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The paper at hand addresses the Economic Lot Scheduling Problem (ELSP), which is concerned with finding a feasible and cost-minimal production schedule for multiple items produced in lots on a single machine. The ELSP started to attract the attention of researchers in the 1950s, where the focus was primarily on the development of simple heuristics for solving the problem. Over the subsequent decades, this topic has frequently been addressed in the literature, with the subject of research being the development of new scheduling policies or solution procedures or extensions of the scope of the original model. To date, a large number of journal articles has been published on the ELSP and its model variants. To identify key research themes, publication patterns and opportunities for future research, the paper at hand applies a content analysis to a sample of 242 papers published on the Economic Lot Scheduling Problem. The results of the content analysis indicate that prior research on this topic had a strong focus on the development of solution methodologies, and that several aspects that are directly connected to lot sizing and scheduling have not attracted much attention in research on the ELSP yet, such as, for example, energy cost and sustainability. [ABSTRACT FROM AUTHOR]

In paper 'Energy cost optimization in two machine Bernoulli serial lines under time-of-use pricing', Cheng, Yan and Gao analyse the structural characteristics of an energy cost optimisation problem, and transform it into optimal allocation of production rate among time periods of different electricity rates. Performance analysis and optimisation play a key role to improve productivity in manufacturing systems. The central theme of this special issue is on Analysis, Design, and Optimisation in Smart and Connected Production and Service Systems. [Extracted from the article]

In total, more than 200 papers were reviewed and classified into 4 categories which are: machine learning assisted VRP modelling, machine learning guided VRP decomposition strategies, machine learning guided perturbative VRP algorithms, and finally learning to construct VRP solutions. It provides an extensive review of vehicle routing (VRP) researches that use both analytical optimisation approaches and machine learning (ML) modules and mechanisms. This special issue largely originated from various discussions during several cross-domain, multi-disciplinary conferences and workshops, especially the 9th Multidisciplinary International Scheduling Conference: Theory and Applications (MISTA2019), which attracted scientists, researchers and practitioners from Computer Science, Operations Research as well as Business and Management. " A Two-Stage Stochastic Programming Model for Collaborative Asset Protection Routing Problem Enhanced with Machine Learning; A Learning Based Matheuristic Algorithm.". [Extracted from the article]

This paper addresses a real life scheduling problem characterised by multi-resource operations whose completion simultaneously requires more than one (renewable) resource of different types. Such problems arise in various companies not only in manufacturing but also in services. Solving such a problem needs to address two interconnected subproblems: a sequencing subproblem and a resource-allocation subproblem if more than one resource is available in some types. The resource-allocation subproblem consists of allocating to each operation the resources it requires while the sequencing subproblem consists of determining the order in which each resource performs the operations assigned to it. This paper focuses on the resource-allocation subproblem. It generalises the basic scheduling problems which consist of determining the operations' starting or completion times for a given processing sequence for every resource. We consider a cost function taking into account the makespan, the cost of resource utilisation, and the load imbalance among the resources of the same type. We first formulate the problem into a mixed-integer linear program (MILP). To efficiently solve it, even in practical-sized instances, an exact algorithm called BD (Benders decomposition with enhancing cuts) is developed where the master problem only considers integer variables. We prove that the slave problem can be transformed into finding the longest paths in a digraph and therefore can be solved with the Bellman–Ford algorithm. To enhance the efficiency of the method, equivalent solutions are limited in the master problem. The performance of the approach is evaluated by comparing it against CPLEX, a state-of-the-art commonplace MILP solver, used to directly solve the initial MILP. The computational results demonstrate that BD provides competitive solutions in all upper and lower bounds. In particular, it improves, compared with CPLEX, the upper and lower bounds by 5.07% and 4.63%, respectively, in solving practical-sized instances. The experiment also shows that considering load balancing can make more rational use of resources and avoid adverse effects caused by excessive workload of staff and imbalanced use of equipment, which is very important in real-world production. [ABSTRACT FROM AUTHOR]

Autonomous vehicle storage and retrieval systems (AVS/RSs) are widely used in e-commerce warehouses due to their high throughput and flexibility. In such systems, storage and retrieval transactions are performed by lifts and vehicles. This paper focuses on the sequencing retrievals problem in an AVS/RS, which is an important problem for daily operations. We formulate this sequencing problem as a mixed-integer program to determine a retrieval sequence for the lift and the vehicles, one that minimises the makespan. A dynamic programming approach is proposed to solve the sequencing problem to optimality. However, the solution time of the dynamic programming method is exponentially increasing in the number of retrieval requests. To be more practical, we present a beam search heuristic that can solve large-sized instances in reasonable time. Computational experiments verify that near-optimal solutions can be found by the beam search heuristic. Compared to commonly used heuristics and straightforward heuristics, the beam search decreases the makespan by up to 15%. Finally, we analyse how vehicle modes impact the makespan, showing evidence that a small makespan can be achieved when considering a realistic mode of vehicles. [ABSTRACT FROM AUTHOR]

