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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]

Nowadays, achieving higher levels of flexibility in manufacturing systems is necessary to maintain and enhance competitiveness. Accordingly, a new generation of production machine, namely Reconfigurable Machine Tool (RMT), has recently been introduced that can be effectively adapted to changes. Nevertheless, such systems are more worker-reliant, and neglecting workforce aspects results in suboptimal or even infeasible production schedules. In this regard, this study investigates an integrated lot-sizing and scheduling problem benefiting from RMTs under workforce constraints. First, a novel Mixed-Integer Linear Programming (MILP) model is provided to formulate the problem. Afterward, to confront the high complexity of the problem, an efficient Decomposition Heuristic (DH) empowered by a tailored feasibility cut is devised. A combination of MILP and Constraint Programming (CP) is employed in the DH to model the relevant master and sub-problems, respectively. Finally, the performance of the DH compared to the MILP model and an extended lower bound is evaluated. Moreover, the advantages of utilizing RMTs in the system are explored based on four defined key performance indicators. [ABSTRACT FROM AUTHOR]

A production plan gives the quantity of products to release on the shop floor in each period, where a period may represent a week or a month. The plan is the basis for negotiating order acceptance and delivery dates with customers and suppliers. The production plan must respect the available capacity on the shop floor, as underloading the shop floor leads to a loss of opportunity, and thus, a loss of competitiveness for the company. To properly manage the production capacity while negotiating with suppliers and customers, the production planners need a tool to accurately estimate the capacity consumption in each period. The computation of capacity consumption requires creating a detailed production schedule which is a complex task. Algorithms that find close to optimal schedules in a complex manufacturing environment are often time-consuming, which is impractical in a negotiation context. We investigate machine learning models to predict capacity consumption. We consider a flexible job-shop as commonly encountered in practice, and proposed several machine learning models. Namely, several variants of linear regression, decision trees, and artificial neural networks. Numerical experiments showed that our models outperform those found by both an exact approach and dispatching rules when computation time is short. [ABSTRACT FROM AUTHOR]

The transformation of production mode leads to the need to strictly ensure the order in-time delivery. The global control ability of manufacturing workshops has become a necessary capability for enterprises. The real-time accurate Order Remaining Completion Time (ORCT) prediction allows managers to master the production schedule fluctuation, which provides criteria for workshop management. Due to the widespread deployment of Internet of Things (IoT) devices in the workshop, the difficulty of systematic processing and analysis of multi-dimensional heterogeneous data has been the main pain point of ORCT prediction. To tackle these problems, a Manufacturing Big Data (MBD)-driven ORCT prediction method based on Salp Swarm Algorithm (SSA) and Bidirectional Long Short-Term Memory (BiLSTM) is proposed. An attribute selection algorithm combined with max-relevance and min-redundancy and regularisation is used to mine key data from MBD. An SSA-BiLSTM model is proposed to achieve efficient and accurate ORCT prediction. The prediction model is supported by BiLSTM, and the hyperparameters are optimised by SSA. Finally, a case study about ORCT prediction in the IoT-enabled manufacturing workshop is presented. The result verifies that the proposed ORCT prediction method has obvious advantages over the other three traditional methods in accuracy and efficiency. [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]

Scheduling is a complex task due to the need to optimise multiple competing objectives and react to unpredictable events that may occur during production execution. The strategy of predictive-reactive scheduling can be used to reconcile the conflict between the original schedule and the current shop floor situation. This study seeks to present an inventory data-driven predictive-reactive production scheduling model that supports the evolving concepts of the Industry 4.0. Periodically, a machine learning technique provides predictive scheduling considering a best-case scenario according to an established Key Performance Indicator (KPI). Then, material non-availability causes disruptions in production, which triggers the Simulation-Based Optimization (SBO) method to handle these events. Thus, SBO provides a reactive schedule with the best set of priority rules to sequence jobs on each machine according to the data on the shop floor. This model was validated with a real case study using data collected from a metal-mechanical company. Considering the service level KPI, the results showed that the model is able to find a better solution in the compared scenarios. Therefore, even in a dynamic and stochastic scenario, with machine breakdowns, quality problems, raw material delays, and accuracy issues, the model proved efficient in mitigating these variations' effects. [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]

