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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]

Shop scheduling is deeply involved in manufacturing. In order to improve the efficiency of scheduling and fit dynamic scenarios, many Deep Reinforcement Learning (DRL) methods are studied to solve scheduling problems like job shop and flow shop. But most studies focus on using the latest algorithms while ignoring that the environment plays an important role in agent learning. In this paper, we design an effective, robust and size-agnostic environment for job shop scheduling. The proposed design of environment uses centralised training and decentralised execution (CTDE) to implement a multi-agent architecture. Together with the observation space we design, environmental information that is irrelevant to the current decision is eliminated as much as possible. The proposed action space enlarges the decision space of agents, which performs better than the traditional way. Finally, Soft Actor-Critic (SAC) algorithm is adapted to learning within this environment. By comparing with traditional scheduling rules, other reinforcement learning algorithms, and relevant literature, the superiority of the results obtained in this study is demonstrated. [ABSTRACT FROM AUTHOR]

This work presents four mixed integer linear programming (MILP) models for the assembly flow shop problem in order to minimize the makespan. This production environment has two stages: production and assembly. The first stage consists of different machines designed to manufacture parts of a product. The second stage is intended for a final assembly. The performance measure considered is highly essential for industries from different segments, as it focuses on the best use of the time available for production. Statistical analysis with different tools was used to assess the performance and efficiency of mathematical models, emphasizing the analysis of performance profiles. Results showed that mathematical models are efficient, and the position-based model presented the best results for small and large instances during computational experimentation. All mathematical models can be used as direct tools in decision-making for the production sequencing problem in the approached environment. [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]

We study a problem from a real-world application, in which a daily set of orders must be processed following two stages, consisting of preparing perishable products on benches and allocating them to conveyors to be packed in disposable trays. Daily decisions must be made regarding the number and start time of working shifts, the number of workers and their allocation to machines, and the scheduling of orders in a two-stage flexible flow shop environment. The flow shop environment of the studied problem is common in many industries of perishable products, making the problem very general. The problem involves a number of operational constraints, and three objective functions that are minimised in a lexicographic way. To solve the problem, we implement a constructive heuristic and embed it within three metaheuristics: a Random multi-start algorithm (MR), a Biased random key genetic algorithm (BRKGA), and a Variable neighbourhood search (VNS) based one. We perform computational experiments over a set of realistic instances, and present a lower bound obtained from a constraint programming model for the scheduling counterpart. The results of the experiments show that the BRKGA is the most effective in practice for the integrated problem of workforce allocation and scheduling. [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]

Multi-variety and small-batch production mode enables manufacturing industries to expeditiously satisfy customers' personalised demands, where a large amount of identical jobs can be split into several sublots, and be processed by reconfigurable machines with multiple machining technics. However, such highly flexible manufacturing environments bring some intractable problems to the production scheduling. Mathematical programming and meta-heuristic methods become less efficient when a scheduling problem contains both discrete and continuous optimisation attributes. Therefore, matheuristic, which combines advantages of the two methodologies, is regarded as a promising solution. This paper investigates a flexible job shop scheduling problem with lot-streaming and machine reconfigurations (FJSP-LSMR) for the total weighted tardiness minimisation. First, a monolithic mixed integer linear programming (MILP) model is established for the FJSP-LSMR. Afterwards, a matheuristic method with a variable neighbourhood search component (MH-VNS) is developed to address the problem. The MH-VNS adopts the classical genetic algorithm (GA) as the framework, and introduces two MILP-based lot-streaming optimisation strategies, LSO1 and LSO2, to improve lot-sizing plans with varying degrees. Four groups of instances are extended from the well-known Fdata benchmark to evaluate the performance of proposed MILP model, LSO1 and LSO2 components, and MH-VNS. Numerical experimental results suggest that LSO1 and LSO2 are efficient in different scenarios, and the proposed MH-VNS can well balance the solution quality and computational costs for reasonably integrating the GA- and MILP-based local search strategies. In addition, a complicated FJSP-LSMR case is abstracted from a real-world shop floor for processing large-sized structural parts to further validate the MH-VNS. [ABSTRACT FROM AUTHOR]