Additive manufacturing (AM) introduces a set of technology-specific problems, such as the proper orientation of parts or the placement of several heterogeneous parts in the same build cycle, which are not addressed by traditional approaches to production planning and scheduling. Although these new production subproblems have been implicitly addressed by several works according to generic nesting and scheduling concepts, a literature review revealed that there is no uniformity in identifying and, thus, solving all these subproblems. For this reason, and as a result of an in-depth analysis of the existent literature on AM production planning and an analogy with classic cutting and packing typologies, the present paper offers a framework to formalise the production planning problem in AM at the operational level. This framework can be used as a reference to focus on and address these AM-related problems for efficient production planning. It is designed at the subproblem level and centres on production order processing in AM. A coding strategy is specifically developed for the framework, which is applied to a review of relevant works that propose models for the production planning of AM systems. Finally, the review results are discussed and possible extensions of the framework are proposed. [ABSTRACT FROM AUTHOR]

Production planning and scheduling for companies with divergent processes, where a single component can be transformed into several finished products, are challenging as planners might face material misallocation issues. In this paper, we address the problem of managing a divergent process with DDMRP stock buffers, where different finished products are bottled with the same component having a fixed batch size. An allocation decision needs to be made to determine the quantities of finished products to be bottled. This study is motivated by a real-life problem faced by a dermo-cosmetic company. We compare and analyze by simulation nine different policies triggering allocation decisions. The first policy is the classic DDMRP rule, while the others are new policies, including a virtual buffer of a generic finished product and ConWIP loops, delaying the allocation decision. Our results show that the policy combining the classic DDMRP rule and a ConWIP loop surrounding a part of the process reduces the work-in-process by 34% compared to the classic DDMRP while ensuring high customer service rates and control of flow times. [ABSTRACT FROM AUTHOR]

This paper introduces the Cyclic Production Routing Problem (CPRP). The CPRP is an extension of the well-known NP-hard Production Routing Problem (PRP), which is a hard-to-solve combinatorial optimisation problem with numerous practical applications in the field of freight transportation, logistics and supply chain management. Under the PRP setting, a manufacturer is responsible for determining production decisions, as well as the timing and quantity of replenishment services offered to a set of geographically dispersed customers over a multi-period time horizon. The problem calls for jointly optimising the production, inventory, distribution and routing decisions. In this paper, the basic PRP model is modified to generate repeatable cyclic production and delivery schedules. A two-commodity flow formulation is proposed along with valid inequalities. Extensive comparisons between the basic PRP and the proposed cyclic variant on well-known benchmark instances are provided. The new variant is significantly harder to solve, especially when the vehicle fleet is limited. From a managerial perspective, the generation of cyclic production-routing schedules significantly increases all costs, whereas the number of vehicle routes required to implement a cyclic schedule is higher. [ABSTRACT FROM AUTHOR]

In this paper, we demonstrate that the relation between two jobs defined by min{ai, bj} ≤ min{bi, aj}, used in Johnson’s theorem, is not transitive. However, both the theorem and Johnson’s algorithm are correct. [ABSTRACT FROM AUTHOR]

This paper provides a systematic review of the Genetic Algorithm (GA)s proposed to solve planning and scheduling problems in Engineer-To-Order (ETO) contexts. Our review focuses on how the key characteristics of ETO projects affect both the problem studied and the GA algorithmic features. Typical ETO projects consist of one-of-a-kind products with complex structures and uncertain designs. A deep analysis of the papers published between 2000 and 2022 enables identifying 10 main characteristics of ETO projects, six activity types, 10 decision types, eight groups of constraints, and 10 optimisation objectives. Our study shows that none of the reported papers integrates all 10 ETO characteristics. The less studied ETO characteristics are incorporating design and engineering information in the problem definition and the design uncertainty. Our review also identifies 10 recurrent encoding formats and emphasises the most frequently used genetic operators. We observed that most planning and scheduling problems consider objectives and decisions related to product customisation or supply chain configuration yielding multi-objective problems. Most multi-objective GAs use a weighted sum or are based on NSGAII. Diversity maintenance methods, adaptive and parameter tunning mechanisms, or hybridisation with machine learning models are still not used in this context. A systematic review of genetic algorithms dedicated to industrial planning and scheduling Analysis on how the characteristics of ETO projects impact the design of genetic representation and operators Recommendation on approaches employed to reach high-quality solutions [ABSTRACT FROM AUTHOR]

The objective of this paper is to examine the use and applications of reinforcement learning (RL) techniques in the production planning and control (PPC) field addressing the following PPC areas: facility resource planning, capacity planning, purchase and supply management, production scheduling and inventory management. The main RL characteristics, such as method, context, states, actions, reward and highlights, were analysed. The considered number of agents, applications and RL software tools, specifically, programming language, platforms, application programming interfaces and RL frameworks, among others, were identified, and 181 articles were sreviewed. The results showed that RL was applied mainly to production scheduling problems, followed by purchase and supply management. The most revised RL algorithms were model-free and single-agent and were applied to simplified PPC environments. Nevertheless, their results seem to be promising compared to traditional mathematical programming and heuristics/metaheuristics solution methods, and even more so when they incorporate uncertainty or non-linear properties. Finally, RL value-based approaches are the most widely used, specifically Q-learning and its variants and for deep RL, deep Q-networks. In recent years however, the most widely used approach has been the actor-critic method, such as the advantage actor critic, proximal policy optimisation, deep deterministic policy gradient and trust region policy optimisation. [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]

