Scheduling Problem Research Articles

Solving problems of volume scheduling for shipbuilding enterprises in conditions of limited resources

The shipbuilding industry development strategy for the period up to 2035 and beyond is aimed at creating a new competitive shipbuilding industry based on the development of scientific, technical and personnel potential, optimization of production capacities, their modernization and technical re-equipment [1]. The paper is devoted to solving problems of volume-calendar production planning for shipbuilding enterprises when coordinating the production capacity of the enterprise with the resource needs to fulfill obligations determined by the generated order portfolio. Shipbuilding and ship repair enterprises are typical representatives of enterprises with single and small-scale production and a long production cycle of the main products [2-4]. The problem is solved at the stage of forming a portfolio of orders, which is based on the limited volumes of resources available to the production system. It is required to determine the amount of missing resources by calendar periods that are necessary for the effective functioning of the production system. Non-stored resources such as labor resources, equipment operating time, are usually taken into account when solving the problems of volumetric or volume-scheduling planning. Such resources being unused in a certain planning cycle cannot be used in subsequent cycles. The procedure for finding missing volumes of resources is formulated as the problem of reducing an incompatible system of linear two-sided algebraic inequalities to a compatible one. To do this, it is proposed to “expand” the initial parameters of the system, taking into account the costs of expansion, so that the system becomes compatible. In the general case, formally, the problem under consideration is close to the problem of finding a Chebyshev point [5] for an incompatible system of linear algebraic equations, i.e. a point that is geometrically the least deviating from all hyperplanes formed by the system constraints. The paper proposes statements and solutions of volume-scheduling problems for the case when the structure of the problem constraints is modeled by a root-oriented weighted tree. This hierarchical structure is typical for shipbuilding enterprises [6].

Probabilistic Multi-Robot Task Scheduling for the Antarctic Environments with Crevasses

This paper deals with the problem of multi-robot task scheduling in the Antarctic environments with crevasses. Because the crevasses may cause hazardous situations when robots are operated in the Antarctic environments, robot navigation should be planned to safely avoid the positions of crevasses. However, the positions of the crevasses may be inaccurately measured due to the lack of sensor performance, the asymmetry of sensor data, and the possibility of crevasses drifting irregularly as time passes. To overcome these uncertain and asymmetric problems, this paper proposes a probabilistic multi-robot task scheduling method based on the Nearest Neighbors Test (NNT) algorithm and the probabilistic modeling of the positions of crevasses. The proposed method was tested with a Google map of the Antarctic environments and showed a better performance than the Ant Colony Optimization (ACO) algorithm and the Genetic Algorithm (GA) in the context of total cost and computational time.

Scheduling of memory chips for final testing on parallel machines considering power constraints and deteriorating effects

This paper delves into the intricate scheduling strategies crucial for the final testing phase of memory chip manufacturing within the semiconductor industry and other related sectors. It specifically addresses the complex serial-batching scheduling problem, where memory chips are tested on parallel machines under power constraints and chip deterioration effects. The processing time for each chip is significantly influenced by both the cumulative processing time of preceding chips and the power requirements for testing. We formulate this real-world optimization problem using a mixed integer nonlinear programming model. Exact solutions for small instances are obtained using a commercial solver. However, due to the model's complexity, we also develop heuristic solutions to efficiently handle larger instances. Based on the derivation of structural properties, we develop two tailored heuristic algorithms to determine the schedule for the final testing of memory chips. Additionally, we propose a refined Variable Neighborhood Search algorithm (VNS-H) that seamlessly integrates five local search strategies with two supplementary heuristic algorithms, dynamically alternating between them to ensure a balance between computational efficiency and the quality of the solutions obtained. Additionally, we establish a lower bound to validate the effectiveness of these solutions, particularly for large-scale instances. To validate the efficacy and robustness of our proposed metaheuristic algorithm, we conduct a rigorous comparison of the VNS-H algorithm with five other metaheuristic algorithms that have promising performance in various optimization problems. The results highlight the superior performance of the VNS-H algorithm. In small-scale instances, our VNS-H algorithm achieves an average makespan that is 5.52% lower compared to the original VNS. For large-scale instances, the VNS-H algorithm reduces the average makespan by 13.46% compared to VNS. Finally, we discuss the managerial implications of our findings, providing insights specifically tailored to semiconductor manufacturing enterprises based on the outcomes of this study.

