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At present, the concept of green and sustainable development has been recognised by everyone. For industrial applications, the concept is both a matter of energy consumption and a matter of production methods. Based on the hybrid flow shop problem, a multi-energy supply system is constructed, and external renewable energy microgrid is introduced to further improve the low-carbon level. From the perspectives of energy supply and internal load, the output of wind power and photovoltaic, energy storage cost and energy consumption cost in the flow shop on a certain day are analysed under the demand–response electricity price. After considering the natural endowments and demand differences of different microgrids, construct a multi-energy complementarity model, determine the coordination transaction strategy among microgrids and obtain the solution of the subproblem and the equilibrium solution of the whole problem. Finally, an example is given to evaluate the effectiveness of the proposed strategy under time-of-use prices. The results show that the proposed strategy can effectively improve the utilisation rate of renewable energy in the flow shop while reducing the overall operating cost. [ABSTRACT FROM AUTHOR]

Planning and scheduling approaches in real manufacturing environments entail the need to cope with random attributes and variables to match the characteristics of real scheduling problems where uncertain events are frequent. Moreover, the capability of devising robust schedules, which are less sensitive to the disruptive effects of unexpected events, is a major request in real applications. In this paper, a branch-and-bound approach is proposed to solve the two-machine permutation flow shop scheduling problem with stochastic processing times. The objective is the minimisation of the value-at-risk of the makespan, to support decision-makers in the trade-off between the expected performance and the mitigation of the impact of extreme scenarios. A Markovian Activity Network (MAN) model is adopted to estimate the distribution of the makespan and assess the value-at-risk for both partial and complete schedules. Phase-type distributions are used to enable general distributions for processing times while maintaining the capability to exploit a Markovian approach. The effectiveness and performance of the proposed approach are demonstrated through a set of computational experiments. [ABSTRACT FROM AUTHOR]

This study addresses a multi-stage flow shop scheduling problem in which a job is reworked when its queue time between two arbitrary stages exceeds an upper limit. The problem is to determine the start times of jobs and rework setups/operations if incurred for the objective of minimising makespan. As an extension of the previous studies, multiple overlapped queue time limits are considered, i.e. some in-between stages of queue time limits for a job are overlapped. A mixed integer programming model is developed and its performance is reported for small-sized test instances. Then, due to the limited applications of optimal solution approaches, a variable neighbourhood search (VNS) algorithm is proposed that generates an initial solution and improves it using a shaking and a local search improvement methods. In addition, it is extended to the general variable neighbourhood search (GVNS) algorithms with variable neighbourhood descent (VND) methods. Computational results show that the GVNS algorithms outperform the VNS algorithm significantly and also give near optimal solutions for small-sized test instances within a reasonable amount of computation times. [ABSTRACT FROM AUTHOR]

Due to the production process or environment, most products need to go through multiple production workshops, from raw materials to finished products. For example, a large structural part must go through a blanking workshop and a machining workshop. However, the research on the serial multi-shop cooperative scheduling problem is insufficient. Different from the single shop scheduling problem, the multi-shop scheduling problem can be regarded as a scheduling problem composed of multiple sub-problems. Therefore, optimisation processes between subproblems may be the key to solving this kind of problem. This paper focuses on the optimisation framework for the serial multi-shop cooperative scheduling problem. A specific serial dual-shop collaborative scheduling problem is abstracted from the production, whose first and second shop is the hybrid flow shop and the job shop, respectively. A disjunctive graph model of this specific problem is constructed. After that, four different optimisation frameworks are proposed, and testing instances are designed to compare these frameworks. Under different optimisation frameworks, the same tabu search algorithm with an efficient neighbourhood structure is used to optimize this problem. Finally, the optimisation results of different frameworks are compared and the results of each optimisation framework are analyzed. [ABSTRACT FROM AUTHOR]

A reinforcement learning-driven brain storm optimisation idea (RLBSO) is proposed in this paper to solve multi-objective energy-efficient distributed assembly no-wait flow shop scheduling problem. The objectives of the problem include minimising the maximum assembly completion time ( C max ), minimising the total energy consumption (TEC) and achieving resource allocation balanced. Four operations, which are critical factory insert, critical factory swap, critical factory insert to other factories, critical factory swap with other factories, are designed to optimise the objective of maximum assembly completion time. Q-learning mechanism is utilised to guide the selection of operations to avoid blind search in the iteration process. The learning mechanism based on clustering mechanism in brain storm optimisation algorithm is utilised to assign products to factories in the objective space according to the processing time of products to balance the resources allocation. The speed of operations on non-critical path is slowed down to reduce TEC regarded with the characteristics of no-wait flow shop scheduling problem. The experimental results under 810 large-scale instances by RLBSO show that the RLBSO outperforms the comparison algorithm for addressing the problem. [ABSTRACT FROM AUTHOR]

Non-permutation flow shop scheduling (NPFS) is an extension of the traditional permutation flow shop scheduling, with a broader solution space. The effectiveness of reinforcement learning in solving flow shop scheduling problems has been demonstrated through its powerful combinatorial optimization capabilities. However, the design and training of the end-to-end policy network is complex, leading to long online training time and limited adaptability of offline training. To overcome these problems, we introduced a NPFS dynamic decision-making process and then proposed a novel NPFS method that combines the Q-learning algorithm with the priority dispatching rule (PDR) set. The NPFS dynamic decision-making process involves decomposing the entire process into multiple sub-job queues for scheduling. The PDR demonstrates better scheduling performance when applied to smaller job queues. By utilizing the Q-learning algorithm, PDRs with superior performance are assigned to sub-scheduling queues based on the generation process of sub-job sequences, resulting in an optimized NPFS strategy. The limited number of PDRs in the PDR set and the small number of sub-job queues in the NPFS process contribute to the efficiency of Q-learning in solving NPFS problem. Finally, we demonstrate the superiority of the proposed NPFS method by a series of numerical experiments using the machine-based assignment PDR method and NSGA-II algorithms as performance benchmarks. [ABSTRACT FROM AUTHOR]

