Scheduling Problem Research Articles

Preference learning based deep reinforcement learning for flexible job shop scheduling problem

The flexible job shop scheduling problem (FJSP) holds significant importance in both theoretical research and practical applications. Given the complexity and diversity of FJSP, improving the generalization and quality of scheduling methods has become a hot topic of interest in both industry and academia. To address this, this paper proposes a Preference-Based Mask-PPO (PBMP) algorithm, which leverages the strengths of preference learning and invalid action masking to optimize FJSP solutions. First, a reward predictor based on preference learning is designed to model reward prediction by comparing random fragments, eliminating the need for complex reward function design. Second, a novel intelligent switching mechanism is introduced, where proximal policy optimization (PPO) is employed to enhance exploration during sampling, and masked proximal policy optimization (Mask-PPO) refines the action space during training, significantly improving efficiency and solution quality. Furthermore, the Pearson correlation coefficient (PCC) is used to evaluate the performance of the preference model. Finally, comparative experiments on FJSP benchmark instances of varying sizes demonstrate that PBMP outperforms traditional scheduling strategies such as dispatching rules, OR-Tools, and other deep reinforcement learning (DRL) algorithms, achieving superior scheduling policies and faster convergence. Even with increasing instance sizes, preference learning proves to be an effective reward mechanism in reinforcement learning for FJSP. The ablation study further highlights the advantages of each key component in the PBMP algorithm across performance metrics.

Production scheduling with multi-robot task allocation in a real industry 4.0 setting

The demand for efficient Industry 4.0 systems has driven the need to optimize production systems, where effective scheduling is crucial. In smart manufacturing, robots handle material transfers, making precise scheduling essential for seamless operations. However, research often oversimplifies the Robotic Flexible Job Shop problem by focusing only on transportation time, ignoring resource allocation and robot diversity. This study addresses these gaps, tackling a Multi-Robot Flexible Job Shop (MRFJS) scheduling problem with limited buffers. It involves non-identical parallel machines and robots with varying capabilities overseeing material handling under blocking conditions. The case study is based on a real Industry 4.0 scenario, where the layout restricts each robotic arm’s access, requiring strategic buffer placement for part transfers. A Mixed-Integer Programming (MILP) model aims to minimize makespan, followed by a new Genetic Algorithm (GA) using Roy and Sussman’s Alternative Graph. Computational tests on various scales and real data from a manufacturing plant demonstrate the GA’s efficacy in solving complex scheduling problems in real-world production settings. Based on the data, the Proposed Genetic Algorithm (PGA), with an average Relative Deviation (ARD) of 0.25%, performed approximately 34% better compared to the Basic Genetic Algorithm (BGA), with an average ARD of 0.38%. This percentage indicates that the PGA significantly outperforms in solving complex scheduling problems.

Energy-Efficient Distributed Welding Shop Scheduling Based on Multi-Objective Seagull Algorithm

For the energy-efficient distributed welding shop scheduling problem, focusing on the scheduling of production in a distributed welding shop, a mathematical model is established with the objective of minimizing the makespan and total energy consumption. In order to solve this optimization problem, an improved multi-objective seagull algorithm (IMOSOA) is proposed. The algorithm introduces three main enhancements: designing a weight matrix based on multiple critical paths to update the number of welders allocated to each job, redesigning the discretization operations of the multi-objective seagull algorithm according to the characteristics of distributed welding shop, and incorporating a Pareto front selection strategy. This strategy uses a new crowding distance calculation to resolve cases where non-dominated solutions at the same dominance level have equal crowding distances, thereby improving the next generation of solutions. These improvements not only reduce the maximum completion time and total energy consumption but also enhance search efficiency. Finally, the IMOSOA is compared with other algorithms under different scale examples, and the results show that the energy consumption is at least 11.7% lower than that of the comparison algorithm, which verifies the superiority of the IMOSOA.

Trustworthy and efficient project scheduling in IIoT based on smart contracts and edge computing

To facilitate flexible manufacturing, modern industries have incorporated numerous modular operations such as multi-robot services which can be expediently arranged or offloaded to other production resources. However, complex manufacturing projects often consist of multiple tasks with fixed sequences, posing a significant challenge for smart factories in efficiently scheduling limited robot resources to complete specific tasks. Additionally, when projects span across factories, ensuring faithful execution of contracts becomes another challenge. In this paper, we propose a modified combinatorial auction method combined with blockchain and edge computing technologies to organize project scheduling. Firstly, we transform efficient resource scheduling into a resource-constrained multi-project scheduling problem (RCPSP). Subsequently, the solution integrates combinatorial auction with random sampling (CA-RS) into smart contracts. Alongside security analysis, simulations are conducted using real data sets. The results indicate that the suggested CA-RS approach significantly enhances efficiency and security in resource arrangement within the industrial Internet of Things compared to baseline algorithms.