Due to today's competitive environment and information boom, companies are concerned about production planning in uncertain conditions. This paper integrates decision-making method with production scheduling model by considering limited resources. In this paper, a new mathematical model is extended for production project scheduling with multiple execution modes. The main aim of the formulation is to plan and schedule real production projects in uncertain environments. A new mixed-integer linear formulation is presented by considering trade-off of cost, time, as well as quality. Cost–time-quality trade-off is extended with the interval information. In the presented model, activity quality could be enhanced by reworking. The interval forms of some parameters, including duration, quality of activities, cost, and total available resources, are obtained by determining weights of experts and aggregating them. The presented group decision-making method is based on a bi-directional projection measure to deal with interval information. Since the mathematical model is multi-objective and some data are interval, a new modified solution method is developed for solving the model. The presented method for both decision-making and mathematical models is investigated by a real-world production project and two datasets to ascertain the accuracy of the model. Finally, an appropriate sensitivity analysis is proposed. [ABSTRACT FROM AUTHOR]

This paper presents a novel quantitative approach and stochastic quadratic optimisation model to maintain supply chain viability under the ripple effect. Instead of viability kernel commonly used in the viability theory, this paper establishes the boundaries on acceptable production states for which the production can be continued under the ripple effect, with no severe losses. For a given implementable portfolio of controls, the boundaries on acceptable production trajectories associated with the two conflicting objectives, cost and customer service level are determined. The decision maker selects a viable production trajectory in-between the two boundary trajectories: the cost-optimal and the service-optimal. The selection depends on the decision maker preference, represented by a chosen weight factor in the optimised quadratic objective function that minimises weighted deviations from the cost-optimal and from the service-optimal production schedules under the ripple effect. The findings indicate that for the extreme values of the weight factor, the viable production trajectory is inclined toward the corresponding boundary trajectory and remains in-between the two boundaries, when both objectives are equally important. Keeping production trajectory in-between the two boundaries makes the supply chain more resilient to disruption risks, while the supply chain resilience diminishes as the production trajectory approaches a boundary trajectory. Then a more severe disruption may push the production outside the viability region and cause greater losses. [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]

This paper focuses on a two-stage machining and welding scheduling problem based on an investigation at a structural metal manufacturing plant, aiming to minimise the total makespan. Several parts processed at Stage one according to classical job-shop scheduling are grouped into a single construction component at the second welding stage. Fabrication of the construction component cannot begin until all comprising parts have been completed at Stage one. This paper establishes a novel mathematic model to minimise the total makespan by mainly considering the dominance relationship between the construction component and the corresponding parts. In order to solve this two-stage problem, we propose an improved harmony search algorithm. A local search method is applied to the best vector at each iteration, so that a more optimal vector can be subsequently realised. The average value, minimum value, relative percentage deviation and standard deviation are discussed in the experimental section, and the proposed local best harmony search algorithm outperforms the genetic algorithm, immune algorithm and harmony search algorithm without local search. Moreover, six optimal solutions are given as Gantt charts, which vividly illustrate that the mathematical model established in this paper can facilitate the development of a better scheduling scheme. [ABSTRACT FROM AUTHOR]

This paper proposes a scheduling strategy for irregular curved blocks to address the complex spatiotemporal coupling scheduling problem related to the entered time, the entered sequence, the setting positions and the rotated angles for the curved blocks in a shipbuilding yard. The strategy presents a makespan-based curved blocks - classification and selection rule to fulfil the programming time for the entry of the curved blocks into the workplace and realises the suppression on the delay. Useless stepping search of curved blocks in occupied workplace is avoided by combining the lowest centre-of-gravity rule with the calculation method of the remained workplace proposed in this paper. A modified genetic ant colony algorithm was proposed, which apply the ease to premature characteristics of GA and the excellent local optimisation ability of ACO, to let and promote the algorithm falls into local optimum. Then the large-scale and full-range mutation will be implemented to make the algorithm jump out of the original local optimisation to search more local optimal solutions so that the global optimal solution can be achieved. Finally, a software system for algorithm verification was developed which conducts the comparative analysis of the algorithms and verifies the validity of the algorithm proposed. [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]

Over the last decades, scheduling theory has been put into practice so as to tackle production process as a combinatorial optimisation problem and specifically as a PFSP (Permutation Flowshop Scheduling Problem). Often, NP-completeness of PFSP leads numerous research towards suggesting heuristic algorithms. The objective is to propose an optimal or near-to-optimal order of n jobs processing on m machines with a minimum completion time of all jobs. In this paper, a two-phase heuristic algorithm will be presented, named IFRS (Improved FRS). FRS, within the first phase, is going to be used to find a superior order of jobs out of Taillard's instances; then the order of jobs will be improved again in phase 2. While running IFRS, a completely new idea, named Pixelation of time matrices, will be used for the very first time and provide a final pattern, which can be used in any heuristic algorithm with makespan criterion. After using the hard benchmark instances of Taillard, the superiority of IFRS over 20 algorithms is going to be shown by tables and statistical graphics. Due to its low makespan values, IFRS benefits flow production, as does NEH. [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]