Nowadays, the focus of flow shops is the adoption of customized demand in the context of service-oriented manufacturing. Since production tasks are often characterized by multi-variety, low volume, and a short lead time, it becomes an indispensable factor to include supporting logistics in practical scheduling decisions to reflect the frequent transport of jobs between resources. Motivated by the above background, a hybrid method based on dual back propagation (BP) neural networks is proposed to meet the real-time scheduling requirements with the aim of integrating production and transport activities. First, according to different resource attributes, the hierarchical structure of a flow shop is divided into three layers, respectively: the operation task layer, the job logistics layer, and the production resource layer. Based on the process logic relationships between intra-layer and inter-layer elements, an operation task–logistics–resource supernetwork model is established. Secondly, a dual BP neural network scheduling algorithm is designed for determining an operations sequence involving the transport time. The neural network 1 is used for the initial classification of operation tasks' priority; and the neural network 2 is used for the sorting of conflicting tasks in the same priority, which can effectively reduce the amount of computational time and dramatically accelerate the solution speed. Finally, the effectiveness of the proposed method is verified by comparing the completion time and computational time for different examples. The numerical simulation results show that with the increase in problem scale, the solution ability of the traditional method gradually deteriorates, while the dual BP neural network has a stable performance and fast computational time. [ABSTRACT FROM AUTHOR]

The flow shop scheduling problem is important for the manufacturing industry. Effective flow shop scheduling can bring great benefits to the industry. However, there are few types of research on Distributed Hybrid Flow Shop Problems (DHFSP) by learning assisted meta-heuristics. This work addresses a DHFSP with minimizing the maximum completion time (Makespan). First, a mathematical model is developed for the concerned DHFSP. Second, four Q-learning-assisted meta-heuristics, e.g. genetic algorithm (GA), artificial bee colony algorithm (ABC), particle swarm optimization (PSO), and differential evolution (DE), are proposed. According to the nature of DHFSP, six local search operations are designed for finding high-quality solutions in local space. Instead of random selection, Q-learning assists meta-heuristics in choosing the appropriate local search operations during iterations. Finally, based on 60 cases, comprehensive numerical experiments are conducted to assess the effectiveness of the proposed algorithms. The experimental results and discussions prove that using Q-learning to select appropriate local search operations is more effective than the random strategy. To verify the competitiveness of the Q-learning assistedmeta-heuristics, they are compared with the improved iterated greedy algorithm (IIG), which is also for solving DHFSP. The Friedman test is executed on the results by five algorithms. It is concluded that the performance of four Q-learning-assisted meta-heuristics are better than IIG, and the Q-learning-assisted PSO shows the best competitiveness. [ABSTRACT FROM AUTHOR]

Production plants have always been confronted with the problem of scheduling, as this has a direct impact on production time and therefore on production costs. This is especially true in today's world, where it is necessary to produce a quality product at a low price and in a short time, while at the same time responding flexibly to customer demands. Due to the complexity and for economic reasons, testing different variants in a real production environment is insufficient and ineffective. For this reason, this paper proposes a new method that combines discrete event simulation and factorial design experiment to find the optimal schedule in hybrid flow shop. It was tested with the goal of achieving the minimum makespan. The results show that this method makes it possible to find improved solution very quickly. Compared to the original production schedule, the makespan could be reduced by 3 hours and 31 minutes which is reduction of 16.3%. The proposed methodology can be used in many discrete and process production plants. [ABSTRACT FROM AUTHOR]

Digitalization plays a crucial role in improving the performance of chemical companies. In this context, different modeling, simulation, and optimization techniques such as MILP, discrete-event simulation (DES), and data-driven (DD) models are being used. Due to their heterogeneity, these techniques must be executed individually, and holistic optimization is manual and time-consuming. We propose Benders decomposition to combine these techniques into one rigorous optimization procedure. The main idea is that heterogeneous models can simultaneously be optimized as Benders subproblems. We illustrate this concept with the distributed permutation flow shop scheduling problem (DPFSP) and assume that a MILP, DES, and DD model exist for three flow shops. Our approach can compute bounds and report gap information on the optimal makespan for five medium-sized literature instances. The approach is promising because it enables the optimization of heterogeneous models and makes it possible to build optimization capabilities on an existing model and tool landscape in chemical companies. [ABSTRACT FROM AUTHOR]

We present an improved analysis of the running time of a dynamic program for the routing flow shop problem with two machines on an asymmetric network. Our analysis is based on structural properties of optimal schedules and significantly improves the bound on the running time of the algorithm obtained in the conference version of our paper (Chernykh, Kononov, and Sevastyanov, in: Kononov, A. et al. (eds) Mathematical optimization theory and operations research. MOTOR 2020. Lecture notes in computer science, Springer, Switzerland, 2020). To the best of our knowledge, our polynomial-time algorithm (under the assumption that the number of network nodes is bounded by any constant) is the first positive result on the complexity of the routing flow shop problem with an arbitrary structure of the transportation network, even in the case of a symmetric network. This result contrasts with the complexity of the two-machine routing open shop problem, which is NP-hard even on the two-node network. [ABSTRACT FROM AUTHOR]

