Search Results (91)

This paper considers the single-machine scheduling problem of total tardiness minimization. Due to its computational intractability, exact approaches such as dynamic programming algorithms and branch-and-bound algorithms struggle to produce optimal solutions for large-scale instances in a reasonable time. The advent of Deep Q-Networks (DQNs) within the reinforcement learning paradigm could be a viable approach to transcending these limitations, offering a robust and adaptive approach. This study introduces a novel approach utilizing DQNs to model the complexities of job scheduling for minimizing tardiness through an informed selection utilizing look-ahead mechanisms of actions within a defined state space. The framework incorporates seven distinct reward-shaping strategies, among which the Minimum Estimated Future Tardiness strategy notably enhances the DQN model’s performance. Specifically, it achieves an average improvement of 14.33% over Earliest Due Date (EDD), 11.90% over Shortest Processing Time (SPT), 17.65% over Least Slack First (LSF), and 8.86% over Apparent Tardiness Cost (ATC). Conversely, the Number of Delayed Jobs strategy secures an average improvement of 11.56% over EDD, 9.10% over SPT, 15.01% over LSF, and 5.99% over ATC, all while requiring minimal computational resources. The results of a computational study demonstrate DQN’s impressive performance compared to traditional heuristics. This underscores the capacity of advanced machine learning techniques to improve industrial scheduling processes, potentially leading to decent operational efficiency. 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

The integration of remote sensing technology and machine learning algorithms represents a new research direction for the rapid and large-scale detection of water stress in modern agricultural crops. However, in solving practical agricultural problems, single machine learning algorithms cannot fully explore the potential information within the data, lacking stability and accuracy. Stacking ensemble learning (SEL) can combine the advantages of multiple single machine learning algorithms to construct more stable predictive models. In this study, threshold values of stomatal conductance (g_s) under different soil water stress indices (SWSIs) were proposed to assist managers in irrigation scheduling. In the present study, six irrigation treatments were established for winter wheat to simulate various soil moisture supply conditions. During the critical growth stages, g_s was measured and the SWSI was calculated. A spectral camera mounted on an unmanned aerial vehicle (UAV) captured reflectance images in five bands, from which vegetation indices and texture information were extracted. The results indicated that g_s at different growth stages of winter wheat was sensitive to soil moisture supply conditions. The correlation between the g_s value and SWSI value was high (R² > 0.79). Therefore, the g_s value threshold can reflect the current soil water stress level. Compared with individual machine learning models, the SEL model exhibited higher prediction accuracy, with R² increasing by 6.67–17.14%. Using a reserved test set, the SEL model demonstrated excellent performance in various evaluation metrics across different growth stages (R²: 0.69–0.87, RMSE: 0.04–0.08 mol m⁻² s⁻¹; NRMSE: 12.3–23.6%, MAE: 0.03–0.06 mol m⁻² s⁻¹) and exhibited excellent stability and accuracy. This research can play a significant role in achieving large-scale monitoring of crop growth status through UAV, enabling the real-time capture of winter wheat water deficit changes, and providing technical support for precision irrigation. Full article

Single-machine due-window assignment scheduling with delivery times and variable processing times is investigated, where the variable processing time of a job means that the processing time is a function of its position in a sequence and its resource allocation. Currently, there are multiple optimization objectives for the due-window assignment problem, and there is a small amount of research on optimization problems where the window starting time, the rejected cost and the optimal scheduling are jointly required. The goal of this paper is to minimize the weighed sum of scheduling cost, resource consumption cost and outsourcing measure under the optional job outsourcing (rejection). Under two resource allocation models (i.e., linear and convex resource allocation models), the scheduling cost is the weighted sum of the number of early–tardy jobs, earliness–tardiness penalties and due-window starting time and size, where the weights are positional-dependent. The main contributions of this paper include the study and data simulation of single-machine scheduling with learning effects, delivery times and outsourcing cost. For the weighed sum of scheduling cost, resource consumption cost and outsourcing measure, we prove the polynomial solvability of the problem. Under the common and slack due-window assignments, through the theoretical analysis of the optimal solution, we reveal that four problems can be solved in $O\left(n^6\right)$ time, where n is the number of jobs. Full article

This paper studies the single-machine scheduling problem with truncated learning effect, time-dependent processing time, and past-sequence-dependent delivery time. The delivery time is the time that the job is delivered to the customer after processing is complete. The goal is to determine an optimal job schedule to minimize the total weighted completion time and maximum tardiness. In order to solve the general situation of the problem, we propose a branch-and-bound algorithm and other heuristic algorithms. Computational experiments also prove the effectiveness of the given algorithms. Full article

