Flow Shop Research Articles

Controllable processing times with limited resources and energy consumption in flow shops: an assessment by simulation

ABSTRACT In production systems, the total energy available is a constraint due to energy costs or power consumption. The control of the processing time can affect the total energy consumed for the task performed. This paper proposes two control policies to change the processing time of stations that composes a flow line under resource consumption constraint in a production period. The first reduces the processing time of one station (centralized), while the second reduces the processing time of more stations (distributed). The introduction of an accumulator of the resources (such as a battery) can use any residual energy of a period in the following period. A multi-agent architecture has been developed to support the proposed models. This architecture decomposes the main problem into several sub-tasks, reducing the computational complexity and enabling the solution of larger and industrial problems. The simulation results highlight how the centralized approach works better when fewer resources are available, and the production line is unbalanced. On the other hand, the distributed model is more suitable for a balanced flow line. The introduction of an accumulator improves the performance of the centralized model compared to the distributed model.

Heuristics for flow shop rescheduling with mixed blocking constraints

Heuristics for flow shop rescheduling with mixed blocking constraints

Cost-based hybrid flow shop scheduling with uniform machine optimization using an improved tiki-taka algorithm

ABSTRACT Cost is the foremost factor in decision-making for profit-driven organizations. However, hybrid flow shop scheduling (HFSS) research rarely prioritizes cost as its optimization objective. Existing studies primarily focus on electricity costs linked to machine utilization. This paper introduces a comprehensive cost-based HFSS model, encompassing electricity, labor, maintenance, and penalty costs. Next, the Tiki-Taka Algorithm (TTA) is improved by increasing the exploration capability to optimize the problem. The cost-based HFSS model and TTA algorithm have been tested using benchmark and case study problems. The results indicated that the TTA consistently outperforms other algorithms. It delivers the best mean fitness and better solution distribution. In industrial contexts, the TTA able to reduces costs by 2.8% to 12.0% compared to other approaches. This holistic cost-based HFSS model empowers production planners to make more informed decisions. Furthermore, the improved TTA shows promise for broader applicability in various combinatorial optimization domains.

Efficient solutions to the m-machine robust flow shop under budgeted uncertainty

Efficient solutions to the m-machine robust flow shop under budgeted uncertainty

Deterministic constructive vN-NEH[formula omitted] algorithm to solve permutation flow shop scheduling problem with makespan criterion

Scheduling jobs in a permutation flow shop (PFS) environment is one of the most studied problems in scheduling theory and practice. In this paper, we propose a new efficient algorithm to solve the permutation flow shop scheduling problem (PFSP) with the makespan criterion. The proposed algorithm, referred to as vN-NEH+, extends the Nawaz–Enscore–Ham (NEH) heuristic by employing the variable-length list (vN-list) of candidate jobs. Extensive numerical experiments on the standard set of benchmarks show that the proposed vN-NEH+ algorithm is one of the most efficient NEH-based deterministic constructive algorithms in terms of trade-off between solution quality and computing time. Moreover, in contrary to existing scheduling methods, vN-NEH+ produces in a single run a set of good quality solutions that can serve as an initial population in population-based metaheuristics for solving PFSPs. Another advantage of vN-NEH+ is that it can work in parallel mode, which is difficult or even impossible with other NEH-based heuristics. In addition to vN-NEH+, we propose a new ART.NEH (Average Relative Time over NEH) indicator to assess the running time of PFSP algorithms. The main advantage of ART.NEH is its hardware/software and instance size independence, which allows an objective and reliable comparison of computational effort of PFSP algorithms. In addition, the idea behind ART.NEH can be easily adopted to reliably assess time complexity of algorithms for solving various other computational problems.