This study aims to address a variant of the hybrid flow shop problem by simultaneously integrating lag times, unloading times, and transportation times, with the goal of minimizing the maximum completion time, or makespan. With applications in image processing, manufacturing, and industrial environments, this problem presents significant theoretical challenges, being classified as NP-hard. Notably, the problem demonstrates a notable symmetry property, resulting in a symmetric problem formulation where both the scheduling problem and its symmetric counterpart share the same optimal solution. To improve solution quality, all proposed procedures are extended to the symmetric problem. This research pioneers the consideration of the hybrid flow shop scheduling problem with simultaneous attention to lag, unloading, and transportation times, building upon a comprehensive review of existing literature. A two-phase heuristic is introduced as a solution to this complex problem, involving iterative solving of parallel machine scheduling problems. This approach decomposes the problem into manageable sub-problems, facilitating focused and efficient resolution. The efficient solving of sub-problems using the developed heuristic yields satisfactory near-optimal solutions. Additionally, two new lower bounds are proposed, derived from estimating minimum idle time within each stage via solving a polynomial parallel machine problem aimed at minimizing total flow time. These lower bounds serve to evaluate the performance of the developed two-phase heuristic, over measuring the relative gap. Extensive experimental studies on benchmark test problems of varying sizes demonstrate the effectiveness of the proposed approaches. All test problems are efficiently solved within reasonable timeframes, indicating practicality and efficiency. The proposed methods exhibit an average computational time of 8.93 seconds and an average gap of 2.75%. These computational results underscore the efficacy and potential applicability of the proposed approaches in real-world scenarios, providing valuable insights and paving the way for further research and practical implementations in hybrid flow shop scheduling. [ABSTRACT FROM AUTHOR]

Prefabricated cabin modular units (PMCUs) are a widespread type of intermediate products used during ship or offshore platform construction. This paper focuses on the scheduling problem of PMCU assembly flow shops, which is summarized as a multi-objective, fuzzy-blocking hybrid flow-shop-scheduling problem based on learning and fatigue effects (FB-HFSP-LF) to minimize the maximum fuzzy makespan and maximize the average fuzzy due-date agreement index. This paper proposes a multi-objective non-dominated sorting gravitational search algorithm (MONSGSA) to solve it. In the proposed MONSGSA, the ranked-order value is used to convert continuous solutions to discrete solutions. Multi-dimensional Latin hypercube sampling is used to enhance initial population diversity. Setting up an external archive to maintain non-dominated solutions while introducing an adaptive inertia factor and a trap avoidance operator to guide individual positional updates. The results of multiple sets of experiments show that Pareto solutions of MONSGSA have better distribution and convergence compared to other competitors. Finally, the instance of PMCU manufacturer is used for validation, and the results show that MONSGSA has better applicability to practical problems. [ABSTRACT FROM AUTHOR]

Improving efficiency in multi-stage flexible flowshop operations is essential for modern industrial systems. Optimizing total completion time while simultaneously considering the unloading and transportation times is vital for enhanced productivity and cost-effectiveness. This study delves into the intricate realm of flexible flow shop scheduling, particularly focusing on scenarios prevalent in modern manufacturing processes such as sand casting. Despite limited exploration in prior literature for particular cases, the significance of this problem underscores the pressing need for efficient algorithms and the exploration of new problem properties. Notably, we unveil the symmetry inherent in the problem, where scheduling from the initial stage to the final one, or vice versa, yields identical optimal solutions, thereby augmenting solution quality. Given the strongly NP-Hard nature of the problem, approximate solutions are preferred, especially for medium to large-scale instances. To address this challenge, we propose a novel two-phase heuristic approach, encompassing both a constructive phase and an improvement phase. Leveraging an existing efficient heuristic tailored for parallel machine scheduling, our method extends to efficiently incorporate considerations for unloading and transportation times. The efficacy of the two-phase heuristic lies in its ability to consistently generate high-quality schedules at each stage. Furthermore, we introduce efficient lower bounds derived from estimating the minimum idle time within each stage, drawing from insights in polynomial parallel machine scheduling with a focus on flow time minimization in preceding stages. These lower bounds serve as critical benchmarks for evaluating the performance of the two-phase heuristic against the relative gap performance measure. Extensive experimentation on benchmark test problems underscores the effectiveness of our proposed algorithms, with results demonstrating an average computation time of 9.48 seconds and a mean relative gap of only 2.42% across varying job and stage quantities up to 200 jobs and 10 stages. [ABSTRACT FROM AUTHOR]

This paper addresses the class of permutation flow shop scheduling where jobs, after their completion, must be grouped in batches. This is a common scheme in industrial environments, where products undergo multiple process steps in different shops and, when completed, must be transported to customers or the next production step. A new optimisation criterion is used, the inter-exit time, i.e., the difference between the completion times of two jobs. An upper bound is proposed and demonstrated for a general permutation flow shop with m machines. [ABSTRACT FROM AUTHOR]

This paper addresses a two-machine re-entrant flow shop scheduling problem with stochastic processing times where each job is expected to require a rework phase, flowing twice within the whole system. Due to the stochastic characteristics of the addressed problem, the proposed approach aims to devise robust schedules, i.e., schedules that are less sensitive to the occurrence of uncertain events, specifically, to the variability of the processing times. Two classes of approaches are proposed: the first is a branch-and-bound algorithm capable of solving the problem optimally, although with limitations regarding the size of the scheduling instances; the second is heuristic algorithms that can be applied to medium/large instances. For both approaches, the goal is to minimise the value-at-risk associated with the makespan, to assist decision-makers in balancing expected performance and mitigating the impact of extreme scenarios. A Markovian Activity Network (MAN) model is exploited to estimate the distribution of the makespan and evaluate its value-at-risk. Phase-type distributions are used to cope with general distributions for the processing times while exploiting a Markovian approach. A set of computational experiments is conducted to demonstrate the effectiveness and performance of the proposed approaches. [ABSTRACT FROM AUTHOR]

