Search Results (44)

For a no-wait flow shop with continuous-flow characteristics, this study simultaneously considers machine setup times and rated processing speed constraints, aiming to minimize the sum of the maximum completion time and the maximum tardiness. First, lower bounds for the maximum completion time, the maximum tardiness, and the total objective function are developed. Second, a mixed-integer programming (MIP) model is formulated for the problem, and nonlinear elements are subsequently linearized via time discretization. Due to the computational complexity of the problem, two algorithms are proposed: a heuristic algorithm with fixed machine links and greedy rules (HAFG) and a genetic algorithm based on altering machine combinations (GAAM) for solving large-scale instances. The Earliest Due Date (EDD) rule is used as baselines for algorithmic comparison. To better understand the behaviors of the two algorithms, we observe the two components of the objective function separately. The results show that, compared with the EDD rule and GAAM, the HAFG algorithm tends to focus more on optimizing the maximum completion time. The performance of both algorithms is evaluated using their relative deviations from the developed lower bounds and is compared against the EDD rule. Numerical experiments demonstrate that both HAFG and GAAM significantly outperform the EDD rule. In large-scale instances, the HAFG algorithm achieves a gap of about 4%, while GAAM reaches a gap of about 3%, which is very close to the lower bound. In contrast, the EDD rule shows a deviation of about 10%. Combined with a sensitivity analysis on the number of machines, the proposed framework provides meaningful managerial insights for continuous-flow production environments. Full article

This article investigates single-machine group scheduling integrated with resource allocation under different due-window ($DIFDW$) assignment. Three distinct scenarios are examined: one with constant processing times, one with a linear resource consumption function, and one with a convex resource consumption function. The objective is to minimize the total cost comprising the maximum earliness/tardiness penalties, the due-window starting time cost, the due-window size cost, and the resource consumption cost. For each problem variant, we analyze the structural properties of optimal solutions and develop corresponding solution algorithms: a polynomial-time optimal algorithm for the case with constant processing times, heuristic algorithms for problems involving linear and convex resource allocation, and the branch-and-bound algorithm for obtaining exact solutions. Numerical experiments are conducted to evaluate the performance of the proposed algorithms. Full article

This study proposes an improved Fruit Fly Optimization Algorithm integrated with Simulated Annealing (SA-FOA) for hybrid flow shop scheduling problems with dual objectives of minimizing makespan and total tardiness. The algorithm adopts a three-stage integration strategy to generate high-quality initial populations, surpassing random initialization. During olfactory search, insertion-based neighborhood operations expand search scope, while visual search incorporates simulated annealing acceptance criteria to escape local optima. Validation employs three scalable instances, comparing SA-FOA against basic FOA and classical scheduling rules. Experimental results demonstrate significant superiority in Inverted Generational Distance (IGD), Non-dominant rate (NR), and Convergence Matrix (C-matrix metrics), highlighting enhanced convergence, distribution, and diversity. Notably, performance advantages amplify with problem scale growth. Full article

For the unrelated parallel machine scheduling problem, an improved Spider Monkey Optimization algorithm incorporating a variable neighborhood search (VNS) mechanism (VNS-SMO) is proposed to minimize the makespan, total tardiness, and total energy consumption. The VNS-SMO incorporates six types of neighborhood searches based on the objective characteristics to strengthen the optimization performance of the algorithm. To verify the effectiveness and superiority of VNS-SMO, first, Taguchi experiments were used to determine the algorithm parameters, and then three instances of different scales were solved and compared with the traditional algorithms NSGA-II, PSO, and SMO. The experimental results indicate that VNS-SMO significantly outperforms the comparison algorithms on IGD, NR, and C-matrix metrics, fully demonstrating its comprehensive advantages in convergence, distribution, and diversity. Full article