In this work, we study the multi-product dynamic lot-sizing problem with capacity constraints and batch ordering. This problem arises in short to medium range production scheduling for several products over a finite number of periods to meet known demand. Each period has a capacity for placing orders, and every order for each product must have a fixed quantity, or batch size, though multiple orders can be placed for each product. We define three mixed-integer linear programming (MILP) models and apply Lagrangian relaxation to formulate the corresponding dual problems by relaxing the capacity constraints. The aim is to identify the dual problem that is the easiest to solve and provides the solution with the smallest duality gap. Subgradient optimisation is applied to solve the preferred Lagrangian dual model, which uses one of two heuristics to find good feasible solutions. We also show that the special case, where the batch sizes for all products are the same, can be modeled as a transportation problem. A set of numerical experiments is designed to compare the performance of the Lagrangian relaxation approach with a commercial MILP solver to identify the version of the subgradient algorithm and the MILP model that provide the best solutions. [ABSTRACT FROM AUTHOR]

In the maintenance optimisation framework, grouping maintenance is a promising solution for maintenance planning of multi-component systems, in which maintenance activities are performed together to reduce maintenance costs. One of the most widely identified challenges in real applications of grouping maintenance is that it may disturb the maintenance workload balance (smoothness), causing many difficulties in production and/or labour scheduling and inventory management. In this study, we propose a joint optimisation approach for maintenance grouping and workload balancing to address the above challenge. First, a mathematical model of the joint optimisation problem was derived. A multi-objective grouping optimisation approach based on the Weighted Sum model and Genetic Algorithm was implemented to determine the Pareto-optimal grouping solution. The proposed approach was applied to a real case study of an automotive plant comprising 40 production lines with 1090 components. The results highlighted the advantages, effectiveness, and flexibility of the proposed maintenance approach in real-world applications. [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]

This study uses an agent-based approach with a combinatorial auction mechanism to solve the joint order acceptance and assembly job shop scheduling problem. A set of jobs is offered. Each job has a revenue, ready time, due date, deadline, and consists of a set of operations with precedence relationships. Jobs that deviate from their due dates incur earliness/tardiness penalties. An operation may require several units of capacity per time unit and a resource could have multiple units of capacity. The manufacturer can reject any job to satisfy the capacity constraints and maximise the overall profit. We develop a mathematical model for the problem, then use an agent-based approach to solve it. First, the relaxed problem is decomposed into a set of job-level subproblems. Each job is optimised individually without considering the capacity constraints. Profitable jobs at the individual level submit their optimal schedules as combinatorial bids to an auctioneer to acquire combinations of resource capacity-time units. Then, the auctioneer records the profit upper bound, resolves capacity conflicts to reach a feasible solution, records the profit lower bound, and updates the dual variables. Experimental results show that the proposed methodology can solve large-sized problems in reasonable CPU times. [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 analyse the joint scheduling of spare parts production and service engineers in a multi-site maintenance system. In the system, for each failure, a service engineer with the required spare part needs to be allocated for on-site maintenance. If one of the required resources is not readily available, the maintenance task can be satisfied via an external channel with quick responsiveness but high involved costs. Service providers need to make an efficient plan, including production scheduling of spare parts, allocation of service engineers and outsourcing strategy. First, a mathematical model with the objectives of minimum total outsourcing costs and minimum weighted tardiness is formulated. Then, a novel and knowledge-based heuristic algorithm is developed, namely progressive Pareto algorithm based on step-size (PPAS). To verify the performance of PPAS, it is compared against other well-known algorithms, including NSGA-II, MOEA/D, NNIA, RIPG, MMOIG and MNNIA. Finally, the effectiveness of the joint scheduling mode is demonstrated by comparing it with the separate optimisation mode of spare parts production and workforce allocation. Highlights Analyse the joint scheduling of spare parts production and service engineers Construct a bi-objective optimisation model Develop a progressive Pareto algorithm based on step-size Verify the superiority of the proposed algorithm and joint scheduling mode [ABSTRACT FROM AUTHOR]

