Job Sequence Research Articles

An Optimization Model for Production Scheduling in Parallel Machine Systems

The efficiency and quality of the manufacturing industry are greatly influenced by production scheduling, which makes it a crucial aspect. A well-designed production scheduling scheme can significantly enhance manufacturing efficiency and reduce enterprise costs. This paper presents a tailored optimization model designed to address a more complex production scheduling problem that incorporates parallel machines and preventive maintenance. The proposed solutions aim to achieve a balance between job sequence and machine reliability, considering the minimum maintenance cost rate for determining maintenance cycles of deteriorating machines in real manufacturing scenarios. Furthermore, the objective of minimizing the maximum completion time guides machine assignment and job sequence based on maintenance constraints. The innovation lies in the introduction of a greedy algorithm that utilizes a water injection model to address this NP-hard integrated problem. A pre-distribution model is constructed using the water injection model, and its solution is utilized as input for constructing the production scheduling model, which aids in determining machine assignment and job sequence. This algorithm demonstrates remarkable effectiveness and efficiency, enabling the achievement of an optimal solution. A numerical example is presented to illustrate the computational process, accompanied by an extensive discussion of the results showcasing improved performance. Furthermore, the optimization model developed in this paper can be adapted to tackle the production scheduling problem with modifications tailored for parallel machines.

Distributionally robust single machine scheduling with release and due dates over Wasserstein balls

Single machine scheduling aims at determining the job sequence with the best desired performance, and provides the basic building block for more advanced scheduling problems. In the present study, a single machine scheduling model with uncertain processing time is considered by incorporating the job release time and due date. The job processing time follows unknown probability distribution, and can be estimated via the historical data. To model the uncertainty, the processing time distribution is defined over a Wasserstein ball ambiguity set, which covers all feasible probability distributions within the confidence radius of the empirical distribution, known as the center of the ball. Then a data-driven distributionally robust scheduling model is constructed with individual chance constraints. In particular, two equivalent reformulations are derived with respect to the ℓ1-norm and ℓ2-norm metrics of the Wasserstein ball, namely, a mixed-integer linear programming and a mixed-integer second order cone programming model, respectively. To accelerate the solving of large-scale instances, a tailored constraint generation algorithm is introduced. In the numerical analysis, the proposed distributionally robust scheduling approach is compared with the state-of-the-art methods in terms of out-of-sample performance.

Open shop scheduling with group and transportation operations by learning-driven hyper-heuristic algorithms

Open shop scheduling problems (OSSPs) are complex scheduling problems, which have been extensively studied in the literature. Group and transportation activities are two important aspects of OSSPs that still need attention. This work considers an OSSP with group and transportation operations to minimize maximum completion time by solving three key sub-problems: job assignment among groups, job sequence in groups and group sequence on machines. Firstly, an integer programming model is formulized to define the problem. Secondly, a learning-driven hyper-heuristic algorithm is developed by incorporating a Q-learning method and four meta-heuristics, i.e., genetic algorithm, artificial bee colony optimization, variable neighborhood search method and Jaya algorithm. The Q-learning method is devised to select the most promising meta-heuristic for performing at each iteration. Three neighborhood structures are designed by integrating critical machines and critical paths. Finally, the developed model is verified by an exact solver CPLEX, and the comparison results exhibit that CPLEX is effective for instances with ten jobs. For the instances with more than ten jobs, the developed algorithm wins CPLEX in terms of computation accuracy and efficiency, signifying its excellent performance in finding better solutions. Furthermore, four meta-heuristics mentioned above and three state-of-the-art meta-heuristics are employed for comparisons in solving a set of benchmark test instances. The results confirm that the formulated model and algorithm have stronger competitiveness in handling the considered problems.

Identical Parallel Machine Scheduling to Minimize Makespan Using Suggested Algorithm Method at XYZ Company

XYZ company produce the various shape of motor spare parts product. The company has threeidentical parallel spot welding machines that use a random method of production scheduling, basedon machine capacity without any sequence of jobs, and only use daily production targets given tooperators. Based on the data, the actual scheduling of the machines has a very large completion timedifference between each machine, or the machine loading is uneven. As a result, the makespanbecomes longer with a value of 440000 seconds (26 days). This research aims to minimize the existingmakespan by giving proposed scheduling, using the suggested algorithm method, which has a smallnumber of iterations and has an optimal result. The method begins with the longest processing timesequence rule which is used as the upper bound for the first iteration, then continued to calculate thelower bound and machine workload. The calculation stops at the 15th iteration because the completiontime value exceeds the lower and upper bound so that the optimal scheduling taken is scheduled inthe 14th iteration with a makespan value of 914412 seconds (16 days). The proposed scheduling canminimize the makespan from the actual schedule by 38%.

