feedback for L-R fuzzy flexible assembly job shop scheduling problem with batch splitting

An Improved Elephant Herding Optimization for Energy-Saving Assembly Job Shop Scheduling Problem with Transportation Times

The energy-saving scheduling problem (ESSP) has gained increasing attention of researchers in the manufacturing field. However, there is a lack of studies on ESSPs in the assembly job shop environment. In contrast with traditional scheduling problems, the assembly job shop scheduling problem (AJSP) adds the additional consideration of hierarchical precedence constraints between different jobs of each final product. This paper focuses on developing a methodology for an energy-saving assembly job shop scheduling problem with job transportation times. Firstly, a mathematical model is constructed with the objective of minimizing total energy consumption. Secondly, an improved elephant herding optimization (IEHO) is proposed by considering the problem’s characteristics. Finally, thirty-two different instances are designed to verify the performance of the proposed algorithm. Computational results and statistical data demonstrate that the IEHO has advantages over other algorithms in terms of the solving accuracy for the considered problem.

A Data-Driven Robust Scheduling Method Integrating Particle Swarm Optimization Algorithm with Kernel-Based Estimation

The assembly job shop scheduling problem (AJSSP) widely exists in the production process of many complex products. Robust scheduling methods aim to optimize the given criteria for improving the robustness of the schedule by organizing the assembly processes under uncertainty. In this work, the uncertainty of process setup time and processing time is considered, and a framework for the robust scheduling of AJSSP using data-driven methodologies is proposed. The framework consists of obtaining the distribution information of uncertain parameters based on historical data and using a particle swarm optimization (PSO) algorithm to optimize the production schedule. Firstly, the kernel density estimation method is used to estimate the probability density function of uncertain parameters. To control the robustness of the schedule, the concept of confidence level is introduced when determining the range of uncertain parameters. Secondly, an interval scheduling method constructed using interval theory and a customized discrete PSO algorithm are used to optimize the AJSSP with assembly constraints. Several computational experiments are introduced to illustrate the proposed method, and these were proven effective in improving the performance and robustness of the schedule.

A learning interactive genetic algorithm based on edge selection encoding for assembly job shop scheduling problem

This paper presents an effective learning interactive genetic algorithm based on edge selection encoding (LIGA-ESE) for solving the assembly job shop scheduling problem (AJSSP), with the aim of minimizing the maximum completion time (makespan). In the LIGA-ESE, a novel ESE based on virtual components for producing every feasible solution generated with acceptable probability is proposed to improve the convergence efficiency. Based on the proposed competition and learning interactive mechanisms, two genetic algorithm populations from obverse and reverse schedules, respectively, compete to improve the utilization of computation resources and the quality of populations. In addition, the influences of parameters are considered, and a learning parameter combination selection mechanism based on historical optimization performance is proposed for further improving the convergence efficiency of the LIGA-ESE. Finally, a numerical simulation is conducted based on widely used AJSSP instances. Comparisons between the LIGA-ESE and existing algorithms and other LIGA-ESE versions demonstrate its effectiveness and superiority in solving the AJSSP.

Adaptive scheduling for assembly job shop with uncertain assembly times based on dual Q-learning

To address the uncertainty of production environment in assembly job shop, in combination of the real-time feature of reinforcement learning, a dual Q-learning (D-Q) method is proposed to enhance the adaptability to environmental changes by self-learning for assembly job shop scheduling problem. On the basis of the objective function of minimising the total weighted earliness penalty and completion time cost, the top level Q-learning is focused on localised targets in order to find the dispatching policy which can minimise machine idleness and balance machine loads, and the bottom level Q-learning is focused on global targets in order to learn the optimal scheduling policy which can minimise the overall earliness of all jobs. Some theoretical results and simulation experiments indicate that the proposed algorithm achieves generally better results than the single Q-learning (S-Q) and other scheduling rules, under the arrival frequency of product with different conditions, and show good adaptive performance. Abbreviations: AFSSP, assembly flow shop scheduling problem; AJSSP, assembly job shop scheduling problem; RL, reinforcement learning; TASP, two-stage assembly scheduling problem

Hybrid algorithm based on improved extended shifting bottleneck procedure and GA for assembly job shop scheduling problem

With the makespan as the optimisation goal, we propose a hybrid solving method that combines improved extended shifting bottleneck procedure (i-ESB) and genetic algorithm (GA) for the assembly job shop scheduling problem (AJSSP). Hybrid genetic algorithm (HGA) uses a GA based on operation constraint chain coding to achieve global search and a local search based on an i-ESB. In the design of i-ESB, an extended disjunctive graph model (EDG) corresponding to AJSSP is presented. The calculation method of the operation head and tail length based on EDG is studied, as well as the searching method of key operations. The Schrage algorithm with disturbance is used to solve the single-machine scheduling subproblem. The selection criterion for bottleneck machines is increased. A greedy bottleneck machine re-optimisation process is designed. The effectiveness and superiority of the proposed algorithm are verified by testing and analysing the relevant examples in the literature.

A Hybrid Algorithm Based on Particle Swarm Optimization and Artificial Immune for an Assembly Job Shop Scheduling Problem

To produce the final product, parts need to be fabricated in the process stages and thereafter several parts are joined under the assembly operations based on the predefined bill of materials. But assembly relationship between the assembly parts and components has not been considered in general job shop scheduling problem model. The aim of this research is to find the schedule which minimizes completion time of Assembly Job Shop Scheduling Problem (AJSSP). Since the complexity of AJSSP is NP-hard, a hybrid particle swarm optimization (HPSO) algorithm integrated PSO with Artificial Immune is proposed and developed to solve AJSSP. The selection strategy based on antibody density makes the particles of HPSO maintain the diversity during the iterative process, thus overcoming the defect of premature convergence. Then HPSO algorithm is applied into a case study development from classical FT06. Finally, the effect of key parameters on the proposed algorithm is analyzed and discussed regarding how to select the parameters. The experiment result confirmed its practice and effectiveness.