The cloud-edge collaborative manufacturing system (CCMS) connects distributed factories to a cloud centre through cloud-edge collaborative communication, introducing both opportunities and challenges to conventional dynamic job scheduling. Enhancing each factory's scheduling performance by sharing general scheduling knowledge among heterogeneous factories under the consideration of data privacy protection remains challenging. To this end, this paper proposes to solve the dynamic job scheduling in the context of CCMS with a novel federated deep reinforcement learning (FDRL) approach. Within each factory, the scheduling objective involves minimising the makespan and energy consumption, accounting for machine warm-up procedures and real-time dynamics. To handle heterogeneous policy structures, we aggregate their hidden parameters through FDRL, with states, actions, and rewards designed to facilitate the aggregation. The two-phase algorithm, comprising iterative local training and global aggregation, trains the scheduling policies. Constraint items are introduced to the loss functions to smooth local training, and the global aggregation considers production scales and obtained objectives. The proposed approach enhances the solution quality and generalisation of each factory's scheduling policy without exposing original production data. Numerical experiments conducted on sixty scheduling instances validate the superiority of the proposed approach compared to twelve dynamic scheduling methods. Compared to independently trained DRL-based approaches, the proposed FDRL-based approach achieves up to an 8.9% reduction in makespan and a 22.3% decrease in energy consumption through knowledge sharing. [ABSTRACT FROM AUTHOR]

In response to the challenges posed by economic globalisation and increasing customer demands, enterprises are compelled to adapt and refine their production models and operational objectives, which motivates this paper to address the integrated production scheduling and vehicle routing problem in the distributed manufacturing environment (IPSVRP-DME). The objective is to simultaneously minimise both total energy consumption and total earliness/tardiness. Initially, a mixed integer programming model is proposed to address small-scale problems using Gurobi. Considering the NP-hardness of the problem, a novel Self-adapted Gaussian Mutation-based Arithmetic Optimiser Algorithm (SGMAOA) is developed to handle medium-scale and large-scale instances. To address the complexity of decision-making, an innovative two-level encoding method that encompasses four decision dimensions is introduced. Additionally, an incremental repair strategy is devised to rectify infeasible solutions caused by unreasonable delivery batching, while a time relaxation strategy is proposed to further enhance service levels without compromising energy consumption. Comparative experiments are conducted to demonstrate the effectiveness of SGMAOA, which is benchmarked against five prominent metaheuristics. In addition, a specific example is applied for the discussion of managerial applications and to illustrate the practicality of the proposed model and solution method. [ABSTRACT FROM AUTHOR]

Due to the severity of resource consumption and uncertainty in orders, new challenges have arisen for production scheduling in enterprises. This paper studies the scheduling problem of minimising the total weighted tardiness for jobs with fuzzy processing times and due dates on identical parallel machines with resource constraint. To address this research problem, we first propose methods to calculate the upper bound of resource consumption and the maximum number of machines that can be used, effectively reducing the search space and improving the algorithm's efficiency. Secondly, a local search algorithm based on job swapping is proposed to enhance the algorithm's performance. Then, repair algorithms based on job removal and job swapping are designed to repair infeasible solutions. Finally, we propose a fuzzy genetic algorithm (FGALS) to solve the problem based on the above elements. Through extensive simulation experiments, the effectiveness and efficiency of the FGALS algorithm are verified by comparing it with commercial solver Gurobi and several meta-heuristic algorithms. [ABSTRACT FROM AUTHOR]

In this paper, a variant of the open shop scheduling problem is considered in which the intermediate storage is forbidden among two adjacent production stages (zero buffer or machine blocking constraint). The performance measure is to minimise the maximal completion time of the jobs (makespan). Since this is an NP-hard problem, a two-stage constraint programming approach is proposed as a new exact method. Computational experiments were carried out on 222 literature problem instances in order to test the performance of the proposed algorithm. The relative deviation is adopted as the performance criteria. Computational results point to the ability of the proposed method to solve large-sized instances in comparison with the developed mixed-integer linear programming model and a simple constraint programming model, both with user cuts. In all set of instances, the proposed two-stage method performed better than benchmarking methods and integer programming models, with average relative deviation regarding objective values as lower as 12%. In addition, the results point to a competitive efficiency in computational times of the proposed method with less than 200 s in the most instances to obtain the optimal solution, in comparison to competitive metaheuristics from literature of the problem, for the tested test instances. [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 multi-objective optimisation problems, optimal decisions need to be made in the presence of trade-offs among conflicting objectives which may sometimes be expressed in different units of measure. This makes it difficult to reduce the problem to a single-objective optimisation. Furthermore, when disruptive changes emerge in manufacturing environments, such as the arrival of new jobs or machine breakdowns, the scheduling system should be adapted by responding quickly. In this paper, we propose a rescheduling architecture for solving the problem based on a predictive-reactive strategy and a new method to calculate the reactive schedule in each rescheduling period. Additionally, we developed a methodology that allows the use of multi-objective performance metrics to evaluate dispatching rules. These rules are applied at a benchmark specifically designed for this paper considering three objective functions: makespan, total weighted tardiness and stability. Three types of disruptions are also considered: arrivals of new jobs, machine breakdowns and variations in job processing times. Results showed that the RANDOM rule provides a better behaviour compared to other evaluated rules and a lower ratio of non-dominated solutions compared to ATC (apparent tardiness cost) and FIFO (first-in-first-out) rules. Moreover, the behaviour of the hypervolume metric depends on the problem dimensions. [ABSTRACT FROM AUTHOR]