This paper proposes a per-machine linear dispatching rule learning approach to improve the scheduling of re-entrant flow shop such as semiconductor fab. Finding an optimal schedule of a complex manufacturing system is intractable; hence, a dispatching rule as a heuristic approach is widely used in actual practice. Also, to develop a good dispatching rule, an automated methodology for developing heuristics, also known as a hyper-heuristic, has been studied extensively. However, most of the literature has focused on finding a single-sophisticated dispatching rule, in which every machine uses the same rule. Such an approach often shows suboptimal performance when the optimal dispatching rule is different on each machine. To solve this problem, we introduce a simple and effective per-machine dispatching rule learning approach, in which each machine has one linear dispatching rule that is optimised by the Gradient-based Evolutionary Strategy (GES). This method is sample-efficient and can be applied to non-differentiable objective functions such as average Cycle Time. The proposed approach was mainly compared to two popular methods based on Genetic Programming (GP) and the Genetic Algorithm (GA) on a four-station and eight-machine re-entrant flow shop. Numerical results show that the proposed approach outperforms widely used methods. [ABSTRACT FROM AUTHOR]

Two hybrid flow shop scheduling lines must be coordinated to assemble batches of terminated products at their last stage. Each product is thus composed of two jobs, each produced in one of the lines. The set of jobs is to be processed in a series of stages to minimize the makespan of the scheduling, but jobs forming a product must arrive at the assembly line simultaneously. We propose a mixed integer linear programming model. Then, based on the model, we propose a pull-matheuristic algorithm. Finally, we present two metaheuristics, a greedy randomized adaptive search procedure and a biased random key genetic algorithm, and compare all the methodologies with real-based instances of a production scheduling problem in the automobile manufacturing industry. The greedy algorithm yields high-quality solutions, while the genetic one offers the best computational times. [ABSTRACT FROM AUTHOR]

We study two scheduling problems in a proportionate flow shop environment, where job processing times are machine independent. In contrast to classical proportionate flow shop models, we assume (in both problems) that processing times are step-deteriorating. Accordingly, each job J j has a normal processing time, a j , if it starts to be processed in the shop no later than its deteriorating date, δ j . Otherwise, the job's processing time increases by b j (the job's deterioration penalty). Our aim is to find a job schedule that minimizes either the makespan or the total load. These two problems are known to be N P -hard for the special case of a single machine, even when all jobs have the same deteriorating date. In this paper, we derive several positive results in relation to the two problems. We first show that the two problems can be represented in a unified way. We then prove that the unified problem is only ordinary N P -hard by providing a pseudo-polynomial time algorithm for its solution. We also show that the pseudo-polynomial time algorithm can be converted into a fully polynomial time approximation scheme (FPTAS). Finally, we analyze the parameterized complexity of the problem with respect to the number of different deteriorating dates in the instance, v δ . We show that although the problem is N P -hard when v δ = 1 , it is fixed parameterized tractable (FPT) for the combined parameters (i) (ν δ , ν a) and (ii) (ν δ , ν b) , where ν a is the number of different normal processing times in the instance, and ν b is the number of different deterioration penalties in the instance. [ABSTRACT FROM AUTHOR]

In order to make the traditional flow shop scheduling model more flexible and intelligent to adapt to different production environments, scheduling strategy of distributed flow shop based on deep learning was proposed. By learning and analyzing a large amount of data in the distributed shop floor system, the strategy gradient method was used to obtain the approximate optimal solution after several iterations of optimization, and a more intelligent and adaptable production planning and scheduling strategy was obtained. It was verified by experiments and simulation. The results show that this method can improve production efficiency and resource utilization, and has potential in cost control. The research provides an advanced scheduling strategy for distributed production environment of manufactur industry, and provides more accurate and intelligent decision reference for shop floor managers. [ABSTRACT FROM AUTHOR]

Purpose: This paper investigates a batch scheduling problem where pre-processing is required for parts before processing, considering time-changing effects from part deterioration and operator learningforgetting. Design/methodology/approach: A mathematical model was developed with the decision variables of the number of batches, the number of pre-processings, batch sizes, and the schedule of processes and pre-processings to minimize total actual flow time. Different numbers of batches were gradually tried and increased until the objective function stopped improving. The minimum number of pre-processings that resulted in a feasible solution was examined at each number of batches. Findings: Our experiment showed that: (1) A faster operator learning led to a lower optimal number of batches and a lower total actual flow time, (2) A faster part deterioration brought a higher number of batches and a higher total actual flow time, (3) The model minimized the number of pre-processings by only scheduling pre-processings before the operations at machine 1, and (4) The model divided the parts into small batches to prevent increased processing time due to part deterioration. Research limitations: The research did not consider multi-due date and multi-item system which require pre-processings with different times and capacities. Practical implications: Production managers should assign fast learning operators to shorter batches and faster deteriorating parts. Originality/value: This research was the first to consider pre-processing in batch scheduling. [ABSTRACT FROM AUTHOR]

Scheduling is one of the many skills required for advancement in today's modern industry. The flow-shop scheduling problem is a well-known combinatorial optimization challenge. Scheduling issues for flow shops are NP-hard and challenging. The present research investigates a two-stage flow shop scheduling problem with decoupled processing and setup times, where a correlation exists between probabilities, job processing times, and setup times. This study proposes a novel heuristic algorithm that optimally sequences jobs to minimize the makespan and eliminates machine idle time, thereby reducing machine rental costs. The proposed algorithm's efficacy is demonstrated through several computational examples implemented in MATLAB 2021a. The results are compared with the existing approaches such as those by Johnson, Palmer, NEH, and Nailwal to highlight the proposed algorithm's superior performance. [ABSTRACT FROM AUTHOR]