Lower and upper bounds for scheduling a real-life assembly problem with precedences and resource constraints

In this work, we consider a real-life scheduling problem involving the production of off-road vehicles using a three-level assembly process, subject to precedence, machines, and resource constraints. This problem shares multiple characteristics with other scheduling problems such as the Parallel Machine Scheduling and Flexible Flow Shop Problems. However, it also comprises less investigated aspects such as a specific job precedence structure resulting in a directed rooted in-tree and a global resource constraint limiting the number of simultaneously active machines. We present a straightforward adaptation of a time-indexed mathematical formulation to the problem and introduce a new lower-bounding procedure. To solve the problem, we propose constructive heuristics based on classical priority rules and adaptations of job sequencing heuristics. We also propose CORE, a specialized approach tailored to leverage the problem structure. All the algorithms are extensively evaluated on two benchmark sets, various shop floor configurations, and eight real-life scenarios. Our results reveal the general effectiveness of job sequencing approaches and demonstrate the overall superiority of CORE.

A new composite heuristic to minimize the total tardiness for the single machine scheduling problem with variable and flexible maintenance

Inspired by a real-world maintenance/job scheduling issue coming from the semiconductor industry, the present paper proposes a new heuristic algorithm structure for the single machine scheduling T-problem with flexible and variable maintenance, job release dates and sequence dependence setup times. Considering the typical short-term production planning needs, a single maintenance problem has to be scheduled within a certain time interval, along with a set of jobs so as to minimize the total tardiness. A twofold contribution emerges from the present paper. First, four mixed-integer linear programming models are developed for the problem at hand and compared in terms of time to convergence and computational complexity. Second, a novel heuristic algorithm, which has been configured into three distinct variants, has been compared with 17 alternative heuristics from the relevant literature based on a comprehensive experimental campaign. The numerical results allow the selection of the most suitable MILP model and confirm the effectiveness of the proposed heuristic approach.

Solving distributed assembly blocking flowshop with order acceptance by knowledge-driven multiobjective algorithm

In the era of Industry 4.0, industrial artificial intelligence technologies make production planning and scheduling systems more flexible. A new distributed assembly blocking flowshop problem with order acceptance and scheduling decisions (DABFSP_OAS) was investigated in this paper. Specifically, three objectives—the makespan, total energy consumption (TEC), and total profit (TP)—were addressed simultaneously. To address this problem, we established a knowledge-driven non-dominated sorting genetic algorithm-II (KDNSGAII). First, three initialization schemes based on the problem-specific property were introduced to generate diverse initial population. Then, to accelerate the convergence process, we developed multiple Pareto-based crossover and mutation operators. In addition, two novel destructive reinsertion strategies based on product and job sequence length were implemented to enhance the development ability of the algorithm. Finally, the designed strategies were evaluated. Comparisons and discussions showed that the KDNSGAII outperformed the other state-of-art multi-objective algorithms in solving DABFSP_OAS.

Joint optimization of job scheduling, condition-based maintenance planning, and spare parts ordering for degrading production systems

The system degrades gradually due to intrinsic properties and the external environment while processing scheduling jobs. Maintenance plays an important role in restoring system performance during the job scheduling process. In contrast to traditional integration studies of scheduling and maintenance, this study further considers spare parts inventory in integrated decision-making. By integrating spare parts ordering information, engineers can meticulously organize maintenance and spare parts replenishment, thereby bolstering system reliability and ensuring smooth production scheduling. This paper presents a mathematical model that jointly optimizes job scheduling, condition-based maintenance planning, and spare parts ordering for deteriorating production systems. The system's degradation state and spare parts inventory state are identified and revealed at the end of the scheduling job. A condition-based maintenance and spare parts ordering policy is triggered based on the captured joint state. Subsequently, we developed a joint optimization model to determine the optimal maintenance thresholds, spare parts ordering thresholds, and job sequences, aimed at minimizing the total weighted expected cost within the scheduling horizon. Finally, an effective genetic algorithm is proposed, and a practical case study involving a rolling mill system is utilized to validate the proposed policy.