New model to streamline customer order scheduling

The Customer Order Scheduling (COS) problem involves organizing a set of orders, each characterized by a release time, a due date, and a processing time, with the objective of minimizing the costs associated with delivery delays. This study introduces an innovative approach, the Streamline COS, which integrates order scheduling optimization with improved resource utilization and a reduction in production inefficiencies. We present a model aimed at minimizing an objective function that encompasses delay penalties and the optimization of resource usage. Additionally, we introduce an optimized COS algorithm, named SCOS (Streamline COS), designed to find the optimal solution. The efficacy of this approach is validated through experiments with several datasets of varying sizes and instances, demonstrating that the Streamline COS method significantly enhances resource management, reduces delays, and optimizes order scheduling, while offering flexible priority management. This approach provides a practical and effective solution to complex scheduling problems and opens new research avenues, particularly in integrating dynamic constraints and leveraging optimization and machine learning techniques for further performance improvements.

A Hybrid Honey Badger Algorithm to Solve Energy-Efficient Hybrid Flow Shop Scheduling Problems

A well-planned schedule is essential to any organization’s growth. Thus, it is important for the literature to cover a more comprehensive range of scheduling problems. In this paper, energy-efficient hybrid flow shop (EEHFS) scheduling problems are considered. Researchers have developed several techniques to deal with EEHFS scheduling problems. Also, researchers have recently proposed several metaheuristics. Honey Badger Algorithm (HBA) is one of the most recent algorithms proposed to solve various optimization problems. The objective of the present work is to solve EEHFS scheduling problems using the Hybrid Honey Badger Algorithm (HHBA) to reduce the makespan (Cmax) and total energy cost (TEC). In the HHBA, a constructive heuristic known as the NEH heuristic was incorporated with the Honey Badger Algorithm. The suggested algorithm’s performance was verified using an actual industrial scheduling problem. The company’s results are compared with those of the HHBA. The HHBA could potentially result in an 8% decrease in total energy cost. Then, the proposed algorithm was applied to solve 54 random benchmark problems. The results of the proposed HHBA were compared with the FIFO dispatching rule, the NEH heuristic, and other metaheuristics such as the simulated annealing (SA) algorithm, the genetic algorithm (GA), the particle swarm optimization (PSO) algorithm, Honey Badger Algorithm, and the Ant Colony Optimization (ACO) algorithms addressed in the literature. Average percentage deviation (APD) was the performance measure used to compare different algorithms. The APD of the proposed HHBA was zero. This indicates that the proposed HHBA is more effective in solving EEHFS scheduling problems.

Piecewise linear value function approximations in nonlinear dynamic scheduling problems with VTOLs

Modern vertical take-off and landing vehicles (VTOLs) could significantly affect the future of mobility. The broad range of their application fields encompasses urban air mobility, transportation and logistics as well as reconnaissance and observation missions in a military context. This article presents an efficient numerical framework for dynamic scheduling of multiple VTOLs. It combines a scheduling problem with optimal trajectory planning. The whole setting is formulated as a mixed-integer bilevel optimization problem. At the upper level, VTOLs are scheduled, and their starting times are computed. The solution of the lower level problem involves the computation of a value function and yields optimal trajectories for every aerial vehicle. In order to solve the bilevel problem, it is recast into a single-level one. The resulting mixed-integer nonlinear program is then piecewise linearized and solved numerically by a mixed-integer linear solver based on the Branch-and-Bound algorithm. Numerical results prove the feasibility of the approach proposed herein.