A heuristic method for multi-objective hybrid flow shop scheduling problem with parent-child relationships and space constraints

ABSTRACT In modern ship manufacturing, a ship is divided into hundreds of blocks in the design stage, and the productivity of the block manufacturing process is vital to ship delivery. This paper investigates the production scheduling problem of ship blocks with the parent-child relationship; this relationship is characterised by the fact that sibling jobs at the same BOM layer must be processed on adjacent machines at their assembly stages. We formulate this problem as a multi-objective hybrid flow shop scheduling problem: the first objective is to minimise the total deviation from the target time of the jobs and the second one is to minimise the total processing time. To solve this problem, we propose a heuristic method based on the multi-objective genetic algorithm, in which an adjacent machine priority method is first proposed to generate feasible solutions that satisfy the space constraints. Then, we improve the individual quality in crossover and mutation of the algorithm via tabu search. We verify the performance of our algorithm by test instances generated from real manufacturing data of a shipbuilding company. Results show that the proposed method outperforms the existing algorithms when identifying the Pareto optimal solutions, especially for large-sized problems.

Multi-mode resource-constrained project scheduling problem with multiple shifts and dynamic energy prices

Considering the characteristics of time-of-use tariffs and multi-shifts in real-life project execution scenarios, we present a multi-mode resource-constrained project scheduling problem with multi-shift and time-of-use tariffs (MRCPSP-MS-TOU). The MRCPSP-MS-TOU is a bi-objective scheduling problem that aims to simultaneously minimise both project duration and energy costs. In this problem, renewable resources are the critical equipment that consumes the most energy and can work continuously for multiple shifts. Activities that require critical equipment with high energy consumption are given priority for shifts with lower electricity prices under time-of-use tariffs. We construct a mixed integer linear programming model for the MRCPSP-MS-TOU. For small-scale projects, the ε-constraint method is implemented to solve the MRCPSP-MS-TOU using the Gurobi optimiser. For large-scale projects, this paper develops meta-heuristic algorithms in the framework of the two non-dominated sorting genetic algorithm versions. The MRCPSP-MS-TOU enables manufacturers and the construction industry to schedule projects using time-of-use tariffs and multi-shifts in a more efficient manner since it can control the intensity of energy consumption, reduce project costs, make full use of energy-intensive equipment, and effectively reduce order delivery time.

A Deep Reinforcement Learning Method Based on a Transformer Model for the Flexible Job Shop Scheduling Problem

The flexible job shop scheduling problem (FJSSP), which can significantly enhance production efficiency, is a mathematical optimization problem widely applied in modern manufacturing industries. However, due to its NP-hard nature, finding an optimal solution for all scenarios within a reasonable time frame faces serious challenges. This paper proposes a solution that transforms the FJSSP into a Markov Decision Process (MDP) and employs deep reinforcement learning (DRL) techniques for resolution. First, we represent the state features of the scheduling environment using seven feature vectors and utilize a transformer encoder as a feature extraction module to effectively capture the relationships between state features and enhance representation capability. Second, based on the features of the jobs and machines, we design 16 composite dispatching rules from multiple dimensions, including the job completion rate, processing time, waiting time, and manufacturing resource utilization, to achieve flexible and efficient scheduling decisions. Furthermore, we project an intuitive and dense reward function with the objective of minimizing the total idle time of machines. Finally, to verify the performance and feasibility of the algorithm, we evaluate the proposed policy model on the Brandimarte, Hurink, and Dauzere datasets. Our experimental results demonstrate that the proposed framework consistently outperforms traditional dispatching rules, surpasses metaheuristic methods on larger-scale instances, and exceeds the performance of existing DRL-based scheduling methods across most datasets.

Deep contextual reinforcement learning algorithm for scalable power scheduling

This article introduces a deep contextual reinforcement learning (DCRL) optimization algorithm to tackle the NP-hard power scheduling problem. The algorithm is based on a multi-agent simulation environment that decomposes the power scheduling problem into sequential Markov decision processes (MDPs). The simulation environment inherently corrects incorrect decisions and adjusts supply capacities so that the MDPs adhere to the optimization constraints. A deep reinforcement learning (DRL) model is trained on these MDPs to provide optimal solutions. Demonstrating its applicability and effectiveness, the proposed method is evaluated on various test systems with different unit numbers, constraints, and production cost functions. The experimental results show that the proposed method has better performance relative to alternative methods, such as binary alternative moth-flame optimization (BAMFO), binary particle swarm optimization (BPSO), teaching learning-based optimization (TLBO), new binary particle swarm optimization (NBPSO), binary learning particle swarm optimization (BLPSO), quasi-oppositional teaching learning-based algorithm (QOTLBO), binary-real-coded genetic algorithm (BRCGA), hybrid genetic-imperialist competitive algorithm (HGICA), three-stage priority list (TSPL), and hybridized evolutionary algorithm and sequential quadratic programming (HEPSQP). The novelties of the proposed method lie in its adaptability to longer planning horizons and linear dimensionality complexity, rendering it suitable for large-scale power systems.