The scheduling problem in additive manufacturing is receiving increasing attention; however, few have considered the effect of scheduling decisions on machine energy consumption. This research focuses on the nesting and scheduling problem of a single selective laser melting (SLM) machine to reduce total energy consumption. Based on an energy consumption model, a nesting and scheduling problem is formulated, and a mixed integer linear programming model is proposed. This model simultaneously determines part-to-batch assignments, part placement in the batch, and the choice of build orientation to reduce the total energy consumption of the SLM machine. The energy-saving potential of the model is validated through numerical experiments. Additionally, the effect of the number of alternative build orientations on energy consumption is explored. Full article

In response to the challenges of dynamic adaptability, real-time interactivity, and dynamic optimization posed by the application of existing deep reinforcement learning algorithms in solving complex scheduling problems, this study proposes a novel approach using graph neural networks and deep reinforcement learning to complete the task of job shop scheduling. A distributed multi-agent scheduling architecture (DMASA) is constructed to maximize global rewards, modeling the intelligent manufacturing job shop scheduling problem as a sequential decision problem represented by graphs and using a Graph Embedding–Heterogeneous Graph Neural Network (GE-HetGNN) to encode state nodes and map them to the optimal scheduling strategy, including machine matching and process selection strategies. Finally, an actor–critic architecture-based multi-agent proximal policy optimization algorithm is employed to train the network and optimize the decision-making process. Experimental results demonstrate that the proposed framework exhibits generalizability, outperforms commonly used scheduling rules and RL-based scheduling methods on benchmarks, shows better stability than single-agent scheduling architectures, and breaks through the instance-size constraint, making it suitable for large-scale problems. We verified the feasibility of our proposed method in a specific experimental environment. The experimental results demonstrate that our research can achieve formal modeling and mapping with specific physical processing workshops, which aligns more closely with real-world green scheduling issues and makes it easier for subsequent researchers to integrate algorithms with actual environments. Full article

This paper presents two novel formulations for scheduling problems, namely order-position hybrid formulation (OPH) and order-disjunctive hybrid formulation (ODH), which extend and combine parts of existing formulation strategies. The first strategy (OPH) is based on sequence position and linear ordering formulations, adding relationships between constraints that allow relaxing some decision variables. The second approach (ODH) is based on linear ordering and disjunctive formulations. In this work, we prove ODH to be the most efficient formulation known so far. The experiments have been carried out with a large set of problems, which consider single machines and identical parallel machines. Computational results show that OPH is better than the rest of the existing formulations for the case of weighted completion objectives, while ODH turns out to be the best approach for most scenarios studied. Full article

This paper studies the single-machine group scheduling problem with convex resource allocation and learning effect. The number of jobs in each group is different, and the corresponding common due dates are also different, where the processing time of jobs follows a convex function of resource allocation. Under common due date assignment, the objective is to minimize the weighted sum of earliness, tardiness, common due date, resource consumption, and makespan. To solve the problem, we present the heuristic, simulated annealing, and branch-and-bound algorithms. Computational experiments indicate that the proposed algorithms are effective. Full article

In the real world of manufacturing systems, production planning is crucial for organizing and optimizing various manufacturing process components. The objective of this paper is to present a methodology for both static scheduling and dynamic scheduling. In the proposed method, a hybrid algorithm is utilized to optimize the static flexible job-shop scheduling problem (FJSP) and dynamic flexible job-shop scheduling problem (DFJSP). This algorithm integrates the genetic algorithm (GA) as a global optimization technique with a simulated annealing (SA) algorithm serving as a local search optimization approach to accelerate convergence and prevent getting stuck in local minima. Additionally, variable neighborhood search (VNS) is utilized for efficient neighborhood search within this hybrid algorithm framework. For the FJSP, the proposed hybrid algorithm is simulated on a 40-benchmark dataset to evaluate its performance. Comparisons among the proposed hybrid algorithm and other algorithms are provided to show the effectiveness of the proposed algorithm, ensuring that the proposed hybrid algorithm can efficiently solve the FJSP, with 38 out of 40 instances demonstrating better results. The primary objective of this study is to perform dynamic scheduling on two datasets, including both single-purpose machine and multi-purpose machine datasets, using the proposed hybrid algorithm with a rescheduling strategy. By observing the results of the DFJSP, dynamic events such as a single machine breakdown, a single job arrival, multiple machine breakdowns, and multiple job arrivals demonstrate that the proposed hybrid algorithm with the rescheduling strategy achieves significant improvement and the proposed method obtains the best new solution, resulting in a significant decrease in makespan. Full article