An adaptive artificial bee colony for hybrid flow shop scheduling with batch processing machines in casting process

Hybrid flow shop scheduling problem (HFSP) with real-life constraints has been extensively considered; however, HFSP with batch processing machines (BPM) at a middle stage is seldom investigated. In this study, HFSP with BPM at a middle stage in hot & cold casting process is considered and an adaptive artificial bee colony (AABC) is proposed to minimise makespan. To produce high quality solutions, an adaptive search process with employed bee phase and adaptive search step is implemented. Adaptive search step, which may be onlooker bee phase or cooperation or empty, is decided by evolution quality and an adaptive threshold. Cooperation is performed between the improved solutions of one employed bee swarm and the unimproved solutions of another swarm. Six search operators are constructed and search operator is adaptively adjusted. A new scout phase is also given. A lower bound is provided and proved. Extensive experiments are conducted. The computational results validate that new strategies such as cooperation are effective and efficient and AABC can obtain better results than methods from existing literature on the considered problem.

Utilization of Johnson's Algorithm for Enhancing Scheduling Efficiency and Identifying the Best Operation Sequence: An Illustrative Scenario

This study's primary objective is the enhancement of makespan optimization, thereby minimizing unproductive time for both machinery and tasks. The research employs a case study methodology, focusing on job scheduling within anElectronicsmanufacturing facility, with a particular emphasis on resource availability. It implements Johnson's algorithm and its expanded versions designed for both two-machine and three-machine scenarios within the context of flow shop scheduling. The principal aim is to identify optimal sequences for scheduling. Within this framework, the investigation computes idle time and makespan metrics for individual machines, utilizing task processing durations and in-out timestamps. The findings reveal anoptimal idle time of 6.21 minutes and a makespan of 142.06minutes for scenarios involving two machines. Furthermore, the research extends its analysis to scenarios with three machines, where two machines are combined in each group, resulting in an optimal idle time of 5.22minutes for combined machine A2, 14.98minutes for combined machine A3, and a makespan of 192minutes. This study provides valuable insights applicable to industries dealing with diverse machinery and components, ultimately contributing to improved scheduling and productivity.

A review and classification of scheduling objectives in unpaced flow shops for discrete manufacturing

A review and classification of scheduling objectives in unpaced flow shops for discrete manufacturing

Heuristic Approach For Weighted Two Stage Flow Shop Model In A String Of Disjoint Job Block Under No Idle Constraint

The current paper investigates a two-stage flow shop scheduling model with no idle restriction, in which jobs are scheduled to run in a string of two job blocks that are disjoint in nature, and the jobs processing time is correlated with probabilities. Owing to inherent usefulness as well as relevance in real-world situations, jobs' weight has additionally included. In order to eliminate machine idle time and cutting machine cost of rental, the reason for the conduct of the study is to provide a heuristic algorithm which, once put into practice, processes jobs in optimal way, guarantees in smallest conceivable make span. Multiple computational examples generated in MATLAB 2019a serve as testament to efficacy of the proposed strategy operates. The outcomes are contrasted with the current methods that Johnson and Palmer have demonstrated.

Mathematical model and knowledge-based iterated greedy algorithm for distributed assembly hybrid flow shop scheduling problem with dual-resource constraints

With the development of economic globalization, distributed hybrid flow shop scheduling problem (DHFSSP) has become prevalent in realistic manufacturing systems. Moreover, to accord with the actual production scenarios and satisfy the requirement of manufacturing market, it is imperative to comprehensively explore various complex manufacturing scenarios (e.g., production assembly) and production-constrained resources (e.g., worker resources) in DHFSSP. However, the integration mode of DHFSSP, assembly shop problem (ASP), and dual-resource constraints (DRC) has not been reported in existing literature. Thus, to fill out this research gap, this paper first attempts to investigate DAHFSSP-DRC with minimization the total tardiness (TTD). To solve this problem, a mixed-integer linear programming (MILP) model and a knowledge-based iterated greedy algorithm (KBIG) are presented. The novelties of KBIG are as follows: (1) An efficient decoding is developed to improve the solution’s quality; (2) A knowledge-based NEH (KB-NEH) initialization strategy is presented to generate an initial solution; (3) A knowledge-based destruction and construction is designed to improve the exploration capability; (4) A product-based local search is proposed to enhance the exploitation capability. Additionally, to validate the proposed model, we implement CPLEX to solve it on 24 small-sized instances. To verify the effectiveness of the proposed KBIG, extensive experiments are conducted to compare with other 7 comparison algorithms on 405 large-sized instances. Experimental results illustrate that KBIG is superior to its competitors.