In this article, maintenance operations were incorporated to the sequence-dependent setup blocking flow shop to minimise total completion time subject to total maintenance costs. A mixed integer linear programming and procedures to incorporate maintenance to job sequence were developed. A constructive heuristic and three metaheuristics, greedy randomised adaptative search procedure (GRASP), discrete artificial bee colony (DABC), variable block insertion heuristic (VBIH) and iterated greedy algorithm (IG), designed to the blocking flow shop with total completion time minimisation were adapted to minimise total maintenance costs and the hierarchical function, respectively.All the methods were applied to solve small and medium and large size instance sets, with respective 1920 and 2200 problems. Experimental results shows that for small size instances set, DABC with α = 20 (DABC(20)) obtained the best trade-off between effectiveness and efficiency. For medium and large size instances set, DABC(20) VBIH with α = 20 (VBIH(20)) generated the best trade-off between quality of solution and computational time. Considering both instances set together, both DABC(20) and VBIH(20) obtained the best performance between quality of solution and computational time. [ABSTRACT FROM AUTHOR]

As businesses gradually transition to the concept of Industry 4.0, they strive to digitize all necessary data. The aim of this article is to demonstrate how the digitalization of shop floor management (dSFM) can enhance the efficiency of production process management, and to propose steps for faster and more effective implementation of dSFM in industrial enterprises. The digitalization of shop floor management increases agility, responsiveness, and overall improves decision-making processes. In the analyzed enterprise, the traditional shop floor management was overly burdensome, accompanied by excessive documentation and inefficient processes. It was necessary to analyze three areas: data collection, information visualization, and the flow of shop floor meetings. Based on this analysis, shortcomings were identified, and measures were proposed to automate routine activities and streamline processes. This case study thus fills a gap in the research by focusing on specific challenges in implementing dSFM in an industrial enterprise. [ABSTRACT FROM AUTHOR]

This paper addresses the economic lot and delivery scheduling problem (ELDSP) within three-echelon supply chains, focusing on the complexities of demand uncertainty, limited shelf-life of products, and sequence-dependency of setups. We develop a novel mixed-integer non-linear programming (MINLP) model for a supply chain comprising one supplier, multiple manufacturers with flexible flow shop (FFS) production systems, and multiple retailers, all operating over a finite planning horizon. The common cycle (CC) strategy is adopted as the synchronization policy. Our model employs fuzzy set theory, particularly the "Me measure," to effectively handle the retailers' demand uncertainty. Our findings indicate that total supply chain costs escalate with an increase in demand, final components' holding costs, and sequence-dependent setup costs, but decrease with increasing production rates. Furthermore, while total costs are significantly sensitive to changes in demand, they are relatively insensitive to fluctuations in sequence-dependent setup times. The models developed offer valuable managerial insights for optimizing costs in synchronized multi-stage supply chains, aiding managers in making informed decisions about production lot sizes and delivery schedules under both deterministic and fuzzy demand scenarios. Additionally, the proposed models bridge key research gaps and provide robust decision-making tools for cost optimization, enhancing supply chain synchronization in practical settings. [ABSTRACT FROM AUTHOR]

Smart manufacturing has boosted the wide application of mobile robots in robotic cells for automated material delivery. However, the mismatching between machine production process and robot movement process causes extensive energy waste. Nevertheless, most existing robotic job-shop scheduling (RJSP) studies mainly focus on minimising makespan but overlook the low energy efficiency problem faced by robotic cells. Motivated by the importance of green smart manufacturing, in this study, we innovatively propose to achieve robotic cell energy saving through coordinating the machine production process and robot movement process. Specifically, both machines and the mobile robot can flexibly adjust operating speeds with a V-scale speed framework. Two novel energy-efficient RJSP approaches (i.e. the RJSP-E and the RJSP-EM) are thus proposed. The RJSP-E focuses on minimising energy consumption, while the RJSP-EM simultaneously considers makespan (i.e. productivity) and energy consumption. Through computational experiments, the RJSP-E demonstrates superior performances in reducing energy consumption (15% on average), at a loss of productivity (20% on average). On the other hand, the RJSP-EM can select the most suitable energy-saving operating speeds without much sacrifice in productivity. Notably, the RJSP-EM can reduce energy consumption by a mean of 10% even without increasing makespan. The RJSP-EM also demonstrates higher solution efficiency. [ABSTRACT FROM AUTHOR]