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

This paper presents a novel solution approach for a variant of the job shop scheduling problem with machine unavailability due to both condition-based preventive maintenance and corrective maintenance following random breakdowns. We first provide an exact mathematical formulation of the problem under simplifying assumptions, namely that the number of breakdowns for each job position on each machine is known, the degradation rates are fixed, and the preventive and corrective maintenance durations are deterministic parameters. Moreover, to handle the more realistic case of stochastic machine degradation, random breakdowns, and uncertain maintenance durations, a simulation-optimisation algorithm is proposed. The real makespan function is first approximated using multiple surrogate measures, which are optimised through independent genetic algorithms. Then, the fittest solutions obtained from these surrogate measures are simulated, and the best among them is added to an elite list, which is included in the genetic algorithms' populations for the next iteration. Schedule robustness is ensured by using an objective function that consists of the weighted average of the expected makespan and its 90th percentile. Furthermore, to reduce the likelihood of falling into a local optimum, a stopping criterion based on simulated annealing is implemented. Numerical experimentation on extended benchmark instances confirmed the validity of the mathematical formulation and the favourable performance of the proposed simulation-optimisation algorithm in terms of computational time and solution quality. [ABSTRACT FROM AUTHOR]

This paper investigates an energy-efficient scheduling problem on unrelated parallel machines considering general position-based deterioration which arises from the labour-intensive textile industry. The actual processing time of a job is not only associated with the job and the machine but also with its position in the processing sequence. The objective is to minimise the total energy consumption with a bounded makespan. To address this problem, we first establish a mixed-integer linear programming (MILP) model. Afterwards, the initial model is improved by deriving lower and upper bounds on the makespan, and an upper bound on the number of jobs processed on each machine. We also develop an iterative heuristic embedded with a variable neighbourhood search procedure (IHVNS). The algorithm obtains initial solutions iteratively by solving assignment problems and then repairs and improves them with the VNS procedure. Computational results demonstrate that the improved model is up to 230 times faster than the original one. Moreover, the proposed heuristic yields excellent solutions with average gaps of less than 0.73% for large-scale instances. Especially, the results reveal that the IHVNS algorithm is more suitable than MILP models for solving large-scale problems with tight makespan restrictions. [ABSTRACT FROM AUTHOR]

This paper proposes a maintenance policy for a k-out-of-n: F system operating to fulfil several jobs without interruptions. The system is replaced when the Nth job completes or at the kth failure, whichever occurs first. So, there are some non-failed components when a replacement is done. These components can be sold as second-hand products to continue working in other systems for a while. The price of them is also considered in the proposed maintenance policy. An optimal maintenance policy is studied to minimise long-run average cost under the constraint of relative mean operating time. Comprehensive numerical studies are done to assess the effect of the model parameters on the optimal solutions. Also, to demonstrate the applicability of the proposed plan, a data set related to wind turbine generator failures is considered as a case study. [ABSTRACT FROM AUTHOR]

This study considers the problem of inventory and scheduling decisions on a reusable transport item (RTI) sharing platform with the collaborative recovery of used RTIs and replenishment of products in a two-tier container management centre (CMC). The products (packaged as full RTIs) are pre-positioned at the regional CMC (R-CMC), and empty RTIs are stored at the CMC hub. Moreover, the CMC replenishes the products and recycles RTIs respectively and periodically. The RTI and products are a set of complementary products, and the replenishment task requires sufficient empty RTIs in stock. Untimely and insufficient RTI returns without considering product inventory changes often result in RTI out-of-stock situations that harm the customer's lean productivity. This paper proposes a machine learning and simulation optimisation (MSO) decision framework to collaboratively assist RTI inventory and scheduling decisions in a two-tier CMC. Based on a case study, we can conclude the decision framework has better performance on the profitability and inventory control capability. Moreover, different inventory and scheduling parameter settings in the two-tier CMCs impact the platform's profitability to derive corresponding management insights, and a decision system can be built based on the above framework. [ABSTRACT FROM AUTHOR]

Steelmaking-Continuous Casting (SCC) is a bottleneck in the steel production process and its scheduling has become more challenging over time. In this paper, we provide an extensive literature review that highlights challenges in the SCC scheduling and compares existing solution methods. From the literature review, we collect the essential features of an SCC process, such as unrelated parallel machine environments, stage skipping, and maximum waiting time limits in between successive stages. We consider an SCC scheduling problem with as objective the minimisation of the weighted sum of cast break penalties, total waiting time, total earliness, and total tardiness. We formulate the problem as a mixed-integer linear programming model and develop an iterated greedy matheuristic that solves its subproblems to find a near-optimal solution. Through numerical experiments, we show that our algorithm outperforms two types of genetic algorithms when applied to test instances. [ABSTRACT FROM AUTHOR]

There is a lack of studies on joint optimisation of flexible job-shop scheduling problem (FJSP) considering energy consumption and production efficiency in the machining-assembly system. Thus, in this paper, we propose a methodology for multi-objective optimisation of energy-aware flexible job-shop scheduling during machining and assembly operations. First, a mixed integrated mathematical model is developed to improve production efficiency and minimise energy consumption. Then, a novel heuristic algorithm integrated particle swarm optimisation (PSO) and genetic algorithm (GA) is developed to address the established multi-objective problem. Moreover, numerical examples are carried out to verify the validity and performance of the solving methods in achieving energy awareness in the manufacturing system. Computational results are presented to demonstrate the advantage of solving the problem compared with the exact method and common heuristic algorithms, and the trade-off between production efficiency and energy efficiency is analysed to make the final decision for managers. [ABSTRACT FROM AUTHOR]