Inspired by real-life applications, mainly in hand-intensive manufacturing, the incorporation of learning effects into scheduling problems has garnered attention in recent years. This paper deals with the flowshop scheduling problem with a learning effect, when minimising the makespan. Four approaches to model the learning effect, well-known in the literature, are considered. Mathematical models are providing for each case. A solver allows us to find the optimal solution in small problem instances, while a Simulated Annealing algorithm is proposed to deal with large problem instances. In the latter, the initial solution is obtained using the well-known Nawaz-Enscore-Ham algorithm, and two local search operators are evaluated. Computational experiments are carried out using benchmark datasets from the literature. The Simulated Annealing algorithm shows a better result for learning approaches with fast learning effects as compared to slow learning effects. Finally, for industrial decision makers, some insights about how the learning effect model might affect the makespan minimisation flowshop scheduling problem are presented. [ABSTRACT FROM AUTHOR]

Human–robot collaboration has been incorporated into production and assembly processes to promote system flexibility, changeability and adaptability. However, it poses new challenges to resource allocation and production scheduling due to its intrinsic uncertainty and also the increasing complexity of resources. This paper investigates a stochastic flow shop scheduling problem in the context of human–robot collaboration. The goal is to achieve efficient utilisation of flexible resources including human workers and cobots and take full advantage of human–robot collaboration in production scheduling. A stochastic Cobb–Douglas production function is utilised to evaluate the production efficiency of human–robot collaboration considering instabilities of human performance. A joint chance-constrained programming model is formulated to ensure that the required system performance can be achieved. A CVaR approximation-based approach is proposed to solve the formulated model with mixed-integer variables and a nonconvex constraint. The effectiveness of the formulated model and the efficiency of the proposed solution approach are evaluated via numerical experiments. Computational results show the superiority of our solution approach over three other approaches including Bonferroni approximation, scenario approach and individual chance-constrained programming. [ABSTRACT FROM AUTHOR]

This work extends the energy-efficient job shop scheduling problem with transport resources by considering speed adjustable resources of two types, namely: the machines where the jobs are processed on and the vehicles that transport the jobs around the shop-floor. Therefore, the problem being considered involves determining, simultaneously, the processing speed of each production operation, the sequence of the production operations for each machine, the allocation of the transport tasks to vehicles, the travelling speed of each task for the empty and for the loaded legs, and the sequence of the transport tasks for each vehicle. Among the possible solutions, we are interested in those providing trade-offs between makespan and total energy consumption (Pareto solutions). To that end, we develop and solve a bi-objective mixed-integer linear programming model. In addition, due to problem complexity we also propose a multi-objective biased random key genetic algorithm that simultaneously evolves several populations. The computational experiments performed have show it to be effective and efficient, even in the presence of larger problem instances. Finally, we provide extensive time and energy trade-off analysis (Pareto front) to infer the advantages of considering speed adjustable machines and speed adjustable vehicles and provide general insights for the managers dealing with such a complex problem. [ABSTRACT FROM AUTHOR]

Nowadays, the manufacturing sector needs higher levels of flexibility to confront the extremely volatile market. Accordingly, exploiting both machine and workforce reconfigurability as two critical sources of flexibility is advantageous. In this regard, for the first time, this paper explores an integrated production scheduling and workforce planning problem in a Reconfigurable Manufacturing System (RMS) benefiting from reconfigurable machines and human-robot collaboration. A new Mixed-Integer Linear Programming (MILP) model and an efficient Constraint Programming (CP) model are developed to formulate the problem, minimising the makespan as the performance metric. Due to the high complexity of the problem, the MILP model cannot handle large-sized instances. Hence, to evaluate the performance of the CP model in large-sized instances, a lower bound is derived based on the relaxation of the problem. Finally, extensive computational experiments are carried out to assess the performance of the devised MILP and CP models and provide general recommendations for managers dealing with such a complex problem. The results reveal the superiority of the CP model over the MILP model in small- and medium-sized instances. Moreover, the CP model can find high-quality solutions for large-sized instances within a reasonable computational time. [ABSTRACT FROM AUTHOR]

This paper studies the customer order scheduling problem in the context of additive manufacturing. The study discusses an integrated problem involving the nesting of parts as well as the scheduling of batches of nested parts onto unrelated parallel machines. A mixed-integer programming model is presented, based on existing formulations from the literature, that integrates different materials and sequence-dependent setup times. Additionally, a metaheuristic based on an iterated local search is proposed for the problem configuration under consideration. Focusing on minimizing the total weighted tardiness of orders, the efficiency of the heuristic approach is evaluated using comprehensive test data. Further, we show the importance of the considered order-related objective by using qualitative analysis. [ABSTRACT FROM AUTHOR]