Solving the project scheduling problem with dependent resource constraints

ABSTRACT Most resource-constrained project scheduling problems consider resources that are independent of the job processing sequence. However, solving project scheduling problems in some industrial manufacturing is challenging because the required resources depend on the job processing sequence in existing scheduling approaches. To address this issue, this paper proposes a dependent resource-constrained project scheduling problem formulated with two types of models: a conceptual model and a binary integer programming model. The performance of four proposed algorithms – binary integer programming, reduced subproblem of the binary integer programming, job sequence assignment, and job as early as possible – is tested on 68 combinations of numerical simulation experiments. The computational results show that the job as early as possible algorithm can find a better approximate solution for solving real-world problems. This achievement aids project managers in generating activity schedules and finding the approximate minimum makespan for a project with dependent resource constraints.

A modified binary bat algorithm for machine loading in flexible manufacturing systems: a case study

The machine loading (ML) problem of flexible manufacturing systems (FMS) has been recognised as one of the most important planning problems in the industry. This study aims to minimise the system unbalance by developing and testing a modified binary bat algorithm (MBBA), which satisfies the technological constraints such as the availability of machine time and tool slots. The proposed algorithm, coded in Matlab®, is tested on a case study referring to a major Italian company, which manufactures equipment and plants for the food industry. Two scenarios are evaluated to this end: an AS IS scenario, reflecting the current configuration of the production system, and a TO BE one, in which the MBBA is implemented for improving the system’s performance, by determining a new sequence of jobs, able to minimise the variance of the processing time across the various machines. The application of the MBBA reveals significant improvements in processing time compared to the approach currently used by the company. The results of the TO BE scenario allow deriving useful indications to operations managers, helping them to identify an alternative strategy to enhance the efficiency of the targeted production department.

A single-individual based variable neighborhood search algorithm for the blocking hybrid flow shop group scheduling problem

The Blocking Hybrid Flow Shop Group Scheduling Problem (BHFGSP) is prevalent within the manufacturing industry, where the ordering of groups poses a significant challenge for dispatchers. Moreover, the blocking constraints associated with jobs significantly influence energy consumption, yet these constraints are often overlooked in algorithm design. To address these issues effectively, a single-individual-based variable neighborhood search strategy is introduced. For the challenge of group ordering, a group-based neighborhood search strategy is proposed. This strategy is complemented by a job-based neighborhood search strategy to tackle the issues of blocking and job sequencing. These two neighborhood search strategies are designed to enhance the performance of the algorithm significantly. Furthermore, to augment the local search abilities of the proposed algorithm, the concept of a single-individual approach from the iterated greedy algorithm is integrated. The performance of the proposed algorithm is validated through 36 instances, demonstrating its efficiency in solving BHFGSPs compared to state-of-the-art algorithms. Notably, the proposed algorithm achieves a reduction in energy consumption by an average of 58% to 63.4% compared to previous best solutions.

A self-learning particle swarm optimization for bi-level assembly scheduling of material-sensitive orders

In modern assembly production, maximizing fulfillment becomes challenging amid resource scarcity and process unpredictability. This study addresses such issues with an effective approach to solving the integrated problem. This confluence presents a scenario where resource allocation mirrors a multidimensional knapsack and job sequencing corresponds to distributed assembly permutation flowshop scheduling, factoring in sequence-dependent setup times. Employing a mixed-integer mathematical model, we capture the configurations and objectives of the integrated problem. A special dual-level cooperative self-learning particle swarm optimization (SLPSO) metaheuristic is developed for improved hierarchical decision-making. Adaptive learning is harnessed to guide dynamic job selection under uncertainty, aiming for the highest total value. To minimize tardiness, a neighborhood search operator customizes sequences for each shop, considering changing setup times between jobs. Benchmark tests have been performed, showing that SLPSO surpasses established genetic algorithms and swarm techniques by 8%–15%. When implemented in an operational traditional pharmaceutical manufacturer, significant improvements were observed. The integrated structure harmonizes planning and scheduling stages, enhancing the algorithm via bidirectional feedback between decisions at various levels under uncertainty, thus providing guidance for real-world production.