Distributed flexible flowshop scheduling is getting more important in the large-scale panel furniture industry. It is vital for a higher manufacturing efficiency and economic profit. The distributed scheduling problem with lot-streaming in a flexible flow shop environment is investigated in this work. Furthermore, the actual constraints of packaging collaborative and machine setup times are considered in the proposed approach. The average order waiting time for packaging and average order delay rate is used as objectives. Non-dominated sorting method is used to handle this bi-objective optimization problem. An improved encoding method was proposed to address the large-scale orders that need to be divided into sub-lots based on genetic algorithm. The proposed approach is firstly validated by benchmark with other multi-objectives evolutionary algorithms. The results found that the proposed approach had a good convergence and diversity. Besides, the influence of the proportion of large-scale orders priority level and sub-lot size was investigated in a panel furniture manufacturing scenario. The results can be concluded that the enterprise could obtain shorter order average waiting time and delay rate when the sub-lot sizes were set as two and the order priority level was allocated in the proportion of 1:2:3:4:5. [ABSTRACT FROM AUTHOR]

This paper presents a novel hybrid approach, fusing genetic algorithms (GA) and penguin search optimization (PSeOA), to address the flow shop scheduling problem (FSSP). GA utilizes selection, crossover, and mutation inspired by natural selection, while PSeOA emulates penguin foraging behavior for efficient exploration. The approach integrates GA's genetic diversity and solution space exploration with PSeOA's rapid convergence, further improved with FSSP-specific modifications. Extensive experiments validate its efficacy, outperforming pure GA, PSeOA, and other metaheuristics. [ABSTRACT FROM AUTHOR]

Bottleneck stage and reentrance often exist in real-life manufacturing processes; however, the previous research rarely addresses these two processing conditions in a scheduling problem. In this study, a reentrant hybrid flow shop scheduling problem(RHFSP) with a bottleneck stage is considered, and an elite-class teaching-learning-based optimization (ETLBO) algorithm is proposed to minimize maximum completion time. To produce high-quality solutions, teachers are divided into formal ones and substitute ones, and multiple classes are formed. The teacher phase is composed of teacher competition and teacher teaching. The learner phase is replaced with a reinforcement search of the elite class. Adaptive adjustment on teachers and classes is established based on class quality, which is determined by the number of elite solutions in class. Numerous experimental results demonstrate the effectiveness of new strategies, and ETLBO has a significant advantage in solving the considered RHFSP. [ABSTRACT FROM AUTHOR]

Scheduling jobs in a no-wait flow shop with the objective of minimising total earliness and tardiness is the problem addressed in this paper. Idle time may be needed on the first machine due to the no-wait restriction. A model is developed that shows additional idle can be inserted on the first machine to help reduce earliness. Several dispatching heuristics previously used in other environments were modified and tested. A two-phased procedure was also developed, estimating additional idle in the first phase, and applying dispatching heuristics in the second phase. Several versions of an insertion improvement procedure were also developed. The procedures are tested on instances of various sizes and due date tightness and range. The results show the two-phase heuristics are more effective than the simple rules, and the insertion search improvement procedure can provide considerable improvements. [ABSTRACT FROM AUTHOR]

The energy consumption loss is high particularly in manufacturing processes involving heating furnaces. Moreover, the mandatory constraints in continuous heating stage bring difficult challenges to production scheduling. To improve the production efficiency and reduce the energy consumption in a hybrid flow shop with continuous and discrete processing stages, this study developed an adaptive selection multi-objective optimization algorithm with preference (ASMOAP). The mandatory constraints of continuous processing stage are transformed into one of the optimization objectives, which is defined as maximum excess value of adjustment time in this paper. A multi-objective optimization scheduling model with the makespan, energy consumption, and maximum excess of adjustment time is established. The optimization preference is designed in the proposed multi-objective optimization algorithm. The maximum excess of adjustment time is set as the multi-objective optimization preference. Three adaptive selection strategies are designed for the algorithm based on the proportions of outstanding and preference individuals to eliminate constraint conflicts. Presented results prove that the proposed algorithm could effectively solve hybrid flow shop scheduling problem considering discrete and continuous processing stages with limited time. It can be applied to obtain a better feasible solution while improving the efficiency and reducing the energy consumed in practical production processes. [ABSTRACT FROM AUTHOR]

Scheduling decisions in mixed-model assembly lines are frequently multi-objective. No work till date has jointly examined the impact of the production sequence in unpaced manual mixed-model assembly lines operated as permutation flow shops concerning a set of objectives broad enough to capture the interests of its customers and suppliers as well as the manufacturer's interests related to productivity, production flow and human aspects. This work sets up a simulation study based on a real unpaced mixed-model assembly line with seven products to analyse the impact of five different sequence types on objectives from all these interest fields while modelling human learning and deterioration effects explicitly. The results show that considerable trade-offs exist as different sequence types are preferred for the various scheduling objectives. For makespan and mean flow time as widely used productivity– and flow-related objectives, cases of conflicts and complementarity can be found depending on the actual operational conditions in terms of product and volume mix. A strong dilemma emerges between supplier– and human-related objectives favouring different sequence types. Concerning due date based customer-related objectives, the preferred sequence type varies with the operational conditions. The observed trade-offs confirm the multi-objective nature of the scheduling decision. [ABSTRACT FROM AUTHOR]