Robust scheduling in a two-machine re-entrant flow shop to minimise the value-at-risk of the makespan: branch-and-bound and heuristic algorithms based on Markovian activity networks and phase-type distributions

Robust scheduling in a two-machine re-entrant flow shop to minimise the value-at-risk of the makespan: branch-and-bound and heuristic algorithms based on Markovian activity networks and phase-type distributions

Mathematical models for multi-stage hybrid assembly flow-shop scheduling with preventive maintenance and release times

Effective job scheduling is crucial in production to reduce costs, improve customer satisfaction, enhance efficiency, and boost competitiveness, leading to transformative impacts in production environments. This article presents a pioneering approach that addresses assembly and processing at multiple stages in the scheduling process. Specifically, we introduce the first formulation of mixed integer linear programs (MILP) for a Multi-stage Hybrid Assembly Flow-shop with identical parallel machines. The models incorporate considerations for job release times and service tasks to implement preventive maintenance and effectively captures the intricacies of a Multistage Assembly flow-shop. Existing literature in Assembly flow-shop scheduling primarily focuses on the two-stage assembly flow-shop scheduling problem (TSAFSP) and its extensions, such as the three-stage assembly flow-shop scheduling problem, the Distributed two-stage assembly flow-shop scheduling problem (DTSAFSP), the Distributed assembly permutation flow-shop Scheduling Problem (DAPFSP), and the multi-stage assembly flow shop (MSAF). Our work deals with a challenging NP-hard problem. Inspired by a real-life production site dedicated to manufacturing heavy machinery, we validate our proposed mathematical models by solving various instances of the problem using exact methods. The experimental results confirm the effectiveness and robustness of our approach in tackling multi-stage hybrid assembly flow shop scheduling challenges.

Effective Two-Phase Heuristic and Lower Bounds for Multi-Stage Flexible Flow Shop Scheduling Problem with Unloading Times

This paper addresses the flexible flow shop scheduling problem with unloading operations, which commonly occurs in modern manufacturing processes like sand casting. Although only a few related works have been proposed in the literature, the significance of this problem motivates the need for efficient algorithms and the exploration of new properties. One interesting property established is the symmetry of the problem, where scheduling from the first stage to the last or vice versa yields the same optimal solution. This property enhances solution quality. Considering the problem’s theoretical complexity as strongly NP-Hard, approximate solutions are preferable, especially for medium and large-scale instances. To address this, a new two-phase heuristic is proposed, consisting of a constructive phase and an improvement phase. This heuristic builds upon an existing efficient heuristic for the parallel machine-scheduling problem and extends it to incorporate unloading times efficiently. The selection of the two-phase heuristic is justified by its ability to generate high-quality schedules at each stage. Moreover, new efficient lower bounds based on estimating minimum idle time in each stage are presented, utilizing the polynomial parallel machine-scheduling problem with flow time minimization in the previous stage. These lower bounds contribute to assessing the performance of the two-phase heuristic over the relative gap performance measure. Extensive experiments are conducted on benchmark test problems, demonstrating the effectiveness of the proposed algorithms. The results indicate an average computation time of 9.92 s and a mean relative gap of only 2.80% for several jobs up to 200 and several stages up to 10.