We study a two-stage hybrid flow shop problem arising from a fine chemicals production facility, where the first stage is a continuous chemical reaction process and the second stage is a discrete filling-packaging process. The objective is to minimise the total weighted completion time through batching of the jobs and scheduling of the batches at first stage and scheduling of the jobs at second stage. We formulate the problem as a mixed integer programming model and develop a Lagrangian relaxation-based framework for solving it, where the original problem is decomposed into family-level subproblems, and each subproblem is transformed into a set-partitioning problem. The subproblems are solved to optimality via branch and price algorithm. We also propose two heuristic algorithms for reducing computational efforts without much loss of solution quality. Finally, we conduct computational experiments with both randomly generated and real data sets to test the performance of the three proposed algorithms and demonstrate that the algorithms perform efficiently. [ABSTRACT FROM AUTHOR]

Dispatching rules are one of the most widely applied methods for solving Dynamic Job Shop Scheduling problems (DJSSP) in real-world manufacturing systems. Hence, the automated design of effective rules has been an important subject in the scheduling literature for the past several years. High computational requirements and difficulty in interpreting generated rules are limitations of literature methods. Also, feature selection approaches in the field of automated design of scheduling policies have been developed for the tree-based GP approach only. Therefore, the aim of this study is to propose a feature selection approach for the Gene Expression Programming (GEP) algorithm to evolve high-quality rules in simple structures with an affordable computational budget. This integration speeds up the search process by restricting the GP search space using the linear representation of the GEP algorithm and creates concise rules with only meaningful features using the feature selection approach. The proposed algorithm is compared with five algorithms and 30 rules from the literature under different processing conditions. Three performance measures are considered including total weighted tardiness, mean tardiness, and mean flow time. The results show that the proposed algorithm can generate smaller rules with high interpretability in a much shorter training time. [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]

Job shop scheduling problem (JSP) is a widely studied NP-complete combinatorial optimisation problem. Neighbourhood structures play a critical role in solving JSP. At present, there are three state-of-the-art neighbourhood structures, i.e. N5, N6, and N7. Improving the upper bounds of some famous benchmarks is inseparable from the role of these neighbourhood structures. However, these existing neighbourhood structures only consider the movement of critical operations within a critical block. According to our experiments, it is also possible to improve the makespan of a scheduling scheme by moving a critical operation outside its critical block. According to the above finding, this paper proposes a new N8 neighbourhood structure considering the movement of critical operations within a critical block and the movement of critical operations outside the critical block. Besides, a neighbourhood clipping method is designed to avoid invalid movement, discarding non-improving moves. Tabu search (TS) is a commonly used algorithm framework combined with neighbourhood structures. This paper uses this framework to compare the N8 neighbourhood structure with N5, N6, and N7 neighbourhood structures on four famous benchmarks. The experimental results verify that the N8 neighbourhood structure is more effective and efficient in solving JSP than the other state-of-the-art neighbourhood structures. [ABSTRACT FROM AUTHOR]