One of the common issues in production scheduling is the flow shop sequencing issue. A specific type of manufacturing process follows a predetermined linear structure in a flow shop. To solve a flow shop problem in a static workshop, the goal of this study is to determine the shortest possible total processing time (make-span) for a sequence of 'n' tasks on 'm' machines. The suggested method is based on how each work slopes as it moves from the first to the last machine. This method is contrasted with four popular heuristics (Palmer, CDS, Dannenbring, NEH). The findings of the study for 'n' x 'm' flow shop sequencing problems show that the proposed method is effective and shows a promising amount of progress when compared to the other four heuristic strategies. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper addresses the challenge of optimizing energy efficiency in production shop scheduling problem, focusing specifically on the constraint of sequence-dependent setup times (FSSP SDST). This study is conducted in the context of promoting green industrial practices. The main objective is to minimize total energy consumption (TEC) in the manufacturing process. We introduce a mathematical model of this problem. To solve this problem, we use the Artificial Bee Colony algorithm (ABC). In addition, the Migrating Birds Optimization (MBO) algorithm will be presented. The effectiveness of the proposed algorithms will be subjected to rigorous evaluation through detailed tests on different instances. This methodical approach will enable us to carry out an in-depth and detailed comparative analysis, highlighting the relative strengths and weaknesses of the algorithms presented in this study. [ABSTRACT FROM AUTHOR]

One of the most widely studied problems in flow shop scheduling is not allowing jobs to wait to be processed at the next stage. This constraint causes the job to be processed immediately at the next stage without waiting, so this problem is popularly called the No-Wait Flow Shop. This article aims to provide a comprehensive review of the No-Wait Flow Shop Scheduling (NWFS) problem based on a survey of published articles from 1999 to 2023. The article review is based on a systematic literature review, and bibliometric analysis is also presented based on the network processed using VOSviewer. One hundred twenty articles were collected from the Scopus database, which was reviewed based on NWFS variants, objective functions, and optimization procedures. The no-wait permutation flow shop scheduling (NWPFS) problem is a variant that researchers have widely investigated. Meta-heuristic procedures are widely applied to solve NWFS problems. In addition, the objective function of minimizing makespan is an objective function that researchers often apply. NWFS research gaps and future research trends are also presented in this paper. [ABSTRACT FROM AUTHOR]

In this paper, a multi-objective permutation flow shop scheduling problem with sequence independent setup time is studied. The bi-objective function that we consider is a linear combination of the makespan and total flow time with a weighted factor for each criterion. We propose a set of exact and approximate methods to minimize the makespan and total flow time in our flow shop optimization problem case. Hence, our main goal is to find the sequence of jobs that minimizes the two criteria of makespan and total flow time. The purpose is to solve this problem, with a mixed integer linear programming model (MILP) and a collection of efficient metaheuristics for different sizes of instances. Moreover, three metaheuristics are used: the Genetic Algorithm (GA), the Iterative Local Search (ILS) algorithm and the Iterated Greedy (IG) algorithm. The three last algorithms GA, ILS and IG are suggested in two ways for exploring the neighborhood. In order to test the efficacy of our resolution approach, different series of instances containing n jobs and m machines are generated randomly ranging from small to relatively large instances. The examination of the suggested simulations allowed us to remark that, for large and medium-scale instances, IG based on the exploration of the neighborhood records the best performances in terms of comparison with the other metaheuristics. [ABSTRACT FROM AUTHOR]

In the context of growing global energy demand, the industrial sector has become one of the significant contributors to the world's energy consumption. To face this challenge, scheduling has been identified as one of the potential methods to reduce energy consumption in industrial operations. This article introduces the mountain gazelle optimizer (MGO) algorithm as a solution to solve the no-wait flow shop scheduling problem with a focus on the main objective of minimizing energy consumption. The research involves comparing the performance of the MGO algorithm with popular algorithms such as grey wolf optimizer (GWO), particle swarm optimization (PSO), and genetic algorithm (GA). In addition, this research also compares the proposed MGO algorithm with the latest advanced algorithms, such as coati optimization algorithm (COA) and fire hawk optimizer (FHO). In this work, the six algorithms were tested on three different scheduling cases by repeating the process 30 times, using a population of 200 and 200 iterations to minimise energy consumption. The performance comparison between these algorithms was analyzed using the One-Way ANOVA statistical test. Based on the results, MGO outperforms GWO, PSO, GA, COA, and FHO algorithms in solving scheduling problems, with the primary function of minimizing energy consumption in Cases 1, 2, and 3. In addition, based on the convergence curve, the MGO algorithm has a better convergence curve compared to GWO, PSO, GA, COA, and FHO; it shows that the intestinal algorithm can reach the optimal solution faster and more stable during iterations than the GWO, PSO, GA, COA, and FHO algorithms. This finding confirms that the MGO algorithm has the potential to be an effective alternative in the scheduling optimization process, significantly reducing energy consumption in the industrial sector. [ABSTRACT FROM AUTHOR]

Energy saving has always been a concern in production scheduling, especially in distributed hybrid flow shop scheduling problems. This study proposes a shuffled frog leaping algorithm with Q-learning (QSFLA) to solve distributed hybrid flow shop scheduling problems with energy-saving(DEHFSP) for minimizing the maximum completion time and total energy consumption simultaneously. The mathematical model is provided, and the lower bounds of two optimization objectives are given and proved. A Q-learning process is embedded in the memeplex search of QSFLA. The state of the population is calculated based on the lower bound. Sixteen search strategy combinations are designed according to the four kinds of global search and four kinds of neighborhood structure. One combination is selected to be used in the memeplex search according to the population state. An energy-saving operator is presented to reduce total energy consumption without increasing the processing time. One hundred forty instances with different scales are tested, and the computational results show that QSFLA is a very competitive algorithm for solving DEHFSP. [ABSTRACT FROM AUTHOR]

Summary: The 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. [ABSTRACT FROM AUTHOR]