Redefining hybrid flow shop group scheduling: Unveiling a novel hybrid modeling paradigm and assessing 48 MILP and CP models

A hybrid flow shop group scheduling problem (HFGSP) involves two distinct sub-problems, the arrangement of groups and the configuration of jobs within each group. Constructing its mathematical model based on the classification of these sub-problems can help better understand the problem's characteristics. However, the existing literature fails to establish MILP models of HFGSP based on the interrelation between each subproblem and the respective process constraints satisfied by each subproblem. To address this gap, our study first categorizes all the constraints in the HFGSP according to several factors: group arrangement, job arrangement within the group, process requirements between groups, process requirements between jobs from the same group, process requirements between adjacent stages, and the relationship between the decision variables of completion time and the objective constraint. Following this classification, we construct 48 available MILP models of HFGSP. Additionally, we also propose an efficient constraint programming (CP) model of HFGSP. Numerous experiments are conducted to verify the correctness and performance of all 48 MILP models across different test instances, analyze the complexities of all models, and excavate their intrinsic characteristics. Through our evaluation for the 48 models, we observe that models 24 and 48 exhibit superior performance. This highlights the effectiveness of the hybrid modeling approach, which synergistically combines sequence-based modeling for groups and position-based adjacent modeling for jobs within each group. The utilization of this hybrid modeling approach enables the construction of high-quality MILP models for addressing the HFGSP problem. Our intention is to bridge the gap between MILP modeling of HFGSP and problem-specific algorithms, thereby providing a comprehensive understanding of the problem and offering potential solutions.

Hybrid grey wolf optimizer for solving permutation flow shop scheduling problem

SummaryThe permutation flow shop scheduling problem, as a classical problem in the scheduling field, is an NP‐hard problem. However, most of the reported algorithms are difficult to achieve good accuracy and efficiency. To address this problem, a hybrid grey wolf optimizer (HGWO) is proposed in this paper. First, one cooperative initialization strategy is proposed to improve the quality of the initial solution based on the improved Nawaz‐Enscore‐Ham (NEH) method and the tent chaotic map method. Second, a levy flight strategy is introduced to balance the exploitation and exploration of the algorithm for the problem's characteristics. Third, the crossover and mutation strategy, and the critical block exchange based on critical path strategy are proposed to avoid falling into the local optimum. In addition, for the best individual, the variable neighborhood descent strategy is proposed to enhance the convergence accuracy of the algorithm. To verify the performance of the proposed algorithm, three different types of instances are selected for comparison experiments with other existing methods, and the experimental results show that the proposed HGWO outperforms other comparison algorithms in solving the problem.

Decomposition Is All You Need: Single-Objective to Multi-Objective Optimization towards Artificial General Intelligence

As a new abstract computational model in evolutionary transfer optimization (ETO), single-objective to multi-objective optimization (SMO) is conducted at the macroscopic level rather than the intermediate level for specific algorithms or the microscopic level for specific operators; this method aims to develop systems with a profound grasp of evolutionary dynamic and learning mechanism similar to human intelligence via a “decomposition” style (in the abstract of the well-known “Transformer” article “Attention is All You Need”, they use “attention” instead). To the best of our knowledge, it is the first work of SMO for discrete cases because we extend our conference paper and inherit its originality status. In this paper, by implementing the abstract SMO in specialized memetic algorithms, key knowledge from single-objective problems/tasks to the multi-objective core problem/task can be transferred or “gathered” for permutation flow shop scheduling problems, which will reduce the notorious complexity in combinatorial spaces for multi-objective settings in a straight method; this is because single-objective tasks are easier to complete than their multi-objective versions. Extensive experimental studies and theoretical results on benchmarks (1) emphasize our decomposition root in mathematical programming, such as Lagrangian relaxation and column generation; (2) provide two “where to go” strategies for both SMO and ETO; and (3) contribute to the mission of building safe and beneficial artificial general intelligence for manufacturing via evolutionary computation.