We investigate a stochastic distributed appointment assignment and scheduling problem, which consists of assigning appointments to distributed service units and determining service sequences at each service unit. In particular, the service time duration and release time uncertainties are well-considered. The solution to this generic problem finds interesting applications in distributed production systems, healthcare systems, and post-disaster operations. We formulate the problem as a two-stage stochastic program to minimise the total transportation cost and expected makespan, idle time or overtime, and apply the sample average approximation method to make the problem tractable. We then develop a stochastic logic-based Benders decomposition method, decomposing the problem into a master problem and a subproblem. The master problem determines the appointment assignment variables, and the subproblem handles the sequence and service start time variables. Benders optimality cuts are generated from the subproblem's solution and added to the master problem. The developed stochastic logic-based method is advantageous since it can manage many scenarios in parallel. We further consider each appointment's due date, minimise the weighted earliness and tardiness, and adjust the developed method to solve this variant. Experiments on random instances demonstrate the excellent performance of the proposed model and methods. [ABSTRACT FROM AUTHOR]

Increased flexibility in job shops leads to more complexity in decision-making for shop floor engineers. Partial Flexible Job Shop Scheduling (PFJSS) is a subset of Job shop problems and has substantial application in the real world. Priority Dispatching Rules (PDRs) are simple and easy to implement for making quick decisions in real-time. The present study proposes a novel method of integrating Multi-Criteria Decision Making (MCDM) methods and the Discrete Event Simulation (DES) Model to define job priorities in large-scale problems involving multiple criteria. DES approach is employed to model the PFJSS to evaluate Makespan, Flow Time, and Tardiness-based measures considering static and dynamic job arrivals. The proposed approach is implemented in a benchmark problem and large-scale PFJSS. The integration of MCDM methods and simulation models offers the flexibility to choose the parameters that need to govern the ranking of jobs. The solution given by the proposed methods is tested with the best-performing Composite Dispatching Rules (CDR), combining several PDR, which are available in the literature. Proposed MCDM approaches perform well for Makespan, Flow Time, and Tardiness-based measures for large-scale real-world problems. The proposed methodology integrated with the DES model is easy to implement in a real-time shop floor environment. [ABSTRACT FROM AUTHOR]

According to [Dolgui, Alexandre, and Jean Marie Proth. 2010. Supply Chain Engineering: Useful Methods and Techniques. Vol. 539. Springer.], advancing tactical levels in production systems has led to the disappearance of static scheduling in favour of dynamic scheduling. Additionally, the evolving challenges in the supply chain paradigm have significantly impacted the organisation of production systems. This shift has moved scheduling issues from the tactical to the strategic level, resulting in linear organisations encompassing scheduling decisions. [Proth, Jean Marie. 2007. "Scheduling: New Trends in Industrial Environment." Annual Reviews in Control 31 (1): 157–166. .] emphasised that real-time scheduling in production systems has become a pivotal area of research. He presented several open problems for researchers to address in this context, including (1) the development of real-time algorithms capable of handling multiple operations on the same product and unrelated resources, (2) adapting previous schedules with certain modifications, (3) addressing unforeseen actions that arise randomly in real-time planning, and (4) exploring cyclic scheduling problems with size limits as alternative solutions to heuristic approaches. This paper reviews the evolving trends in light of J.M. Proth's predictions and advice within the aforementioned domains. [ABSTRACT FROM AUTHOR]

In this paper, we address a Stochastic-Demand Assembly Job Shop Scheduling Problem (SD-AJSSP) in the presence of the commonality of sub-assemblies across products. We propose a new production methodology, named Assemble-to-Order with Commonality of Sub-Assemblies (ATO-CS) to not only solve the SD-AJSSP, but also, achieve a successful implementation of a mass customisation system by collectively aiming to (1) keep the production costs low by leveraging upon commonality of sub-assemblies in products' BOM and producing sub-assemblies on a mass scale during one of the two stages of production, (2) minimise the loss due to excess inventory build-up in anticipation of stochastic demand of products by postponing the production of certain apex sub-assemblies in products' BOM until the actual demand is realised, and (3) reduce the time of the products' delivery to customers. The ATO-CS method determines optimum production levels as well as schedules assembly operations/jobs over the machines at each stage of production, where the second stage is an assembly job shop and is shown to outperform commonly-used production methodologies. We also develop an algorithm for its implementation and show its efficacy over the use of the state-of-the-art commercial solver CPLEX® in obtaining a lower solution cost and smaller optimality gap. [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]