For solving the distributed assembly flow shop scheduling problem with fuzzy processing time (FDAPFSP), a regional biogeography-based optimization algorithm (RBBO) is proposed to minimize the maximum fuzzy completion time. The mathematical model is provided. In RBBO, all habitats are divided into regions based on the habitat suitability index, and the habitats of each region are subject to cross-regional migration and replacement procedures. A critical factory optimization strategy is developed to enhance local search capability. Taguchi method is used to determine the parameters of RBBO. In ten FDAPFSP instances, comparative testing of RBBO algorithm with various heuristic and swarm intelligence algorithms are conducted. The computation results show that in ten FDAPFSP cases, the proposed RBBO outperforms other algorithms in nine out of ten FDAPFSP cases. [ABSTRACT FROM AUTHOR]

Energy-efficient scheduling problems with additional resources are seldom studied in hybrid flow shops. In this study, an energy-efficient hybrid flow shop scheduling problem (EHFSP) with additional resources is studied in which there is asymmetry in the machine. An adaptive two-class teaching-learning-based optimization (ATLBO) which has multiple teachers is proposed to simultaneously minimize the makespan and the total energy consumption. After two classes are formed, a teacher phase is first executed, which consists of teacher self-learning and teacher training. Then, an adaptive learner phase is presented, in which the quality of two classes is used to adaptively decide the learner phase or the reinforcement search of the temporary solution set. An adaptive formation of classes is also given. Extensive experiments were conducted and the computational results show that the new strategies are effective and that ATLBO was able to provide better results than comparative algorithms reported in the literature in at least 54 of 68 instances. [ABSTRACT FROM AUTHOR]

This paper deals with a reentrant hybrid flow shop problem with sequence-dependent setup time and limited buffers where there are multiple unrelated parallel machines at each stage. A mathematical model with the minimization of total weighted completion time is constructed for this problem. Considering the complexity of the problem at hand, an effective cooperative adaptive genetic algorithm (CAGA) is proposed. In the algorithm, a dual chain coding scheme and a staged-hierarchical decoding approach are, respectively, designed to encode and decode each solution. Six dispatch heuristics and a dynamic adjustment method are introduced to define initial population. To balance the exploration and exploitation abilities, three effective operations are implemented: (1) two new crossover and mutation operators with collaborative mechanism are imposed on genetic algorithm; (2) an adaptive adjustment strategy is introduced to re-optimize better solutions after mutation operations, where ant colony search algorithm and modified greedy heuristic are intelligently switched; (3) a reset strategy with dynamic variable step strategy is embedded to re-generate some non-improved solutions. A Taguchi method of design of experiment is adopted to calibrate the parameter values in the presented algorithm. Comparison experiments are executed on test instances with different scale problems. Computational results show that the proposed CAGA is more effective and efficient than several well-known algorithms in solving the studied problem. [ABSTRACT FROM AUTHOR]

This proof-of-concept study provides a novel method for robust-stable scheduling in dynamic flow shops based on deep reinforcement learning (DRL) implemented with OpenAI frameworks. In realistic manufacturing environments, dynamic events endanger baseline schedules, which can require a cost intensive re-scheduling. Extensive research has been done on methods for generating proactive baseline schedules to absorb uncertainties in advance and in balancing the competing metrics of robustness and stability. Recent studies presented exact methods and heuristics based on Monte Carlo experiments (MCE), both of which are very computationally intensive. Furthermore, approaches based on surrogate measures were proposed, which do not explicitly consider uncertainties and robustness metrics. Surprisingly, DRL has not yet been scientifically investigated for generating robust-stable schedules in the proactive stage of production planning. The contribution of this article is a proposal on how DRL can be applied to manipulate operation slack times by stretching or compressing plan durations. The method is demonstrated using different flow shop instances with uncertain processing times, stochastic machine failures and uncertain repair times. Through a computational study, we found that DRL agents achieve about 98% result quality but only take about 2% of the time compared to traditional metaheuristics. This is a promising advantage for the use in real-time environments and supports the idea of improving proactive scheduling methods with machine learning based techniques. [ABSTRACT FROM AUTHOR]

Permutation flow shop scheduling problem (PFSP) is a well-known NP-hard problem with extensive engineering relevance. Consequently, various meta-heuristics have been proposed to obtain near optimum solutions. However, most of them involve tuning algorithm-specific parameters, which leads to excessive computational complexities. A recently developed meta-heuristic named Jaya algorithm is simple yet efficient as it is a parameter-less algorithm, thus does not require tuning of algorithm-specific parameters. However, as the problem size grows, Jaya algorithm loose solution diversity and tends to get trapped at local optima. To alleviate such drawbacks while retaining the parameter-less feature of Jaya, the present paper proposes a Hybrid Iterated Greedy based Jaya algorithm (HIGJ). The proposed approach combines a novel integration of Jaya's population-based optimization with the single solution-based iterated greedy algorithm for enhancing population members to retrieve improved solutions. The objective is to minimize the makespan. The destruction and construction phase of Iterated Greedy (IG) is embedded into the best solution of Jaya algorithm. Furthermore, the local search method is incorporated to improve the overall quality of candidate solutions resulting in faster convergence towards the optimal solution. An exhaustive comparative study along with statistical analysis is conducted with public benchmarks to realize the effectiveness of the proposed HIGJ algorithm. Computational results reveal that HIGJ yields improved solutions and outperforms some of the efficient meta-heuristics available in the literature. [ABSTRACT FROM AUTHOR]