Enhanced Monte‐Carlo tree search for dynamic flexible job shop scheduling with transportation time constraints

AbstractWith the increasing uncertainty and complexity of industrial production, dynamic events are inevitably happened during the production process. This paper deals with the transportation time constrained dynamic flexible job shop scheduling problem with machine breakdown, new jobs arrival, jobs cancellation, and processing time change of operations. Considering the actual production situation, a makespan rescheduling model based on transportation time is established. A Monte‐Carlo tree search based algorithm is proposed to solve the dynamic flexible job shop scheduling problem such that the makespan is minimized. In order to improve the accuracy of the developed algorithm and the quality of the obtained scheduling schemes, subtree keeping policy, multi‐branching simulation, reinforcement learning, greedy strategy, and expectation‐best evaluation method are employed. Moreover, a subtree pruning policy is embedded to improve the search efficiency of the developed algorithm. Simulation experiments are conducted on a series of instances of different sizes to compare the developed approach with the GA‐based scheduling approach and the Monte‐Carlo tree search based approach. The simulation results indicate that the developed approach is superior to the existing scheduling approaches in terms of the qualities of the obtained solutions.

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.

Optimising resource-constrained fleet selective maintenance with asynchronous maintenance breaks

This paper offers a novel and significant extension of the Fleet Selective Maintenance Problem (FSMP) by considering asynchronous maintenance breaks and resource-constrained maintenance planning. This constitutes a significant shift from the conventional focus on synchronous breaks for the FSMP formulated to plan maintenance for fleets of mission-critical systems. This paper establishes a theoretical link between the Selective Maintenance Problem (SMP) and the Resource Constrained Project Scheduling Problem (RCPSP). The proposed FSMP formulation for asynchronous breaks is more general and versatile in adapting to a broad spectrum of operational constraints and resource scarcities. Numerical experiments are conducted that highlights the trade-offs between the timing and quality levels of maintenance activities and the consumption of resources that maintenance planners can make to obtain the best system performance for the budget and maintenance windows available.

Evolutionary Algorithm for the Earliness - Tardiness Project Scheduling Problem

Completing too early or too late can cause damage to the project. For example, in transporting goods to the seaports, if the shipping arrives too early, it will take time and cost to stay at the dock. In the other case, shipping too late will reduce the quality of the product and break the contract. The goal of this paper is to minimize the tardiness and earliness of those projects. First, some related studies are briefly introduced, thereby showing the role and practical applications of the MS-RCPSP (Multi-Skill Resource Constrained Project Scheduling Problem) problem and the two factors of earliness and delay in scheduling problems. The roles of earliness and tardiness in scheduling problems are also described. At the same time, the new contribution of this research is also highlighted, which is the proposal for the latest problem E-RCPSP (Earliness tardiness MS-RCPSP). This problem is the first problem in the MS-RCPSP family that considers the sum of earliness and tardiness as the objective, which has never been considered in previous studies. Then, the mathematical model of the proposed E-RCPSP problem, which includes the objective function, project components and constraints is introduced. To solve the proposed problem, two approximate algorithms based on the evolutionary algorithms GA (Genetic Algorithm) and DE (Differential Evolution) are introduced. In the last section of the article, the performance of these two algorithms is verified and compared with each other through experiments conducted on the iMOPSE benchmark dataset.}\Keywords{Network Resources Management, Earliness-Tardiness cost, Resource-constrained project scheduling, Evolutionary Algorithms, Differential evolution algorithms.

Two-stage learning scatter search algorithm for the distributed hybrid flow shop scheduling problem with machine breakdown

The distributed hybrid flow shop scheduling problem with machine breakdown is investigated to reduce the negative impact on real production caused by machine breakdown events. (DHFSPMB). DHFSPMB comprises two subproblems: the maintenance problem with machine breakdown and the distributed hybrid flow shop scheduling problem (DHFSP). A rescheduling method is designed to address the maintenance problem. Subsequently, a two-stage learning scatter search (TLSS) algorithm is proposed for optimizing the DHFSP when the machines break down. Firstly, a mixed integer programming model for DHFSPMB is constructed. Secondly, TLSS employs an improved reinforcement learning approach to enhance the capability of exploration by guiding the direction of global search. A two-stage approach is designed to address the lack of knowledge in the early periods of learning. Finally, a hybrid search strategy is devised to enhance the development capability of TLSS. The experimental results demonstrate that the TLSS algorithm outperforms the comparison algorithms in effectively addressing the DHFSPMB.