Smart manufacturing that involves tight integration of the physical system and cyber system is a hot topic in both industry and academia in the era of the Internet and big data. However, the dynamic and uncertain manufacturing environment introduces a significant adaptive issue of production scheduling, which is one of the pivotal tasks for smart manufacturing. This paper focuses on this problem and proposes a closed-loop adaptive scheduling solution based on the Cyber-Physical Production System (CPPS) with four phases: production data acquisition (PDA), dynamic disturbance identification (DDI), scheduling strategy adjustment (SSA), and schedule scheme generation (SSG). In the DDI phase, in view of the disturbance classification, a disturbance identification procedure based on CPPS monitoring is studied to ensure real-time response. In the SSA phase, an industrial big-data-driven scheduling strategy adjustment method is proposed, which consists of GA-based offline knowledge learning and KNN-based online adjustment, to enhance the system adaptability. We apply and verify the proposed adaptive scheduling solution on an experimental semiconductor manufacturing system, and the results demonstrate that the proposed method outperforms the dynamic scheduling method in terms of multiple objectives under different disturbance levels. [ABSTRACT FROM AUTHOR]

To quickly manufacture multi-variety and low-volume products, manufacturing factories are increasingly sharing resources on collaborative production networks. However, the reliability of communication between factories cannot be fully guaranteed using traditional centralised approaches. Emerging blockchain technology can solve this problem due to its characteristics such as decentralisation and security. In this context, an integrated optimisation problem of multi-factory production and blockchain-secured collaborative maintenance is studied in this paper. Two scenarios are introduced with respective Q learning-based solution frameworks to solve the integrated problem. In the simulation scenario, preventive maintenance (PM) with flexible time windows is integrated with multi-factory production scheduling for reducing the probability of machine failures, and an initial integrated optimisation scheme is obtained. To make it more realistic, inevitable failures are considered in the actual production scenario, and the proposed collaborative maintenance strategy is triggered. Specifically, a corrective maintenance (CM) strategy is carried out immediately on the failed machine in case of a failure, followed by the PM on machines of the same type as the failed machine in other factories and the rescheduling of unprocessed jobs. Through a series of numerical studies, the effectiveness of the proposed optimisation approach and maintenance strategy is validated, and some interesting managerial implications also rise. [ABSTRACT FROM AUTHOR]

Chemotherapy scheduling at cancer treatment centres is a complex problem due to high and growing demand, diversity of treatment protocols, limitations on resources and the need to coordinate treatment session times with laboratory preparation of medication. Over a given planning horizon, treatment centres assign patients first to specific days (interday scheduling) and then to specific times within each day (intraday scheduling), the latter process including the definition of medication preparation time. This paper addresses the intraday scheduling problem using an integer programming model that attempts to schedule all patients assigned to the horizon, and the preparation of the medication to be administered, simultaneously. The linear relaxation of the model formulation, which is based on treatment patterns, is solved using column generation. The proposed approach allows for medication preparation on the day of treatment or a previous day subject to time slot availability. A case study is conducted using actual data from a Chilean cancer centre to compare through simulation the schedules generated by the proposed approach and the centre's manual method. The results show that the proposed approach performs better on makespan, treatment chair occupancy, number of overtime hours and finding solutions at high demand levels. [ABSTRACT FROM AUTHOR]

In both manual and automated warehouses, a combination of efficient zoning and picker routing plays an important role in improving travel time, congestion, and system throughput. This paper considers the order picker routing problem in a dynamic and synchronised zoning environment, where the items corresponding to each customer order are picked simultaneously in multiple zones, and zones may change between different orders. The objective is to minimise the maximum time of completing the picking activities in any zone. Using a min–max type of objective not only minimises the makespan of an order picking wave, but it also helps balance the workload of the order pickers more effectively. We present a mathematical model for the optimal solution of this problem, as well as a dynamic programming approach to find the optimal solution for the case where a zone is a set of adjacent aisles. Computational experiments on randomly generated instances show that the dynamic programming approach is able to find optimal solutions in negligible computational times. [ABSTRACT FROM AUTHOR]

A single-machine scheduling problem with new maintenance activities is examined in this paper. In the scheduling literature, it is often assumed that the interval between maintenance activities is fixed or within a specified time frame. However, this assumption may not hold true in many real-world situations, such as the maintenance activities in wafer manufacturing of semiconductor. Before the wafer manufacturing process starts, it is imperative that the wafers go through a number of cleaning operations to avoid contamination. Using a cleaning agent as the main material of wafer cleaning, the contamination will be dissolved and removed from wafer surface. In case of contamination being accumulated substantial and going beyond a permitted value, the cleaning agent is highly likely to damage the wafer surfaces. Thus, the interval between maintenance activities in the wafer manufacturing process is deemed irregular. The objective function of the proposed problem is to minimise total completion time. Addressing the problem, a binary integer programming model is formulated in this paper. Furthermore, with the research problem being NP-hard, a heuristic based on two special properties is proposed to address the problem. To evaluate and validate the proposed heuristic, a new lower bound is further developed. Extensive experiments have been conducted showing that the proposed heuristic efficiently yields a near-optimal solution with an average percentage error of 15.4 from lower bound. [ABSTRACT FROM AUTHOR]