Multi-Objective Q-Learning-Based Brain Storm Optimization for Integrated Distributed Flow Shop and Distribution Scheduling Problems

In recent years, integrated production and distribution scheduling (IPDS) has become an important subject in supply chain management. However, IPDS considering distributed manufacturing environments is rarely researched. Moreover, reinforcement learning is seldom combined with metaheuristics to deal with IPDS problems. In this work, an integrated distributed flow shop and distribution scheduling problem is studied, and a mathematical model is provided. Owing to the problem’s NP-hard nature, a multi-objective Q-learning-based brain storm optimization is designed to minimize makespan and total weighted earliness and tardiness. In the presented approach, a double-string representation method is utilized, and a dynamic clustering method is developed in the clustering phase. In the generating phase, a global search strategy, a local search strategy, and a simulated annealing strategy are introduced. A Q-learning process is performed to dynamically choose the generation strategy. It consists of four actions defined as the combinations of these strategies, four states described by convergence and uniformity metrics, a reward function, and an improved ε-greedy method. In the selecting phase, a newly defined selection method is adopted. To assess the effectiveness of the proposed approach, a comparison pool consisting of four prevalent metaheuristics and a CPLEX optimizer is applied to conduct numerical experiments and statistical tests. The results suggest that the designed approach outperforms its competitors in acquiring promising solutions when handling the considered problem.

Optimizing production scheduling with the Rat Swarm search algorithm: A novel approach to the flow shop problem for enhanced decision making

The Rat Swarm Optimizer (RSO) algorithm is examined in this paper as a potential remedy for the flow shop issue in manufacturing systems. The flow shop problem involves allocating jobs to different machines or workstations in a certain order to reduce execution time or resource use. The objective function is used by the RSO method to optimize the results after mapping the rat locations to task-processing sequences. The RSO method successfully locates high-quality solutions to the flow shop problem when compared to other metaheuristic algorithms on diverse test situations. This research helps to improve the flexibility, lead times, quality, and efficiency of the production system. The paper introduces the RSO algorithm, creates a mapping strategy, redefines mathematical operators, suggests a method to enhance the quality of solutions, shows how successful the algorithm is through simulations and comparisons, and then uses statistical analysis to confirm the algorithm's performance.

A Reinforcement Learning Approach to Robust Scheduling of Permutation Flow Shop.

The permutation flow shop scheduling problem (PFSP) stands as a classic conundrum within the realm of combinatorial optimization, serving as a prevalent organizational structure in authentic production settings. Given that conventional scheduling approaches fall short of effectively addressing the intricate and ever-shifting production landscape of PFSP, this study proposes an end-to-end deep reinforcement learning methodology with the objective of minimizing the maximum completion time. To tackle PFSP, we initially model it as a Markov decision process, delineating pertinent states, actions, and reward functions. A notably innovative facet of our approach involves leveraging disjunctive graphs to represent PFSP state information. To glean the intrinsic topological data embedded within the disjunctive graph's underpinning, we architect a policy network based on a graph isomorphism network, subsequently trained through proximal policy optimization. Our devised methodology is compared with six baseline methods on randomly generated instances and the Taillard benchmark, respectively. The experimental results unequivocally underscore the superiority of our proposed approach in terms of makespan and computation time. Notably, the makespan can save up to 183.2 h in randomly generated instances and 188.4 h in the Taillard benchmark. The calculation time can be reduced by up to 18.70 s for randomly generated instances and up to 18.16 s for the Taillard benchmark.

Minimizing fuzzy makespan in a distributed assembly flow shop by using an efficient artificial bee colony algorithm

Assembly flow shop scheduling problem (AFSP) in a single factory has attracted widespread attention over the past decades; however, the distributed AFSP with DPm → 1 layout considering uncertainty is seldom investigated. In this study, a distributed assembly flow shop scheduling problem with fuzzy makespan minimization (FDAFSP) is considered, and an efficient artificial bee colony algorithm (EABC) is proposed. In EABC, an adaptive population division method based on evolutionary quality of subpopulation is presented; a competitive employed bee phase and a novel onlooker bee phase are constructed, in which diversified combinations of global search and multiple neighborhood search are executed; the historical optimization data set and a new scout bee phase are adopted. The proposed EABC is verified on 50 instances from the literature and compared with some state-of-the-art algorithms. Computational results demonstrate that EABC performs better than the comparative algorithms on over 74% instances.