Dynamic resource allocation and scheduling for appointment-based systems with walk-ins

Effectively managing constrained and perishable capacity amid fluctuating demands is a common challenge in service industries, often addressed through appointment-based systems that incorporate walk-ins. Balancing appointments and walk-ins is crucial for enhancing system value and maintaining stability. In this article, we study an integrated decision problem for appointment scheduling and resource allocation across multiple facilities, considering stochastic demands from three segments: priority customers, walk-in customers, and appointment customers. We formulate the problem as a sequential scheduling-allocation challenge using stochastic dynamic programming. Leveraging the anti-multimodularity of the value function, we fully characterize the optimal dynamic resource allocation policy and its monotone structural properties under any appointment schedule. Given the complexity and intractability of optimal scheduling with dynamic resource allocation, we introduce two suboptimal scheduling policies—vertical scheduling and horizontal scheduling—and a heuristic allocation policy. Additionally, we create an Upper Bound (UB) for the original problem as a surrogate, establishing an asymptotically optimal UB for the scaled problem through its objective value and a corresponding lower bound through its solution. This UB solution serves as an efficient and effective heuristic, demonstrating superior performance compared with the combined performance of suboptimal scheduling policies with optimal dynamic resource allocation, especially as problem size increases. It also holds significant practical implications for integrated pooling systems.

A multi-objective Immune Balancing Algorithm for Distributed Heterogeneous Batching-integrated Assembly Hybrid Flowshop Scheduling

Driven by economic globalization, global supply chain collaboration has gained significant importance, fostering the emergence of distributed manufacturing. This paper addresses the Distributed Heterogeneous Batching-integrated Assembly Hybrid Flowshop Scheduling (DHBIAHFS) problem within the pharmaceutical industry. Jobs are allocated to factories for processing, batched within defined lot sizes for transportation, and subsequently assembled into products to minimize the maximum completion time and tardy product count. Effective lot sizing during transport is emphasized between factories and assembly machines. Drawing inspiration from the biological immune system’s balancing mechanisms, we propose a Multi-objective Immune Balancing Algorithm (MOIBA) equipped with learning and repairing mechanisms. Each solution is structured with three nested sequences, and composite heuristic evaluations are employed to generate high-quality initial solutions. The performance of each solution is assessed based on both fitness and diversity metrics. Customized crossover and mutation operators are introduced with dynamically adjusted probabilities reflective of immune response dynamics. Quantitative analysis validates our mathematical model and the distinct components of MOIBA. We compare MOIBA’s efficiency against six other effective multi-objective strategies using three performance metrics. Stability and robustness assessments, conducted through variance examination and statistical testing, offer insights into MOIBA’s consistency and reliability across diverse problem instances.

Optimal scheduling study of green warehousing microgrid based on improved sparrow search algorithm

Combining green warehousing with wind-solar-storage systems can enhance economic power consumption, energy saving, and emission reduction in green warehousing. To achieve efficient and stable operation of the wind-solar-storage microgrid, this paper proposes an optimal microgrid scheduling strategy based on the Improved Sparrow Algorithm (ISSA). Firstly, a comprehensive benefit model is established based on the economic and environmental benefits of microgrid daily operation. Then, an innovative improved sparrow search algorithm is proposed, which aims to improve the global search and local search capability of the microgrid scheduling problem by introducing improvements such as Logistic-Circle chaotic mapping, Bottle Sea Sheath swarm optimization algorithm, dynamic inertia weights, water wave dynamic factor, and Cauchy-Gaussian variational strategy. Finally, the microgrid optimal scheduling model is solved by the improved sparrow search algorithm and compared with other algorithms. In this paper, Matlab 2016b is used for simulation, and the simulation results show that the ISSA algorithm outperforms other algorithms in terms of solution stability and optimization search capability. Under three modes of operation, ISSA improves the microgrid operation revenue by 6.29%, 5.98%, and 6.31% at least. Therefore, the optimal scheduling scheme obtained based on ISSA improves the daily operating total revenue and the system operation stability of the microgrid.