Automated mobile robots routing and job assignment in automated factory

In the era of Industry 4.0, smart manufacturing and automated factories require advanced software and hardware resources. The decisions on AMR routing and job assignment are two of the key issues in automated factories. In this paper, we investigate the key issues by establishing a mixed integer linear programming model to minimize the makespan for a batch of products. As the problem considers the joint optimization of AMR routing, job-to-AMR assignments, job-to-machine assignments, and job sequencing on machines, the proposed model is comprehensive but complex, with million integer variables and constraints. To tackle this complexity, we introduce a hybrid heuristic approach based on variable neighborhood search and adaptive large neighborhood search algorithms. Three accelerating tactics, two specific neighborhood structures, and six tailored operators are devised to handle large-scale instances efficiently. Remarkably, our metaheuristic can handle 280 jobs within 800 s, resulting in twice the efficiency achieved by traditional factories. Some managerial implications are also obtained based on sensitivity analysis, which may be potentially useful to increase the operational efficiency in automated factory management.

Scheduling maintenance activities subject to stochastic job-dependent machine deterioration

This paper considers a maintenance scheduling problem on a single machine with a fixed job sequence involving job-dependent, stochastic deterioration. If the machine breaks down, then a time-consuming emergency maintenance activity needs to be conducted. Instead, planned maintenance activities can be conducted between jobs in order to improve the machine’s state and, thus, prevent the machine from breaking down. We distinguish two types of machines differing in the flexibility regarding the point of time when the maintenance activities need to be scheduled. The goal is to minimize the total expected completion time of jobs. We formalize two optimization problems, analyze their computational complexities, develop exact solution approaches, and conduct a computational study. Here, we show that our approaches can solve large instances to optimality within short run times and we analyze the advantage gained by planning maintenance activities depending on the actual state of the machine.

Novel integer L-shaped method for parallel machine scheduling problem under uncertain sequence-dependent setups

We study scheduling problems on unrelated parallel machines with uncertainty in job processing and sequence-dependent setup times. We first formulate this problem as a two-stage stochastic program using a scenario-based approach, in which the first-stage decisions involve job-machine assignments, and the second-stage deals with job sequencing. We then propose an innovative modified integer L-shaped method, uniquely designed to decompose the primary problem into independent subproblems at both the scenario and machine levels. We have augmented this method with a specialized integer optimality cut, which is further strengthened using a sequential lifting procedure. To broaden the applicability of our model and solution, we have adapted it to a distributionally robust optimization (DRO) framework under Wasserstein ambiguity. This process involves reformulating the DRO model into a mixed-integer linear program (MILP) using conic duality theory. Additionally, we integrate a distribution separation program to define the worst-case probability distribution during each iteration of the proposed integer L-shaped method, enhancing the computational speed for solving the DRO model. We conducted a series of numerical experiments to illustrate the effectiveness and scalability of the proposed solution methodology, which demonstrated highly promising results. Our innovative decomposition algorithms showed superior performance, achieving solution times that are significantly faster (up to two orders of magnitude) compared to the traditional integer L-shaped method for the stochastic scheduling model and the direct MILP reformulation of the DRO model. These results were obtained for problem instances solved to the exactness within the time limit. Moreover, the solution derived from the DRO model exhibited greater robustness in out-of-sample analysis with simulated data compared to the solution obtained from the stochastic model.

An improved genetic algorithm based on reinforcement learning for aircraft assembly scheduling problem