The unique topic of allocating and scheduling tasks on a single machine in a multitasking environment is the main emphasis of this research, which also takes into account the effects of worsening maintenance and job-dependent aging effects. In this scenario, the performance and efficiency of the machine in handling different tasks should be symmetric, without significant bias due to the nature or size of the tasks. In a multitasking environment, waiting for jobs can disrupt the processing of the primary job being currently handled. As a result, the actual time required to complete a task becomes erratic and contingent upon the duration of the disruption. In addition to figuring out the best time for maintenance, where to put the due-window, and how big it should be in a multitasking environment, the primary objective is to minimize the costs associated with meeting due-window regulations. To tackle this problem, we propose two optimal algorithms. Additionally, we conduct numerical experiments to compare our approach with the classic due date assignment problem. Interestingly, we observe that in most cases, the average and minimum percentage costs tend to increase as the quantity of jobs increases. However, it is noteworthy that, when the number of jobs is relatively small, specifically when it does not exceed 20, there are instances where these costs decrease with an increase in the number of jobs. Full article

This paper investigates a two-machine group scheduling problem with sequence-independent setup times and round-trip transportation times, which is derived from the production management requirements of modern steel manufacturing enterprises. The objective is to minimize the makespan. Addressing limitations in prior studies, we consider a critical but largely ignored transportation method, namely round-trip transportation, and restricted transporter capacity between machines. To solve this problem, a mixed-integer programming model is first developed. Then, the problem complexity is analyzed for situations with both single and unlimited transporters. For the NP-hard case of a single transporter, we design an efficient two-stage heuristic algorithm with proven acceptable solution quality bounds. Extensive computational experiments based on steel plant data demonstrate the effectiveness of our approach in providing near-optimal solutions, and the maximum deviation between our algorithm and the optimal solution is 1.38%. This research can provide an operable optimization method that is valuable for group scheduling and transportation scheduling. Full article

The problem of the approximation of the coefficients of the objective function of a scheduling problem for a single machine is considered. It is necessary to minimize the total weighted completion times of jobs with unknown weight coefficients when a set of problem instances with known optimal schedules is given. It is shown that the approximation problem can be reduced to finding a solution to a system of linear inequalities for weight coefficients. For the case of simultaneous job release times, a method for solving the corresponding system of inequalities has been developed. Based on it, a polynomial algorithm for finding values of weight coefficients that satisfy the given optimal schedules was constructed. The complexity of the algorithm is $O\left(n^2(N+n)\right)$ operations, where n is the number of jobs and N is the number of given instances with known optimal schedules. The accuracy of the algorithm is estimated by experimentally measuring the function $\epsilon (N,n)=\frac{1}{n}{\sum }_{j=1}^n\frac{\mid w_j-w_j^0\mid }{w_j^0}$, which is an indicator of the average modulus of the relative deviation of the found values $w_j$ from the true values $w_j^0$. An analysis of the results shows a high correlation between the dependence $\epsilon (N,n)$ and a function of the form $\alpha \left(n\right)/N$, where $\alpha \left(n\right)$ is a decreasing function of n. Full article

In this paper, we investigate a single machine scheduling problem with a proportional job deterioration. Under release times (dates) of jobs, the objective is to minimize the total weighted completion time. For the general condition, some dominance properties, a lower bound and an upper bound are given, then a branch-and-bound algorithm is proposed. In addition, some meta-heuristic algorithms (including the tabu search ($TS$), simulated annealing ($SA$) and heuristic ($NEH$) algorithms) are proposed. Finally, experimental results are provided to compare the branch-and-bound algorithm and another three algorithms, which indicate that the branch-and-bound algorithm can solve instances of 40 jobs within a reasonable time and that the $NEH$ and $SA$ are more accurate than the $TS$. Full article

In this paper, we consider different due-date assignment scheduling with group technology and resource allocation on a single machine, where the due date of each job may be different. Under constant processing times, the objective function is to minimize the scheduling cost (i.e., the weighted sum of earliness, tardiness, and due-date assignment cost, where the weights are position dependent). Under some optimal properties, we prove that this problem can be solved in $O(\zeta log\zeta )$ time, where $\zeta$ is the number of jobs. The problem is also extended to cases which include linear and convex functions of the quantity of resource allocation. The objective function is minimizing the sum of the scheduling cost and the resource-consumption cost. For the special case of linear and convex functions, we show that the problem is polynomially solvable in $O\left({\zeta }^3\right)$ time. Full article