Machine configuration is a crucial strategic decision in designing a flow shop system (FSS) and directly affects its performance. This involves selecting device suppliers and determining the number of machines to be configured. This study addresses a bi-objective optimization problem for an FSS that considers repair actions and aims to determine the most suitable machine configuration that balances the production reliability and purchase cost. A nondominated sorting genetic algorithm II (NSGA-II) is used to determine all the Pareto solutions. The technique for order preference by similarity to an ideal solution is then used to identify a compromise alternative. It is necessary to assess the production reliability of any machine configuration identified by the NSGA-II. The FSS under the machine configuration is modeled as a multistate flow shop network, and Absorbing Markov Chain and Recursive Sum of Disjoint Products are integrated into the NSGA-II for reliability evaluation. The experimental results of solar cell manufacturing demonstrate the applicability of the proposed hybrid method and validate the efficiency of the NSGA-II compared with an improved strength Pareto evolutionary algorithm. [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 competition and the volatility of today's production context require that enterprises are able to rapidly adapt to changes, reducing total costs in production. The main relationship between producer and consumer can be conducted through Make-To-Order (MTO) or Make-To-Stock (MTS) systems. This study proposes a hybrid MTS and MTO production system with a dynamic decoupling point. The proposed model concerns the monitoring of earliness and tardiness of customer orders to move the decoupling point towards MTS or MTO. Simulation models are proposed to test the proposed model following periodic or continuous review. The numerical results highlight that the best dynamic approach is the periodic review, which is more effective when the customer demand rate is higher. [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]

With the increasing level of manufacturing and the rapid development of the market economy, enterprises need to improve the level of service to meet the individual needs of customers. Among them, urgent order is a common problem faced by order-oriented enterprises, but it brings additional profits to enterprises and also causes damage to the stability of production. To address this challenge, this paper takes the hybrid flow shop as the research object, considers the equipment switching strategy, AGV transportation device and the carrying capacity of the shop buffer, establishes a mathematical model with the optimization objectives of minimizing the total energy consumption, minimizing the maximum completion time and minimizing the production cost, and proposes the Improved Red-billed Blue Magpie Optimizer (IRBMO) based on the complete re-scheduling strategy for solving the problem. In this algorithm, according to the characteristics of the hybrid flow shop, a strategy approach based on workpiece-equipment two-layer encoding and decoding is adopted, and a Logistic Chaos Mapping backward learning strategy is proposed to generate the initial population; an adaptive cross-variance operator is introduced to balance the algorithm's search capability. For the emergency order insertion scenario, a comparison test with real workshop data is carried out through the extension of the algorithm, which verifies the feasibility of the IRBMO algorithm in complex combinatorial optimization problems and the superiority of the solving effect. It provides new ideas for the green and efficient production scheduling technology of manufacturing enterprises, and has practical application value for promoting the sustainable development of the production system. [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 work presents two solution methods for the m-machine robust permutation flow shop problem with processing time uncertainty. The goal is to minimize the makespan of the worst-case scenario by utilizing an approach based on budgeted uncertainty, in which only a subset of operations will reach their worst-case processing time values. To obtain efficient solutions to this problem, we first extend an existing two-machine worst-case procedure, based on dynamic programming, generalizing it to m machines. The worst-case calculation is then incorporated into two proposed solution methods: an exact column-and-constraint generation algorithm and a GRASP metaheuristic. Based on experiments with four sets of literature-based instances, empirical results demonstrate the ability of the GRASP to efficiently produce an optimal or near-optimal solution in most cases. [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]

In this paper, an improved Beluga Whale Optimization algorithm based on data mining and scheduling rules with AdaBoost(IBWO-DDR-AdaBoost) rule heuristic scheduling method for solving job-shop scheduling problems (JSP) is proposed, in which data mining-extracted dispatching rules are incorporated into the heuristic algorithm to guide the optimization process. Firstly, an AdaBoost-CART integrated learning algorithm is introduced to evolve dispatching knowledge from historical data and convert it into effective dispatching rules. Secondly, in order to address the issues of local optimality and slow convergence speed faced by the beluga whale optimization algorithm (BWO) when solving JSP, this study presents an improved beluga whale optimization algorithm (IBWO) that incorporates two enhancement mechanisms: a neighborhood search strategy based on greedy thinking and genetic operators. These enhancements aim to improve both the efficiency and quality of reconciliation in scheduling, ultimately leading to better scheduling schemes. Furthermore, the extracted scheduling rules obtained through the AdaBoost-CART integrated learning algorithm are embedded into the improved beluga optimization algorithm, enabling real-time solution updates for optimized schedules. Finally, extensive simulation tests are conducted on JSP benchmark examples of varying scales with minimizing maximum completion time as the objective function for schedule optimization. The simulation results demonstrate the significant advantages of our proposed IBWO-DDR-AdaBoost rule heuristic scheduling method in terms of accuracy, performance optimization, and convergence speed. [ABSTRACT FROM AUTHOR]