From Integer Programming to Machine Learning: A Technical Review on Solving University Timetabling Problems

Solving the university timetabling problem is crucial as it ensures efficient use of resources, minimises scheduling conflicts, and enhances overall productivity. This paper presents a comprehensive review of university timetabling problems using integer programming algorithms. This study explores various integer programming techniques and their effectiveness in optimising complex scheduling requirements in higher education institutions. We analysed 95 integer programming-based models developed for solving university timetabling problems, covering relevant research from 1990 to 2023. The goal is to provide insights into the evolution of these algorithms and their impact on improving university scheduling. We identify that the implementation rate of models using integer programming is 98%, which is much higher than 34% implementation rates using meta-heuristics algorithms from the existing review. The integer programming models are analysed by the problem types, solutions, tools, and datasets. For three types of timetabling problems including course timetabling, class timetabling, and exam timetabling, we dive deeper into the commercial solvers CPLEX (47), Gurobi (11), Lingo (5), Open Solver (4), C++ GLPK (4), AIMMS (2), GAMS (2), XPRESS (2), CELCAT (1), AMPL (1), and Google OR-Tools CP-SAT (1) and identify that CPLEX is the most frequently used integer programming solver. We explored the uses of machine learning algorithms and the hybrid solutions of combining the integer programming and machine learning algorithms in higher education timetabling solutions. We also identify areas for future work, which includes an emphasis on using integer programming algorithms in other industrial areas, and using machine learning models for university timetabling to allow data-driven solutions.

Bayesian Learning Based Elitist Nondominated Sorting Algorithm for a Kind of Multi-objective Integrated Production Scheduling and Transportation Problem

This paper focuses on a kind of multi-objective integrated production scheduling and transportation problem (MIPSTP), which is encountered in many real-life industrial processes. MIPSTP contains a production stage for processing products and a transportation stage for transporting products. In MIPSTP, we consider a dedicated integration of distributed scheduling and transportation regarding the two stages, arising from a practical project for a cooperative iron and steel company. The objective of MIPSTP is to minimize the total completion time of each factory and total transportation cost. To solve the problem, a Bayesian learning-based elitist nondominated sorting algorithm (BLENSA) is proposed. The primary highlights of this work are two-fold: 1) new solution structures of MIPSTP and 2) novel search model of BLENSA. For the solution structures, we propose for the first time the mathematical description of MIPSTP, accounting for several features in applications and so is different from conventional scheduling problems. For the search model of BLENSA, we propose a Bayesian learning-based probability model to learn valuable knowledge about nondominated solutions. Thereby, BLENSA combines the Bayesian learning-based probability model to produce a candidate population (CP) and the nondominated sorting method to generate a main population (MP). Next, we propose a greedy competition strategy to construct MP from CP and MP for the next generation. Results of experiments on 57 test instances and a real-life case study demonstrate the effectiveness and practical values of BLENSA.

Deep reinforcement learning for Agile Earth Observation Satellites scheduling problem with variable image duration

The Agile Earth Observation Satellites (AEOS) possess active imaging capabilities, which enable variable image durations during observations. Due to the problem’s high complexity, traditional heuristic algorithms are unable to provide optimal solutions within a feasible timeframe. In this paper, we propose an improved deep reinforcement learning approach (IDRL), including IDRL based on optimal observation quality (IDRL-MQ) and IDRL based on the longest observation duration (IDRL-MD), to solve the multi-objective scheduling problem for AEOS with variable image duration (MO-SPVID). Two different strategies IDRL-MQ and IDRL-MD, were designed to determine the start time and duration of observation. The experimental results demonstrate that IDRL-MD outperforms both IDRL-MQ and the superior heuristic algorithm ALNS-NSGAII in terms of solution quality and solution diversity. The demonstrated effectiveness of the appropriate heuristic strategies provides evidence for their rationality. Furthermore, the results obtained on instances of varying scales indicate that IDRL exhibits a high level of generality and robustness.

Minimising makespan and total tardiness in no-wait open-shop scheduling problems using metaheuristic algorithms: a narrative review

Minimising makespan and total tardiness in no-wait open-shop scheduling problems using metaheuristic algorithms: a narrative review

Resource-constrained project scheduling problem: Review of recent developments

The Resource-Constrained Project Scheduling Problem (RCPSP) remains a critical area of study in project management, focusing on optimizing project schedules under constraints such as limited resources and task interdependencies. This review synthesizes advancements from 2016 to 2024, encompassing problem variants, optimization techniques, objectives, and real-world applications. Key developments include the evolution of hybrid metaheuristics, multi-objective optimization approaches, and the integration of stochastic models to enhance robustness against uncertainties. Furthermore, the application of machine learning and sustainability-driven models has expanded the practical scope of RCPSP in dynamic and complex environments. Challenges such as scalability, uncertainty management, and the need for practical implementations are addressed, with future directions emphasizing AI integration, decentralized scheduling, and real-time adaptive solutions. This study provides a comprehensive perspective on RCPSP, bridging theoretical research with practical implications for diverse industries.