Demand response (DR) is considered as one of the most important measures for balancing energy supply and demand in the smart grid paradigm. Incentive-based programs, one manifestation of DR, contribute to short-term system stability and prevent critical periods when system stability is at risk by enabling the system operator (SO) to directly change total energy demand. The fact that a third party would be empowered to interfere with internal operations is, however, also one of the major drawbacks of DR that prevents especially industrial consumers from participating with full capacity in such programs. This paper considers an alternative Incentive-based program with application to a discrete manufacturing facility where load reduction curves (LRCs) are generated a priori outlining the potential load reduction in the DR period. The SO uses the LRC to determine the desired level of load reduction for critical periods. To illustrate the generation of the LRC, this paper builds on a flexible flow shop (FFS) formulation for a discrete manufacturing facility and presents a model that includes multiple machine modes and product- and machine-specific energy consumption trajectories. Based on the FFS, a procedure is developed to generate the LRC. The paper also investigates the potential of including a battery energy storage system (BESS) into the production facility and illustrates the effects of the BESS on the LRC. [ABSTRACT FROM AUTHOR]

Resource scheduling has been one of the most prominent problems due to its technical challenges and prevalence in real-life. In this paper, we focus on an extension of the parallel machine scheduling problem with additional resources, which can be classified as a static resource-constrained parallel machine scheduling problem with unspecified job-machine assignment. The novelty of the problem we tackle stems from the additional resource that consists of components with discrete levels. The allocation of this resource to machines induces general covering constraints. This distinct characteristic of the additional resource also arises in a real-life audit scheduling problem, in which local branches of a financial firm are to be audited by a set of auditors with different experience levels. The quantification of the auditor experience and the branch experience requirement enable us to model this problem as an extension of the aforementioned scheduling problem with extra constraints related to the auditing process. We propose mathematical models for these problems and two constructive heuristic algorithms. The upper bounds attained by these algorithms are improved by a tabu-search algorithm, and an efficient lower bounding technique is developed for comparative purposes. We conduct extensive computational experiments to assess the performance of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Given the high demand for energy in the manufacturing industry and the increasing use of renewable but volatile energy sources, it becomes increasingly important to coordinate production and energy availability. With the help of incentive-based programmes, grid operators can incentivise consumers to adjust power demand in critical situations such that grid stability is not threatened. On the consumer side, energy-efficient scheduling models can be used to make energy consumption more flexible. This paper proposes a bi-objective job-shop scheduling problem with variable machine speeds that aims on minimising the total energy consumption and total weighted tardiness simultaneously. We use a genetic algorithm to solve the model and derive Pareto frontiers to analyse the trade-off between both conflicting objectives. We gain insights into how incentive-based programmes can be integrated into machine scheduling models and analyse the potential interdependencies and benefits that result from this integration. [ABSTRACT FROM AUTHOR]

The paper presents a discrete-time mixed-integer linear programming (MILP) model for a generalised flexible job-shop scheduling problem as represented by a state-task network. The problem is characterised by reentrant flow, sequence-dependent changeover time, machine downtime, and skilled labour requirements. Two preprocessing procedures are proposed to reduce the size of the MILP model, and represent a major contribution of the research. The procedures reduce the number of assignment variables by exploiting job precedence and workforce qualifications. Machine availability for each task is determined as a function of possible start and end times, given duration, and maintenance schedule. The overall objective is to maximise the number of scheduled tasks while minimising their total finish time. Computational experiments are conducted with real and randomly generated instances. The results show that optimal solutions can be obtained for medium-size problems within a reasonable amount of time, primarily due to the use of the preprocessing procedures. [ABSTRACT FROM AUTHOR]

Current studies on scheduling of machines and transporters assume that either a single transporter or an infinite number of homogeneous transporters such as AGVs or mobile robots are available to transport semi-finished jobs, which seems very restrictive in practice. This paper addresses this gap by studying a job-shop scheduling problem that incorporates a limited number of heterogeneous transporters, where the objective is to minimize the makespan. The problem is modelled using mixed-integer linear programming and constraint programming. Different structure-based branch-and-bound algorithms with two lower-bounding strategies are also developed. A comprehensive numerical study evaluates the proposed models and algorithms. The research demonstrates that the adjustment of the proposed MILP model outperforms the existing formulation when applied to the homogeneous case. The study also uncovers interesting practical implications, including the analysis of the impact of different transporter types in the system. It shows that utilizing a fleet of heterogeneous transporters can improve the overall performance of the job shop compared to a relevant homogeneous case. The importance of the study is emphasized by highlighting the negative consequences of disregarding transporters' differences during the scheduling phase. [ABSTRACT FROM AUTHOR]

An introduction is presented for this issue which includes research papers from the 8th MOSIM international conference that focus on topics such as theory and practice related to optimisation methods in manufacturing, inventory control, and stochastic machine scheduling.

This paper proposes a multi-site global optimisation model of blending operations, alternative routings and order scheduling with a co-production flow. It is performed in a phosphoric supply chain owning three open-pit mines of different geological structures and chemical compositions, each having a dry blending plant. One main challenge of the phosphate industries is to produce merchantable ores (MO) that verify a quality charter (chemical composition) with chemical heterogeneous source ores (SO). Thus, a process of SO blending followed by a treatment is mostly necessary to obtain the required MO. Six alternative routings exist to produce an MO; one of them involving a calcination plant generates a co-product. The model objective is to determine the least costly production programme of a set of MO orders to be delivered within precise time windows, in given quantities and compliance with a specific quality charter, by assigning for each MO its blending plant, routing, blend of SOs and production schedule; it also defines the feeding of the blending plants. A real case study illustrates the proposed model. [ABSTRACT FROM AUTHOR]