The flexible job shop scheduling problem (FJSP) becomes significantly more complex when real-world factors such as due dates, sequence-dependent setup times, and processing times are considered as multiple criteria. This study presents a hybrid scheduling approach that combines a genetic algorithm (GA) and variable neighborhood search (VNS), where several dispatching rules are used to create the initial population and improve exploration. The multiple objectives are to minimize makespan, total tardiness, and total setup time while improving overall production efficiency. To test the proposed approach, standard FJSP datasets were extended with due dates and setup times for two different environments. Due dates were generated using the Total Work Content (TWK) method. This study also introduces a dynamic scheduling framework that addresses dynamic events such as machine breakdowns and new job arrivals. A rescheduling strategy was developed to maintain optimal solutions in dynamic situations. Experimental results show that the proposed hybrid framework consistently performs better than other methods in static scheduling and maintains high performance under dynamic conditions. The proposed method achieved 6.5% and 2.59% improvement over the baseline GA in two different environments. The results confirm that the proposed strategies effectively address complex, multi-constraint scheduling problems relevant to Industry 4.0 and smart manufacturing environments. Full article

This paper examines the impact of two storage policies—dedicated storage (D-SLAP) and randomized storage (R-SLAP)—on warehouse operational efficiency. It integrates the Storage Location Assignment Problem (SLAP) with the unrelated parallel machine scheduling problem (UPMSP), which represents the scheduling of the material handling equipment (MHE). This integration is intended to elucidate the interplay between storage strategies and scheduling performance. The considered evaluation metrics include transportation cost, average waiting time, and total tardiness, while accounting for product arrival and demand schedules, precedence constraints, and transportation expenses. Additionally, considerations such as MHE eligibility, resource requirements, and available storage locations are incorporated into the analysis. Given the complexity of the combined problem, a tailored Non-dominated Sorting Genetic Algorithm (NSGA-II) was developed to assess the performance of the two storage policies across various randomly generated test instances of differing sizes. Parameter tuning for the NSGA-II was conducted using the Taguchi method to identify optimal settings. Experimental and statistical analyses reveal that, for small-size instances, both policies exhibit comparable performance in terms of transportation cost and total tardiness, with R-SLAP demonstrating superior performance in reducing average waiting time. Conversely, results from large-size instances indicate that D-SLAP surpasses R-SLAP in optimizing waiting time and tardiness objectives, while R-SLAP achieves lower transportation cost. Full article

To address the multi-objective flexible job shop scheduling problem in rolling production mode (FJSP-RPM), this study proposes a Multi Objective Improved of Salp Swarm Algorithm (MISSA) that simultaneously optimizes equipment utilization and total tardiness. The MISSA generates initial population through various heuristic strategies to improve the initial population quality. The exploitation capability of the algorithm is enhanced through the global crossover strategy and variety of local search strategies. In terms of improvement strategies, the MISSA (using all three strategies) outperforms other incomplete variant algorithms (using only two strategies) in three metrics: Generational Distance (GD), Inverted Generational Distance (IGD), and diversity metric, achieving superior results in 9 test cases, 8 test cases, and 4 test cases respectively. When compared with NSGA2, NSGA3, and SPEA2 algorithms, the MISSA demonstrates advantages in 8 test cases for GD, 8 test cases for IGD, and 7 test cases for the diversity metric. Additionally, the distribution of the obtained solution sets is significantly better than that of the comparative algorithms, which validats the effectiveness of the MISSA in solving FJSP-RPM. Full article