Discrete Time/Cost Trade-off Project Scheduling Problem with Tardiness Bounds

Discrete Time/Cost Trade-off Project Scheduling Problem with Tardiness Bounds

Benchmark for the scheduling problems of airport ground support operations and a case study

Benchmark for the scheduling problems of airport ground support operations and a case study

You are entitled to access the full text of this document A novel hybrid algorithm of cooperative variable neighborhood search and constraint programming for flexible job shop scheduling problem with sequence dependent setup time

This study focuses on the flexible job shop scheduling problem with sequence-dependent setup times (FJSP-SDST), and the goal is minimizing the makespan. To solve FJSP-SDST, first, we develop a constraint programming (CP) model to obtain optimal solutions. Due to the NP-hardness of FJSP-SDST, a CP assisted meta-heuristic algorithm (C-VNS-CP) is designed to make use of the advantages of both CP model and cooperative variable neighborhood search (C-VNS). The C-VNS-CP algorithm consists of two stages. The first stage involves C-VNS, for which eight neighborhood structures are defined. In the second stage, CP is used to further optimize the good solution obtained from C-VNS. In order to prove the efficiency of the C-VNS algorithm, CP model, and C-VNS-CP algorithm, experiments of 20 instances are conducted.

Seru scheduling problem with lot streaming and worker transfers: A multi-objective approach

Seru scheduling problem with lot streaming and worker transfers: A multi-objective approach

Integrating sequence-dependent setup times and blocking in hybrid flow shop scheduling to minimize total tardiness

This study addresses the minimization of total tardiness in a hybrid flow shop scheduling problem with sequence-dependent setup times and blocking constraints. Each production stage includes multiple machines, and there are no buffers between the stages. The setup time required to process a job depends on the previously processed job. Two mixed-integer linear programming models are developed to formulate the problem. Moreover, an iterative local search algorithm and hybrid genetic algorithms are proposed to have quality solutions with minimal computational efforts. Several computational tests are conducted to tune the heuristic parameters for better performance. Computational experiments are carried out to evaluate the performance of solution methodologies in terms of quality and time. The results indicate that while mixed-integer programming models can solve small-size problem instances, they are not capable of solving large-sized instances. However, the proposed heuristic algorithms find quality solutions for all instances in a very short time.

A hybrid approach of genetic algorithm and truncated branch-and-bound for seru scheduling problem with sequence-dependent setup time

A hybrid approach of genetic algorithm and truncated branch-and-bound for seru scheduling problem with sequence-dependent setup time

The shared autonomous vehicle’s scheduling and routing problem when providing the trip-chain based service for users

Shared autonomous vehicle (SAV) is expected to become an essential transportation mode. However, the studies on its scheduling and routing problems are all based on peer-to-peer (P2P) service, which refers to a pickup and delivery on a single trip. The P2P service ignores the correlations between sub-trips and users' journey continuity. To address this problem, a trip-chain based (TCB) service is proposed in SAV system, where users can choose paying and keep SAVs (PKSS) with no waiting time. Furthermore, based on the network flow theory, an integer linear programming model was established to decide optimal SAV's routing and scheduling. Finally, experiments are conducted in Beijing, China. Compared with the P2P service, the TCB service can not only increases operators' profitability but also reduces users' waiting time, provided that the operators set the price for PKSS between 0.1 and 0.65 CNY per minute.

Computational Study on Job Flow Shop Scheduling Using MiniMax Optimizing Algorithm

Shop scheduling is a critical part of manufacturing systems. The goal is to find an efficient schedule that optimizes system performance. Finding a feasible schedule becomes more difficult as the number of jobs and machines increases. The present research aims to study the computational study of different optimization methods to solve job flow shop scheduling problems. This paper reviews computational research of varying optimization methods to solve job flow shop scheduling problems. We discuss Johnson's algorithm, Campbell, Dudek, and Smith's (CDS) Approach, and Gantt chart and propose a Minimax optimization. This new method has the least processing time in the machine in the current situation. We present substantial computational results using MiniMax optimization techniques. From the result, we can conclude that the proposed algorithm gives less processing time and more frequently an optimal schedule than the other studied methods.