The assembly work of aircraft occupies a significant portion of the time in aircraft manufacturing. The aircraft assembly operations are highly challenging in the generation of production plans due to multiple constraints in the scheduling process. In addressing the aircraft assembly scheduling problem with the objective of minimizing the duration of assembly operations, a mathematical model has been established. This model incorporates characteristics such as job sequencing constraints, resource constraints, spatial constraints, and others, the problem-solving process is divided into two stages: determining the priority sequence of tasks and establishing the start times for each task. Proposing an improved genetic algorithm based on Q-learning, referred to as QIGA (Q-learning-based Improved Genetic Algorithm), utilizing Q-learning to dynamically adjust the crossover and mutation probability parameters during each iteration to enhance the algorithm’s convergence speed and search capabilities. Constructing a Markov Decision Process (MDP) model to dynamically adjust the crossover and mutation probability in the problem, proposing a state set partition rule based on the population’s fitness values, setting the action set to represent crossover and mutation probabilities in different intervals. Additionally, designing reward rules based on the population’s performance. Finally, the effectiveness of the proposed algorithm is verified with a real case containing 44 assembly operations, and the results show that the algorithm can solve the aircraft assembly scheduling problem well. Validating the feasibility and optimization effectiveness of the algorithm through various aircraft assembly scheduling cases of different scales. The experimental results indicate that, compared to traditional meta-heuristic algorithms, the proposed algorithm demonstrates superior optimization performance in aircraft assembly scheduling problems. It effectively reduces the total duration of aircraft assembly operations.

Dynamic flexible scheduling with transportation constraints by multi-agent reinforcement learning

Reinforcement learning-based methods have addressed production scheduling problems with flexible processing constraints. However, delayed rewards arise due to the dynamic arrival of jobs and transportation constraints between two successive operations. The flow time of operations can only be determined after processing due to the possibility that the solution for job sequencing may change if new operations are inserted in dynamic environments. Job sequencing is often overlooked in single-agent-based scheduling methods. The lack of information sharing between multiple agents necessitates that researchers manually design reward functions to fit the relationship between optimization objectives and rewards, thereby reducing the accuracy of the learned policies. Thus, this paper proposes a multi-agent-based scheduling optimization framework that facilitates collaboration between the agents of both machines and jobs to address dynamic flexible job-shop scheduling problems (DFJSP) with transportation time constraints. Then, this paper formulates the Partial Observation Markov Decision Process and constructs a reward-sharing mechanism to tackle the delayed reward issue and facilitate policy learning. Finally, we develop an improved multi-agent dueling double deep Q network algorithm to optimize scheduling policy during long-term training. The results show that, compared with the state-of-the-art methods, the proposed method efficiently shortens the weighted flow time under the trained and unseen scenarios. Additionally, the case study results demonstrate its efficiency and responsiveness. It indicates that the proposed method efficiently addresses production scheduling problems with complex constraints, including the insertion of jobs, transportation time constraints, and flexible processing routes.

Proportionate Flow Shop Scheduling with Job-dependent Due Windows and Position-dependent Weights

In this paper, we deal with the different due windows assignment proportionate flow shop problem with position-dependent weights, where the sequence is a permutation. The objective is to determine an optimal job sequence and due windows of all jobs such that the weighted sum of earliness–tardiness, the starting time and size of all due windows is to be minimized, where the weight is not related to the job but to the position in which some job is scheduled, i.e., position-dependent weights. According to a series of optimal properties, we prove that the problem can be solved in polynomial time [Formula: see text], where [Formula: see text] is the number of jobs.

Scheduling with jobs at fixed positions

In this paper, we study classical single machine scheduling problems with the additional constraint that a set of special jobs must be scheduled at certain positions in the job sequence. In other words, a special job must start when a certain number of jobs have finished on the machine. We analyze several classical objective functions for this more general setting with the additional constraint of fixed positioned jobs. We show that for some of them they are still polynomially solvable. Then, we focus on the objective of minimizing the number of tardy jobs. Considering the case of just one special job, this allows for a polynomial-time algorithm.

Blockchain design for optimal joint production and maintenance over multiple periods for oil-filling production lines

Joint maintenance and production planning result in enhanced system efficiency and a significant reduction in expensive costs. Therefore, this research proposed an integrated blockchain design of two optimization models for the joint scheduling and sequencing of production orders and maintenance jobs over multiple periods with probabilistic and stochastic parameters for the oil-filling process. In the scheduling model, the objective function was to minimize total production and maintenance costs. Further, the sequencing model aimed to minimize the total overtime cost and the sum start times of jobs and orders. The proposed models were implemented on five production lines of five-liter lube oil bottles. Results showed that the developed optimization models effectively achieved concurrent production and maintenance planning at minimal total cost. In practice, this results in effective resource utilization, and saving costly production and maintenance costs. In conclusion, the developed blockchain design is valuable in developing, managing, and controlling optimal joint production and maintenance planning of oil-filling production lines.