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]

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]

Lot splitting is one of the effective technologies of time-based strategy and has been widely studied in a variety of production environments. Nevertheless, the literature on its application in seru production has been highly scarce until now. Seru system is composed of simple equipment and multi-skilled workers, which can be quickly converted from the traditional assembly line to seru units. As an innovative production mode, seru production inevitably allows applying lot splitting in the real world. Therefore, a multi-objective model is studied for line–cell conversion with lot splitting, aiming at determining the trade-off among makespan, inter-seru system balancing, and intra-seru system balancing. Due to the proposed model's NP-hard nature, an improved NSGA-II was developed to solve it. Finally, extensive numerical simulations are conducted. Compared to no lot splitting, lot splitting is improved by 4.2% and 3.7% in terms of inter-seru system balancing and makespan respectively. The better efficiency and effectiveness of the improved NSGA-II are proved by comparisons with other state-of-the-art algorithms. Additionally, a sensitivity analysis is conducted to ascertain the degree of contribution of the model parameters towards the value of objectives, which provides management implications to support the decision-making of seru production for the enterprise. [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]

A set of jobs has to be processed on identical machines. Every job may be processed on any available machine without preemptions. The criterion is to minimise the makespan (i.e. the completion time of the last job in a schedule). During the realisation of a schedule, durations of some jobs may deviate from the initial values estimated before scheduling. Other jobs have fixed durations that are known before scheduling. We conduct a stability analysis of the optimal semi-active schedule. First, we derive necessary and sufficient conditions for an optimal schedule to be unstable with respect to infinitely small variations of the non-fixed durations (the stability radius of an unstable schedule is equal to zero). Second, we show that the stability radius of an optimal schedule could be infinitely large. Furthermore, several lower and upper bounds on the stability radius have been established. Third, we derive a formula and develop an algorithm for calculating stability radii. [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]

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 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]

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]

Motivated by the practical research and development (R&D) process in high-end equipment manufacturing, this study investigates a bi-level scheduling problem in a complex R&D project network, where each project contains multiple modules with a complete task network. In the bi-level scheduling problem, the upper-level problem is that the R&D project leader makes the decision on allocating all R&D project modules to limited R&D researchers and the objective is to minimise the total penalty cost of all projects, and the lower-level problem is that the researchers schedule and sort the assigned tasks to minimise their minimum makespan. The different capacity of researchers is considered, and some structural properties are derived based on the capacity analytics. To tackle this complex scheduling problem, an effective Variable Neighborhood Search algorithm based on the 'less is more' concept is proposed, where a Multi-Greedy Heuristic is incorporated. Interestingly, we observe that simpler algorithmic strategies may lead to better algorithmic performance. Computational experiments are carried out to demonstrate that the performance of the proposed algorithm is efficient and stable. [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]

We examine the parallel machine scheduling problem where a set of jobs are to be processed by a set of unrelated parallel machines. We examine the most general among the variations for which an exact method has been proposed regarding makespan minimisation. This is because, apart from unrelated machines, we allow for (i) job splitting: each job's quantity can be split and processed by multiple machines simultaneously; (ii) sequence- and machine-dependent setup times: the setup time when job j succeeds k is different than the time when k succeeds j and varies also per machine m; and (iii) setup resource constraints: the number of setups that can be performed simultaneously on different machines is restricted. We present novel lower bound formulations and a heuristic that solves instances of up to 1000 jobs in a few minutes at an average gap of less than 20 %. Then, we propose a logic-based Benders decomposition, which, coupled with our heuristic, solves instances of up to 200 jobs and 20 machines to near optimality in less than two hours. Our method is used for a broad range of instances from textile manufacturing, thus yielding valuable managerial insights on makespan's versatility under varying machines or resources. [ABSTRACT FROM AUTHOR]