A multi-objective decision-making framework using preference selection index for assembly job shop scheduling problem

Assembly job shop scheduling problem (AJSSP) is an important NP-hard scheduling problem very difficult to solve because of its complex precedence relationship between jobs and product structures. In the present work, a systematic multi-attribute decision-making methodology namely, preference selection index method is adopted for ranking priority dispatching rules for scheduling an assembly job shop. A simulation model of an assembly job shop with seven work stations and one assembly station is developed for the purpose of experimentation. Eight priority dispatching rules from literature are identified and incorporated in the simulation model. Performance measures considered for analysis include mean flow time, maximum flow time, mean tardiness, maximum tardiness and machine utilisation. Products with single level assembly structure, two level assembly structure and three level assembly structure are examined to demonstrate and to check the applicability of the proposed methodology. The best performing priority dispatching rules are determined in a multi-objective environment.

A multi-objective decision-making framework using preference selection index for assembly job shop scheduling problem

A multi-objective decision-making framework using preference selection index for assembly job shop scheduling problem

Development and comparison of multiple genetic algorithms and heuristics for assembly production planning

Assembly jobs with tree-structured precedence constraints in their bill-of-materials structure are a generalized version of traditional jobs involving only line-structured precedence constraints. The assembly job shop scheduling problem deals with assembly jobs, in contrast to job shop scheduling which deals with only traditional jobs. This research explores the ability of different genetic algorithms (GAs) to solve the assembly job shop scheduling problem. The objective is to minimize the makespan (maximum completion time) of a given set of assembly jobs. Random key GAs are proposed which differ using three factors: decoding, schedule justification and individual rearrangement. The three factors have two, seven and two levels, respectively, resulting in 28 different GAs. Specifically, we have conducted a full factorial design of GAs using forward/backward decoding, 0–6 local steps of justification, with/without individual rearrangement. The aim is to test the performance of GAs using different factor settings. As benchmarks, two heuristics have been proposed. Lingo, a software tool for linear and non-linear optimization problems is also used for solution by setting the time limit to 30 min. The experiments have revealed significant effects of the aforesaid three factors on the performance of the GAs.

A comparison of hybrid genetic algorithm and hybrid particle swarm optimization to minimize makespan for assembly job shop

Very often, studies of job shop scheduling problem (JSSP) ignore assembly relationship and lot splitting. If an assembly stage is appended to JSSP for the final product, the problem then becomes assembly job shop scheduling problem (AJSSP). To allow lot splitting, lot streaming (LS) technique is examined in which jobs may be split into a number of smaller sub-jobs for parallel processing on different stages such that the system performance may be improved. In this study, the system objective is defined as the makespan minimization. In order to investigate the impact of LS on the system objective under different real-life operating conditions, part sharing ratio (PSR) and system congestion index (SCI) are considered. PSR is used to differentiate product-specific components from general-purpose, common components, and SCI for creating different starting conditions of the shop floor. Both PSR and CSI are useful as part sharing (also known as component commonality) is a common practice for manufacturing with assembly operations and system loading is a significant factor in influencing the shop floor performance. Since the complexity of AJSSP is NP-hard, a hybrid genetic algorithm (HGA) and a hybrid particle swarm optimization (HPSO) are proposed and developed to solve AJSSP in consideration of LS technique. Computational results show that for all test problems under various system conditions, HGA can significantly outperform HPSO. Also, equal-sized lot splitting is found to be the most beneficial LS strategy especially for medium-to-large problem size.

Integrating order review/release and dispatching rules for assembly job shop scheduling using a simulation approach

This paper deals with an assembly job shop scheduling problem considering two phases of control: order review/release (ORR) and dispatching rules. Dispatching rules have been intensively used in earlier job shop research. Such rules determine the processing sequence of jobs waiting in the queues of corresponding machines. In recent years, ORR emerges as another option for job shop control and has received increasing attention. Such control determines when to release jobs to the shop floor. Different ORR mechanisms have been devised and are reported to bring several advantages such as reduced inventory cost of early finished orders, controlled and balanced shop load levels and shorter order flow time. Previous studies on ORR often assume a simplified job shop without assembly operations, while this research applies ORR to an assembly job shop. The aim of this research is to evaluate the ability of different combinations of ORR-dispatching rules in optimising due date and flow time related performance measures. Full factorial experiment has been designed for a simulated assembly job shop. Results show that both ORR and dispatching rules are highly relevant with respect to the due date and flow time related performance measures. Particularly, the incorporation of ORR control into the existing control of dispatching rules is highly important for better performance of assembly job shop control.

A resource-constrained assembly job shop scheduling problem with Lot Streaming technique

To ensure effective shop floor production, it is vital to consider the capital investment. Among most of the operational costs, resource must be one of the critical cost components. Since each operation consumes resources, the determination of resource level is surely a strategic decision. For the first time, the application of Lot Streaming (LS) technique is extended to a Resource-Constrained Assembly Job Shop Scheduling Problem (RC_AJSSP). In general, AJSSP first starts with Job Shop Scheduling Problem (JSSP) and then appends an assembly stage for final product assembly. The primary objective of the model is the minimization of total lateness cost of all final products. To enhance the model usefulness, two more experimental factors are introduced as common part ratio and workload index. Hence, an innovative approach with Genetic Algorithm (GA) is proposed. To examine its goodness, Particle Swarm Optimization (PSO) is the benchmarked method. Computational results suggest that GA can outperform PSO in terms of optimization power and computational effort for all test problems.