In a complex and dynamic job shop containing logistics factor, schedule needs to be generated rapidly, so the real-time scheduling method is more suitable for such scenario. Such method takes advantage of local information within a short time due to the rapid changes of information under uncertain environment. Therefore, how to make use of the future information by prediction while ensuring the robustness of schedule is a valuable problem. To solve it, firstly, a new real-time scheduling model and algorithm is proposed. There is a new kind of release moment of task information which can give AGVs the longest time to prepare for the task than existing research. Secondly, a real-time information update mechanism is designed to increase schedule's robustness. Finally, a large-scale and dynamic job shop simulation experimental platform is developed. Dynamic factors include the random insertion of orders and failures of equipment. Results show that the method proposed outperforms existing research in terms of customer satisfaction, equipment utilisation and energy consumption. The robustness of schedule can also be acceptable. This paper also finds a rule that in job shop with the large proportion of logistics transportation time, the above method can achieve more competitive results. [ABSTRACT FROM AUTHOR]

The article focuses on the problem of a reentrant flow shop with identical jobs and makespan minimisation objective. After presenting an optimal integer programming formulation for the problem, we consider the case of unit processing times. We correct two results published a few decades ago regarding two greedy heuristic algorithms. In some cases, these algorithms lead to an optimal solution, but they are generally not optimal. We point out the advantages of each of the two heuristic algorithms and, by machine learning analysis, discuss features that differentiate between them. [ABSTRACT FROM AUTHOR]

Given the fact that finding the optimal sequence in a flexible flow shop is usually an NP-hard problem, priority-based sequencing rules are applied in many real-world scenarios. In this contribution, an innovative reinforcement learning approach is used as a hyper-heuristic to dynamically adjust the k-values of the ATCS sequencing rule in a complex manufacturing scenario. For different product mixes as well as different utilisation levels, the reinforcement learning approach is trained and compared to the k-values found with an extensive simulation study. This contribution presents a human comprehensible hyper-heuristic, which is able to adjust the k-values to internal and external stimuli and can reduce the mean tardiness up to 5%. [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]

We addressed the multistage assembly flow shop problem with post-processing and makespan minimization, a production environment commonly encountered in diverse industries such as automotive, dental, medical equipment, and clothing manufacturing. In this context, we presented an innovative mixed-integer linear programming model with a position-based strategy. Our proposed formulation demonstrated remarkable efficiency when compared to the model of the literature. It achieved optimal solutions in 77.16% of instances, with an average optimality gap of 10.59%. This study constitutes a significant contribution to the efficient resolution of a practical and frequently encountered scheduling problem that has received relatively limited attention in existing literature. The findings highlight the crucial role of mathematical optimization models as valuable decision-making tools for scheduling within the addressed production system. [ABSTRACT FROM AUTHOR]

This paper studied an integrated process planning and scheduling problem from a machining workshop for large-size valves in a valve manufacturing plant. Large-size valves usually contain several key parts and are generally produced in small-series production. Almost all the parts need to be manufactured in the same workshop at the same time in the plant. Facilities have to handle various items in one order, including different models, sizes, and types. It is a classical NP-hard problem on a large scale. An improved NSGA-II algorithm is suggested to obtain satisfactory solutions for makespan and manufacturing costs, which involve large optimization parameters and interactions. A two-section encoding method and an inserting greedy decoding method are chosen to enable the algorithm. The dynamic population update strategy based on dynamic population update and the adaptive mutation technique depending on the population entropy changing rate are selected for enhancing both the solution quality and population diversity. The methodology was successfully implemented in a real-life case at a major valve machining workshop operated by Yuanda Valve Company in China. By taking into account realistic factors and restrictions that have been identified from a real-world manufacturing setting, this technique aids in bridging the knowledge gap between present IPPS research and practical valve production implementations. [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]