3D printing technology is fundamentally transforming how companies are run and managed today. This work analyzes the problem of integrated production and transportation of automotive spare parts in the context of 3D printing. We consider two sets of customers – scheduled and breakdown maintenance – serviced by the same resource but with distinct delivery modes. We propose a mixed-integer programming (MIP) formulation for optimally solving small problem instances. We develop an exact approach based on column generation (CG) for large cases by reformulating the MIP model as a set-covering problem through Dantzig-Wolfe decomposition. We design and deploy two acceleration strategies for the quicker convergence of the CG approach. Through extensive computational experiments, we establish the superiority and suitability of the proposed solution methodology for solving real-life problems at terse computational times. [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]

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]

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]

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]

In the automotive industry, a great challenge of production scheduling is to sequence cars on assembly lines. Among a wide variety of scheduling approaches, academics and manufacturers pay close attention to two specific models: Mixed-Model Sequencing (MMS) and Car Sequencing (CS). Whereas MMS explicitly considers the assembly line balance, CS operates with sequencing rules to find the best car sequence fulfilling the assembly plant requirements, like minimising work overload for assembly workers. Meanwhile, automakers including Renault Group are increasingly willing to consider other requirements, like end-to-end supply chain matters, in production planning and scheduling. In this context, this study compares MMS- and CS-feasible solution spaces to determine which workload-oriented sequencing model would be the most appropriate to later integrate new optimisation. We introduce two exact methods based on Dynamic Programming to assess the gap between both models. Numerical experiments are carried out on real-life manufacturing features from a Renault Group assembly plant. They show that MMS generates more feasible sequences than CS regardless of the sequencing rule calculation method. Only the sequencing rules used by real-life production schedulers result in a higher number of distinct feasible sequences for CS, highlighting that the plant might selecta sequence with work overload situations. [ABSTRACT FROM AUTHOR]

To remain competitive in the current e-commerce environment, warehouses are expected to handle customer orders as efficiently and quickly as possible. Previous research on order picking in a static context has shown that integrating batching, routing and scheduling decisions leads to better results than addressing these planning problems individually. In this study we propose an integrated solution approach that is able to deal with dynamic order arrivals, a problem often encountered in practice. Furthermore, we demonstrate the need to anticipate on future order arrivals to keep customer service levels high. We develop a new large neighbourhood search algorithm to solve the online, integrated batching, routing and scheduling problem. First, the algorithm is shown to outperform the current state-of-the-art static solution algorithm. Next, we develop an experimental design based on real-life data, to test the applicability of the model in different settings. The results of this experimental design are used to obtain insights on the particularity of this online, integrated problem. The effect of several real-life characteristics is demonstrated by using an ANOVA, leading to several managerial insights that may help companies to operate efficiently without jeopardising customer satisfaction. [ABSTRACT FROM AUTHOR]

We study an integrated optimisation problem with blending, scheduling, and routing components for a melted material blending production system. The problem is formulated as a mixed-integer linear programming model that considers the blending machine environment, due dates, target amounts, required chemical compositions of the products, and ready times of the materials in containers. This model aimed to determine the container pairings, blending plants for container pairs, and schedules for blending operations while minimising the total end time of material usage, total penalty for violating component specifications, and employee workload. Further, we propose a three-stage approach that involves solving a relaxed problem and then resolving the problem with fixed variables. We developed a combinatorial Benders decomposition algorithm with a minimal infeasible subsystem identification algorithm for the blending scheduling problem. The experimental results indicate that the proposed method can find high-quality solutions within a reasonable amount of time. [ABSTRACT FROM AUTHOR]

Aiming at the joint optimisation problem of uncertain distributed manufacturing and preventive maintenance (PM) for semiconductor wafers considering multi-energy complementary (UDMPM-MEC), a bi-level integrated scheduling model is constructed with interval makespan, total interval carbon emissions and total interval cost as the optimisation objectives. The upper model is used to obtain the joint optimisation scheduling scheme of distributed manufacturing and PM, and the lower model determines the energy allocation scheme on this basis. Given the problem characteristics, we propose an improved multi-objective whale swarm algorithm (IMOWSA). By designing jobs-to-factories allocation strategy, synchronous scheduling maintenance strategy, multi-energy complementary energy allocation decoding strategy, individual distance calculation strategy, multi-neighbourhood search strategy and deduplication strategy, the local and global search are effectively balanced, and the convergence precision is improved. A large number of simulation experiments and comparative analyses show that the IMOWSA algorithm is feasible and effective to solve this problem. [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]