This paper studies a new variant of integrated production scheduling and vehicle routing problem where production of customer orders are performed under job-shop environment and order deliveries are made by a heterogeneous fleet of vehicles, each of which is allowed to take multiple trips. Two conflicting objectives are considered, namely minimisation of the total amount of CO2 emitted by the vehicles and minimisation of maximum tardiness resulting from late deliveries. To this end, we present a bi-objective mixed-integer programming formulation. Augmented ε-Constraint (Augmecon) method is implemented to find Pareto optimal solutions. Due to problem complexity, Augmecon cannot provide solutions even with small-sized problems. Thus, we adopt Pareto Local Search (PLS) and non-dominated sorting genetic algorithm-II (NSGA-II) for practical sized instances. For small-sized instances involving 5, 6, and 7 customers, experimental results indicate that CPU time of Augmecon are 11, 84, and 524 sec, respectively with an average number of Pareto efficient solution of 3.5. In terms of hypervolume index, Augmecon shows the best performance, followed by NSGA-II with 11.32% and PLS with 20.75% degradation for small-sized instances. For medium and large-sized instances, PLS shows worse performance than NSGA-II by 16.87% and 40.48%. [ABSTRACT FROM AUTHOR]

Sterile services departments are special units designed to perform sterilisation operations in an efficient way within a hospital. The delays in sterilisation services cause significant disruptions on surgery schedules and bed management. To prevent the delays, an upper time limit can be imposed on the time spent in the sterilisation services. In this paper, we propose a mathematical modelling approach for the optimum capacity planning of a sterilisation service unit considering the uncertainties in the sterilisation process. The model aims to find the optimum capacity on four tandem steps of the sterilisation whilst at the same time minimising the total cost and keeping the maximum time in the system below a limit. Assuming general distributions for service and interarrival times, an approximation structure based on robust optimisation is used to formulate the maximum time spent in the system. We analysed the structural property of the resulting model and found that the relaxed version of the model is convex. The real data from a large sterilisation services unit is used for computational experiments. The results indicated that the approximation fits well against the simulated maximum time in the system. Other experiments revealed that an upper limit of 7 hours for the sterilisation services balances the cost vs. robustness trade-off. [ABSTRACT FROM AUTHOR]

Severe environmental problems have made green scheduling an emerging research hotspot. In this paper, a permutation flow shop energy-efficient scheduling problem that considers multiple criteria is investigated. The aim is to find the optimal job processing sequence and conveyor speed that minimise both the makespan and total energy consumption. In addition to two types of common criteria, namely, machine-based criterion (i.e. sequence-dependent setup time) and energy-based criteria (including both the transportation time control strategy and machine shutdown strategy), a human-based criterion (i.e. a position-based learning effect) is introduced. A bi-objective programming model is developed, and a multi-objective iterated greedy (MOIG) is designed to reach the Pareto front of the model. Considering that there are two types of decisions in the model (i.e. job sequence and conveyor speed), two algorithm alternatives are designed based on the job sequence and conveyor speed, respectively. Meanwhile, an acceptance criterion with advantages in terms of the convergence speed and solution diversity is proposed. Existing algorithms, including NSGA-II and MOEA/D, are introduced to evaluate the performance of the MOIG. The results emphasise the efficiency of the MOIG. Overall, the model and MOIG effectively improve the green efficiency of enterprises and can reasonably control operating costs. [ABSTRACT FROM AUTHOR]

This paper studies a two-agent scheduling problem on mixed batch machines in parallel. A mixed batch machine can process several jobs simultaneously as a batch, as long as the number of jobs in the batch does not exceed the machine capacity. The processing time of a mixed batch is the weighted sum of the maximum processing time and the total processing time of jobs in the batch. The objective is to minimise the weighted sum of two agents' makespans. We present four approximation algorithms based on two strategies: the machine-centric strategy and the agent-centric strategy. For each strategy, a full batch longest processing time (FBLPT) rule and a longest processing time greedy (LPTG) rule are used. We conduct theoretical analyses based on the worst-case performance ratio to provide the provable guarantees on the performances of the algorithms, and simulation analyses based on randomly generated instances to evaluate the average performances of the algorithms. Furthermore, we verify the consistency between the theoretical and simulation results. The algorithms using agent-centric strategy perform better than ones using machine-centric strategy. Finally, we provide managerial insights for the problem by analysing the technological parameters of batches, importance of agents, and demand seasonality. [ABSTRACT FROM AUTHOR]

With city logistics becoming more and more important, increasing attention has been paid to the 'last-mile delivery' in urban areas. We investigate a novel crowdsource-enabled integrated production and transportation scheduling problem in the paper. The problem is first formulated into a mixed-integer linear program and its strong NP-hardness is proved. To better understand this complex problem, two sub-problems: a production and transportation scheduling problem and a crowdsourced bid selection problem are analysed. Based on problem properties, a Genetic Algorithm (GA) and a lower bound (LB) are developed to solve the original problem. Experimental results with up to 100 customers show that the GA outperforms the well-known commercial MIP solver CPLEX. Especially, (1) the GA can yield near-optimal solutions for all the tested instances with an average gap of 10.17% from the lower bound, while CPLEX provides feasible solutions only for instances with no more than 30 customers; (2) the average computation time of the GA is only 0.93% of that required by CPLEX; Besides, sensitivity analysis demonstrates advantages of introducing crowdsourced delivery into city logistics. [ABSTRACT FROM AUTHOR]