This paper addresses the triangle width problem, which generalizes the classic two-machine flexible job-shop problem (FJSP) with tooling constraints. This new problem can be studied from three different angles: scheduling, matrix visualization, and vertex ordering in hypergraphs. We prove the equivalence of the different formulations of the problem and use them to establish the N P -Hardness and polynomiality of several of its subcases. This problem allows us to find more elegant (and probably shorter) proofs for several combinatorial problems in our analysis setting. Our study provides an elegant generalization of Johnson's argument for the two-machine flow shop. It also shows the relation between the question: "Is a matrix triangular?" and the "k-visit of a graph". [ABSTRACT FROM AUTHOR]

As a significant branch of production scheduling problem, the Flexibility Job Shop Scheduling Problem (FJSP) is a typical NP-hard problem. Most conventional flexible workshop scheduling primarily focuses on performance aspects involving production efficiency such as time and quality. In recent years, due to increased energy costs and environmental pollution, 'low-carbon scheduling' has garnered attention as a new scheduling paradigm among scholars and engineers. This paper investigates a low-carbon flexible Job shop scheduling problem, proposing a Grey Wolf Optimization algorithm (SC-GWO), aiming to minimize the sum of carbon emission costs and makespan costs. This algorithm employs the Grey Wolf Algorithm (GWO) as the fundamental optimization method, adaptively choosing between global and local searches based on the dispersion degree of individuals. Firstly, integrating the Sine Cosine Algorithm (SCA), the sinusoidal cosine search mechanism is applied to GWO to enhance its local search capability. Secondly, a new leader selection mechanism is introduced to prevent leaders from falling into local optima, thus improving the algorithm's global exploration capability. Utilizing a nonlinear convergence factor strategy controls the global exploration and local exploitation capabilities in different algorithm stages, enhancing optimization accuracy and accelerating convergence, achieving a dynamic balance between the two. Finally, validation of the SC-GWO algorithm's ability to solve low-carbon scheduling problems in flexible job shop scheduling instances is conducted. Experimental results demonstrate the superior performance of SC-GWO in solving low-carbon flexible workshop scheduling instances. Comparative experiments against four other advanced algorithms on 22 classic benchmark test functions confirm SC-GWO's better convergence. Through standard test functions like Bandimarte instances applied to solve FJSP, experimental results showcase the excellent optimization performance of SC-GWO. Compared to HGWO and GWO, the makespan time is reduced by 22.25% and 39.27%, respectively. The proposed SC-GWO algorithm demonstrates favorable solving effects on flexible job shop scheduling instances, meeting actual production scheduling needs. [ABSTRACT FROM AUTHOR]

Due to the huge magnitude expansion of data volume, the application of cloud computing and the Internet of Things is growing year by year. However, more and more industrial production requires real-time and efficient handling of resource scheduling. Therefore, this paper develops a deep learning-based knowledge graph framework for resource scheduling decision of enterprise. Single-objective and multi-objective problems for computing resources are studied, and the network nodes of computing resources are set with the help of network topology theory. For the single-objective problem, the mathematical model is constructed with the optimization objective of minimizing the time delay. For the multi-objective problem, the mathematical model is constructed with the optimization objectives of minimizing both time delay and energy consumption. Combining the historical scheduling scheme with the introduction of a genetic algorithm, an initial optimization method is proposed for the scheduling problem of mixed flow shop, and the optimization problem is solved to minimize the maximum completion time. The simulation experiments are conducted to evaluate the proposed method, and the obtained results show that the proposal can well realize intelligent management scheduling decision for enterprises. [ABSTRACT FROM AUTHOR]