Energy-efficient multi-objective distributed assembly permutation flowshop scheduling by Q-learning based meta-heuristics

This study addresses energy-efficient multi-objective distributed assembly permutation flowshop scheduling problems with minimisation of maximum completion time, mean of earliness and tardiness, and total carbon emission simultaneously. A mathematical model is introduced to describe the concerned problems. Five meta-heuristics are employed and improved, including the artificial bee colony, genetic algorithms, particle swarm optimization, iterated greedy algorithms, and Jaya algorithms. To improve the quality of solutions, five critical path-based neighborhood structures are designed. Q-learning, a value-based reinforcement learning algorithm that learns an optimal strategy by repeatedly interacting with the environment, is embedded into meta-heuristics. The Q-learning guides algorithms intelligently select appropriate neighborhood structures in the iterative process. Then, two machine speed adjustment strategies are developed to further optimize the obtained solutions. Finally, extensive experimental results show that the Jaya algorithm with Q-learning has the best performance for solving the considered problems.

Combining meta-heuristics and Q-learning for scheduling lot-streaming hybrid flow shops with consistent sublots

This study addresses a hybrid flow shop scheduling problem by considering consistent sublots (HFSP_CS) in lot-streaming. The objective is to minimize the maximum completion time (makespan). By mathematically formulating the HFSP_CS, a mathematical model is established. Next, novel combinations of four meta-heuristics and Q-learning-based improvement tactics are proposed for tackling the related problems for the first time. Drawing upon problem-specific characteristics, five local search operators are employed and selected appropriately by utilizing Q-learning throughout the iterations. Furthermore, the model's veracity is demonstrated through the utilization of the CPLEX solver. Then, by resolving 128 instances, the enhanced algorithms showcase their effectiveness. The results show that the artificial bee colony algorithm integrated with Q-learning is the most competitive algorithm among the tested algorithms.

An adaptive shuffled frog-leaping algorithm for flexible flow shop scheduling problem with batch processing machines

Batch Processing Machines (BPM) and transportation are seldom studied simultaneously in Flexible Flow Shop. In this study, Flexible Flow Shop Scheduling Problem (FFSP) with BPM at the last stage and transportation is considered and an adaptive shuffled frog-leaping algorithm (ASFLA) is proposed to minimize makespan. To produce high-quality solutions, a heuristic is employed to produce initial solution, two groups are formed by using all memeplexes, then an adaptive memeplex search is implemented, in which the number of searches is dynamically determined by the quality of the memeplex, an adaptive group search is also conducted by exchanging memeplexes or supporting of the worse memeplex. A novel population shuffling and the worst memeplex elimination are proposed. A number of computational experiments are executed to test the new strategies and performances of ASFLA. Computational results demonstrate that new strategies are effective and ASFLA is a very competitive algorithm for FFSP with BPM and transportation.

Interval Constrained Multi-Objective Optimization Scheduling Method for Island-Integrated Energy Systems Based on Meta-Learning and Enhanced Proximal Policy Optimization

Multiple uncertainties from source–load and energy conversion significantly impact the real-time dispatch of an island integrated energy system (IIES). This paper addresses the day-ahead scheduling problems of IIES under these conditions, aiming to minimize daily economic costs and maximize the output of renewable energies. We introduce an innovative algorithm for Interval Constrained Multi-objective Optimization Problems (ICMOPs), which incorporates meta-learning and an improved Proximal Policy Optimization with Clipped Objective (PPO-CLIP) approach. This algorithm fills a notable gap in the application of DRL to complex ICMOPs within the field. Initially, the multi-objective problem is decomposed into several single-objective problems using a uniform weight decomposition method. A meta-model trained via meta-learning enables fine-tuning to adapt solutions for subsidiary problems once the initial training is complete. Additionally, we enhance the PPO-CLIP framework with a novel strategy that integrates probability shifts and Generalized Advantage Estimation (GAE). In the final stage of scheduling plan selection, a technique for identifying interval turning points is employed to choose the optimal plan from the Pareto solution set. The results demonstrate that the method not only secures excellent scheduling solutions in complex environments through its robust generalization capabilities but also shows significant improvements over interval-constrained multi-objective evolutionary algorithms, such as IP-MOEA, ICMOABC, and IMOMA-II, across multiple multi-objective evaluation metrics including hypervolume (HV), runtime, and uncertainty.

Machine hearing for predictive maintenance of BLDC motors

PurposeThe purpose of this paper is to approach predictive maintenance (PdM) of brushless direct current (BLDC) motors using audio signal processing and extracting statistical and spectral features to train classical machine learning (ML) models.Design/methodology/approachThe proposed methodology relies on classification predictive model that shows the motors prone to failure. To verify this, the model was implemented and tested with audio data. The trained models are then deployed to an Industrial Internet of Things (IIoT) application built using Django.FindingsThe implementation of the methodology allows for achieving performance as high as 92% accuracy, proving that spectral features should be considered when training ML models for PdM.Originality/valueThe proposed model is an effective decision-making tool that provides an ideal solution for preventive maintenance scheduling problems for BLDC motors.