The use of electric vehicles in urban transportation is increasing daily due to their energy efficiency and environmental friendliness. In last-mile logistics, route optimization must consider charging station locations while balancing operational costs and customer satisfaction. In this context, solutions for cost-oriented route optimization have been presented in the literature. On the other hand, customer satisfaction is also important for third-party logistics companies. This study discusses the Capacitated Electric Vehicle Routing Problem with Time Windows (CEVRPTW) encountered in last-mile logistics. This article defines the objective function of minimizing total tardiness and compares the routes between the service provider logistics company and the customer receiving the service. In this study, the CEVRPTW was solved for the minimum total tardiness objective function with the hybrid adaptive large neighborhood search (ALNS) algorithm. The success of ALNS was proven by comparing the differences between the optimal solutions obtained with the CPLEX Solver and the ALNS solutions. Tardiness objective function-specific operators for ALNS are proposed and supported by local search and VNS algorithms. The findings of this study contribute to the literature by analyzing the balance trade-offs between customer-oriented and cost-oriented and the effect of time windows on the number of vehicles. Full article

Dynamic scheduling for flexible job shops under machine breakdown is a complex and challenging problem due to its valuable application in real-life productions. However, prior studies have struggled to perform well in changeable scenarios. To address this challenge, this paper introduces a dual-objective deep reinforcement learning (DRL) to solve this problem. This algorithm is based on the Double Deep Q-network (DDQN) and incorporates the attention mechanism. It decouples action relationships in the action space to reduce problem dimensionality and introduces an adaptive weighting method in agent decision-making to obtain high-quality Pareto front solutions. The algorithm is evaluated on a set of benchmark instances and compared with state-of-the-art algorithms. The experimental results show that the proposed algorithm outperforms the state-of-the-art algorithms regarding machine offset and total tardiness, demonstrating more excellent stability and higher-quality solutions. At the same time, the actual use of the algorithm is verified using cases from real enterprises, and the results are still better than those of the multi-objective meta-heuristic algorithm. Full article

This paper presents a robust and adaptable framework for predictive–reactive rescheduling in identical parallel-machine environments. The proposed Multi-Purpose Intelligent Utility (MIU) methodology utilizes heuristic methods to efficiently address the computational challenges associated with NP-hard scheduling problems. By incorporating 13 diverse dispatching rules, the MIU framework provides a flexible and adaptive approach to balancing critical production objectives. It effectively minimizes total weighted tardiness and the number of tardy jobs while maintaining key performance metrics like stability, robustness, and nervousness. In dynamic manufacturing environments, schedule congestion and unforeseen disruptions often lead to inefficiencies and delays. Unlike traditional event-driven approaches, MIU adopts a periodic rescheduling strategy, enabling proactive adaptation to evolving production conditions. Comprehensive rescheduling ensures system-wide adjustments to disruptions, such as stochastic changes in processing times and rework requirements, without sacrificing overall performance. Empirical evaluations show that MIU significantly outperforms conventional methods, reducing total weighted tardiness by 50% and the number of tardy jobs by 27% on average across various scenarios. Furthermore, this study introduces novel quantifications for nervousness, expanding the scope of stability and robustness evaluations in scheduling research. This work contributes to the ongoing discourse on scheduling methodologies by bridging theoretical research with practical industrial applications, particularly in high-stakes production settings. By addressing the trade-offs between improving the objective function or improving the rescheduling performance, MIU provides a comprehensive solution framework that enhances operational performance and adaptability in complex manufacturing environments. Full article

In this paper, a Distributed Mixed No-Idle Permutation Flowshop Scheduling Problem with Sequence-Dependent Setup Times (DMNIPFSP/SDST) is studied. Firstly, a multi-objective optimization model with completion time (makespan), Total Energy Consumption (TEC), and Total Tardiness (TT) as objectives is established. Based on problem characteristics and multi-objective characteristics, a Q-Learning Evolutionary Algorithm (QLEA) is proposed. Secondly, in order to improve the quality and diversity of the initial solution, two improved initialization strategies are proposed. Based on the characteristics of the problem solved (In the distributed system, symmetry design is adopted to ensure that the load of each workstation is relatively balanced in different time periods, avoid resource waste or bottleneck, and achieve the goal of no idle.), a novel population updating mechanism is designed to balance the ability of global exploration and local development of the algorithm. At the same time, a variable neighborhood local search based on Q-Learning is used to refine the non-dominated solution, thus guiding the population evolution. Finally, the simulation results show that this method has good performance in solving the multi-objective DMNIPFSP/SDST and can provide good economic benefits for enterprises. Full article