In today's customer-centric economy, the demand for personalized products has compelled corporations to develop manufacturing processes that are more flexible, efficient, and cost-effective. Flexible job shops offer organizations the agility and cost-efficiency that traditional manufacturing processes lack. However, the dynamics of modern manufacturing, including machine breakdown and new order arrivals, introduce unpredictability and complexity. This study investigates the multiplicity dynamic flexible job shop scheduling problem (MDFJSP) with new order arrivals. To address this problem, we incorporate the fluid model to propose a fluid randomized adaptive search (FRAS) algorithm, comprising a construction phase and a local search phase. Firstly, in the construction phase, a fluid construction heuristic with an online fluid dynamic tracking policy generates high-quality initial solutions. Secondly, in the local search phase, we employ an improved tabu search procedure to enhance search efficiency in the solution space, incorporating symmetry considerations. The results of the numerical experiments demonstrate the superior effectiveness of the FRAS algorithm in solving the MDFJSP when compared to other algorithms. Specifically, the proposed algorithm demonstrates a superior quality of solution relative to existing algorithms, with an average improvement of 29.90%; and exhibits an acceleration in solution speed, with an average increase of 1.95%. [ABSTRACT FROM AUTHOR]

The frequently evolving manufacturing system necessitates real-time large-scale data analytics, surpassing the capabilities of classical systems or human skills, necessitating knowledge development and self-adaptive control. Unpredictable real-time events in smart factories cause changes in the effectiveness of planned schedules or tasks; even slight interruptions can accumulate to make the preplanned schedule unoptimized, if not impossible. To meet the required production efficiency, typical dynamic scenarios on the shop floor, such as failures, random job arrivals, and machine setup, must be addressed quickly. Hence, this study proposes a novel Triple Deep Q Network (TDQN) approach for learning high-quality dispatching rules for addressing the Flexible Job Shop Scheduling Problem (FJSSP) in uncertainty. For the dispatching rule-based FJSSP, the Markov Decision Process (MDP) to choose a suitable operation-machine (O-M) pair is formulated to allow operation selection and resource assignment resolutions to be made simultaneously. The performance of the TDQN method is investigated against the Double Deep Q Network (DDQN) and Deep Q Network (DQN) approach and found to be more stable. Moreover, among the 29 different shopfloor configuration settings, TDQN performed better in 62.07% of the overall instances, while DDQN and DQN performed better in only 31.03% and 6.9% of instances, respectively. [ABSTRACT FROM AUTHOR]

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

In this paper, we investigate a scheduling problem with optional job rejection in a proportionate flow shop setting, where the job processing times are machine independent. A solution to our problem is characterized by (i) partitioning the set of jobs into a set of accepted jobs and a set of rejected jobs, and (ii) scheduling the accepted jobs in a proportionate flow shop setting. The aim is to find a solution to minimize the sum of total weighted late work of the accepted jobs and total rejection cost of the rejected jobs. When all jobs share a common due date, we show that the single-machine case is -hard by reduction from the Subset Sum problem. When the operations of all jobs have equal processing times, we solve the case in O (n 3) time by reducing it into a linear assignment problem. For the general problem, we first provide a pseudo-polynomial-time algorithm via the dynamic programming method, then we convert it into a fully polynomial time approximation scheme. As a byproduct, we also resolve an open question in the literature. [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 this paper, we consider an application of lot-streaming for processing a lot of multiple items in a hybrid flow shop (HFS) for the objective of minimizing makespan. The HFS that we consider consists of two stages with a single machine available for processing in Stage 1 and m identical parallel machines in Stage 2. We call this problem a 1 + m TSHFS-LSP (two-stage hybrid flow shop, lot streaming problem), and show it to be NP-hard in general, except for the case when the sublot sizes are treated to be continuous. The novelty of our work is in obtaining closed-form expressions for optimal continuous sublot sizes that can be solved in polynomial time, for a given number of sublots. A fast linear search algorithm is also developed for determining the optimal number of sublots for the case of continuous sublot sizes. For the case when the sublot sizes are discrete, we propose a branch-and-bound-based heuristic to determine both the number of sublots and sublot sizes and demonstrate its efficacy by comparing its performance against that of a direct solution of a mixed-integer formulation of the problem by CPLEX®. [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]