The gap between production scheduling theory and practice still persists as theoretical scheduling models do not cover real-world characteristics such as the multidimensional nature of scheduling decisions appropriately. Moreover, the set of objectives used in classical scheduling does not fully capture multidimensional scheduling decisions. This work therefore reviews which further objectives besides the classical ones have been established so far, which objectives are currently discussed in the literature, and identifies gaps for additional objectives for unpaced flow shops with discrete products. The aim is to provide a clustering of scheduling objectives that covers the multidimensional nature of scheduling decisions holistically. The scheduling objectives are clustered with respect to the respective stakeholders of the supply chain: customer, manufacturer and supplier. Within the objectives of interest for the manufacturer, objectives are further clustered into productivity-, flow- and human-related objectives. The classification serves as basis for the choice of a meaningful subset of objectives in industrial practice. [ABSTRACT FROM AUTHOR]

Smart production scheduling has gained significant attention due to advancements in industrial informatics and technologies that enable the monitoring, control, and adaptation of task scheduling in response to disruptive events. These events can include machine breakdowns, variations in task processing times, and the arrival of new or unexpected tasks. Concurrently, sustainable production scheduling aims to optimize task scheduling by considering economic, environmental, and social factors. This paper introduces a novel optimization model for the development of smart and sustainable production scheduling in a distributed permutation flow shop. The proposed model aims to minimize the makespan while simultaneously limiting the number of lost working days and energy consumption. It also strives to increase job opportunities within acceptable limits. To evaluate the proposed model, we conduct numerical simulations using various examples and a real-case study focusing on auto workpiece production. The results demonstrate the superior performance of the proposed model. Sensitivity analyses are performed to assess the model's ability to deal with disruptions and uncertainties while satisfying economic, environmental, and social considerations. [ABSTRACT FROM AUTHOR]

Energy-efficient scheduling plays a pivotal role in distributed sustainable manufacturing. This study provides the first attempt to use a knowledge-based bi-objective collaborative optimization algorithm with Q-learning (KBCQL) to address an energy-efficient distributed assembly blocking flow shop scheduling problem (EEDABFSP) considering the total assembly completion time and total assembly energy consumption. Constructive heuristics are introduced to establish a favorable initial population characterized by high quality and diversity. Experimental results on benchmark instances demonstrated that the proposed KBCQL can effectively balance these two objectives and outperform comparative algorithms for solving the EEDABFSP problem. [ABSTRACT FROM AUTHOR]

In this work, we will study a permutation flow shop scheduling problem under the constraint of sequence independent setup time. In our case, each machine requires a certain setup time to process all the different jobs assigned to it. Hence, this setup time will be independent of sequence of jobs, but will depend only on the nature of machine. The optimization objective is to minimize the maximum tardiness criterion. To solve this optimization problem, an exact method, heuristics and metaheuristics are the three main resolution methods that we have used. The exact method is represented by the mixed integer linear programming (MILP) model. In terms of the second category of resolution methods, we have been focused on two methods, the first is a modified heuristic based on Johnson rule (HBJR) while the second is based on the Nawaz–Enscore–Ham (NEH) algorithm. Finally, three metaheuristics have been used, namely the iterated local search (ILS) method, the iterated greedy (IG) algorithm and the genetic algorithm (GA). Our numerical results indicate that for the problems with small size instances, the NEH heuristic outperforms HBJR approach, while for relatively large size instances, the developed IG algorithm gives best results than both other metaheuristics ILS and GA. [ABSTRACT FROM AUTHOR]

In today's world, a situational awareness of sustainability is becoming increasingly important. Leaving a better world for future generations is becoming the main interest of many studies. It also puts pressure on managers to change production methods in most industries. Reducing carbon emissions in industry today is crucial to saving our planet. Theoretical research and practical industry requirements diverge, even though numerous researchers have tackled various strategies to handle carbon emission problems. Therefore, this work considers the carbon emission problem of the furniture manufacturing industry in Hosur, Tamilnadu, India. The case study company has a manufacturing system that resembles a hybrid flow shop (HFS) environment. As the HFS scheduling problems are NP-hard in nature, exact solution techniques could not be used to solve the problems. Hence, a sequential hybrid optimization algorithm (SHOA) has been developed in this paper to minimize the carbon footprint. In the SHOA, the pigeon-inspired optimization algorithm (PIOA) is hybridized sequentially with the firefly algorithm (FA). A computational experimental design is proposed to analyze the efficiency of the introduced strategy, and the solutions indicate that the developed approach could reduce the carbon footprint by up to 9.82%. The results motivate us to implement the proposed algorithm in the manufacturing industry to reduce the carbon footprint. [ABSTRACT FROM AUTHOR]

Consideration of upstream congestion caused by busy downstream machinery, as well as transportation time between different production stages, is critical for improving production efficiency and reducing energy consumption in process industries. A two-stage hybrid flow shop scheduling problem is studied with the objective of the makespan and the total energy consumption while taking into consideration blocking and transportation restrictions. An adaptive objective selection-based Q-learning algorithm is designed to solve the problem. Nine state characteristics are extracted from real-time information about jobs, machines, and waiting processing queues. As scheduling actions, eight heuristic rules are used, including SPT, FCFS, Johnson, and others. To address the multi-objective optimization problem, an adaptive objective selection strategy based on t-tests is designed for making action decisions. This strategy can determine the optimization objective based on the confidence of the objective function under the current job and machine state, achieving coordinated optimization for multiple objectives. The experimental results indicate that the proposed algorithm, in comparison to Q-learning and the non-dominated sorting genetic algorithm, has shown an average improvement of 4.19% and 22.7% in the makespan, as well as 5.03% and 9.8% in the total energy consumption, respectively. The generated scheduling solutions provide theoretical guidance for production scheduling in process industries such as steel manufacturing. This contributes to helping enterprises reduce blocking and transportation energy consumption between upstream and downstream. [ABSTRACT FROM AUTHOR]