In this paper, we address biopharmaceutical manufacturing scheduling problems with heterogeneous parallel mixed flowshops. The mixed flowshop consists of three stages, one batch process and two continuous processes. The objective function is to minimize the total tardiness. We formulated a mixed-integer linear programming model for the problem to obtain optimal solutions to small-size problems. We present a genetic algorithm and particle swarm optimization, which are used to find efficient solutions for large-size problems. We show that the particle swarm optimization outperforms the genetic algorithm in large-size problems. We conduct a sensitivity analysis to obtain managerial insights using the particle swarm optimization algorithm. Full article

This study evaluates the efficiency of a swarm intelligence algorithm called marriage in honey-bee optimization (MBO) in solving the single-machine weighted earliness/tardiness problem, a type of NP-hard combinatorial optimization problem. The goal is to find the optimal sequence for completing a set of tasks on a single machine, minimizing the total penalty incurred for tasks being completed too early or too late compared to their deadlines. To achieve this goal, the study adapts the MBO metaheuristic by introducing modifications to optimize the objective function and produce high-quality solutions within reasonable execution times. The novelty of this work lies in the application of MBO to the single-machine weighted earliness/tardiness problem, an approach previously unexplored in this context. MBO was evaluated using the test problem set from Biskup and Feldmann. It achieved an average improvement of 1.03% across 280 problems, surpassing upper bounds in 141 cases (50.35%) and matching or exceeding them in 193 cases (68.93%). In the most constrained problems (h = 0.2 and h = 0.4), the method achieved an average improvement of 3.77%, while for h = 0.6 and h = 0.8, the average error was 1.72%. Compared to other metaheuristics, MBO demonstrated competitiveness, with a maximum error of 1.12%. Overall, MBO exhibited strong competitiveness, delivering significant improvements and high efficiency in the problems studied. Full article

This study investigates the integrated multi-objective scheduling problems of job shops and material handling robots (MHR) with minimising the maximum completion time (makespan), earliness or tardiness, and total energy consumption. The collaborative scheduling of MHR and machines can enhance efficiency and reduce costs. First, a mathematical model is constructed to articulate the concerned problems. Second, three meta-heuristics, i.e., genetic algorithm (GA), differential evolution, and harmony search, are employed, and their variants with seven local search operators are devised to enhance solution quality. Then, reinforcement learning algorithms, i.e., Q-learning and state–action–reward–state–action (SARSA), are utilised to select suitable local search operators during iterations. Three reward setting strategies are designed for reinforcement learning algorithms. Finally, the proposed algorithms are examined by solving 82 benchmark instances. Based on the solutions and their analysis, we conclude that the proposed GA integrating SARSA with the first reward setting strategy is the most competitive one among 27 compared algorithms. Full article

In this paper, we investigate a rescheduling problem with rejection and an operator non-availability period on a single machine. An optimal original schedule with the objective of minimizing the total weighted completion time has been made in a deterministic production scheduling system without an unavailable interval. However, prior to the start of formal job processing, a time interval becomes unavailable due to the operator. No jobs can start or complete in the interval; nonetheless, a job that begins prior to this interval and finishes afterward is possible (if there is such a job, we call it a crossover job). In order to deal with the operator non-availability period, job rejection is allowed. Each job is either accepted for processing or rejected by paying a rejection cost. The planned original schedule is required to be rescheduled. The objective is to minimize the total weighted completion time of the accepted jobs plus the total penalty of the rejected jobs plus the weighted maximum tardiness penalty between the original schedule and the new reschedule. We present a pseudo-polynomial time dynamic programming exact algorithm and subsequently develop it into a fully polynomial time approximation scheme. Full article