Solving Scheduling Problems Research Articles

A speed-up procedure and new heuristics for the classical job shop scheduling problem: A computational evaluation

The speed-up procedure proposed for the permutation flowshop scheduling problem with makespan minimisation (commonly denoted as Taillard’s acceleration) remains, after 30 years, one of the most important and relevant studies in the scheduling literature. Since its proposal, this procedure has been included in countless approximate optimisation algorithms, and its use is mandatory for several scheduling problems. Unfortunately, despite the importance of such a procedure in solving scheduling problems, we are not aware of any related speed-up procedure proposed for the classical job-shop scheduling problem. First, this study aims to fill this gap by proposing a novel speed-up procedure for the job-shop scheduling problem with makespan minimisation, capable of reducing the complexity of insertion-based procedures n times. Second, to test its performance, the procedure is embedded in a critical-path-based local search method. Furthermore, we thirdly propose five constructive and composite heuristics to obtain high-quality solutions in short time intervals. The composite heuristics apply the previous procedure to reduce their computational efforts. Finally, to complete the study, we conduct an extensive computational evaluation on 243 test instances from eight distinct benchmarks. In this evaluation, 30 heuristics are re-implemented and compared under the same computer conditions. The results indicate the superiority of the proposed approaches compared to the competitive algorithms for the problem under study.

Scheduling in a Simple Assembly Robotics Cell to Minimize Earliness and Tardiness

Background: Robotics Assembly Cells (RAC) have been designed to meet the flexibility requirements demanded by today's globalized market. The objective is to manufacture a vast variety of products at a low cost, which requires equipment with a high level of flexibility, such as robots. The need to schedule a great variety of jobs in an RAC is a very relevant issue, as efficiency and productivity depend on the sequence in which jobs are scheduled. Studies around this matter have developed models with analytical and heuristic approaches, as well as simulation methods and genetic algorithms, seeking to improve performance measures based mainly on time, utilization, and costs. Method: The purpose of this article is to formulate an exact mathematical model using mixed-integer linear programming (MILP) to optimize small scheduling problems. The objective is to minimize the measure of performance related to the tardiness and earliness of jobs. This optimization aims to mitigate the effects of delays in product deliveries, queue times, and work-in-process inventory in subsequent processes. Doing so facilitates adherence to agreed-upon delivery deadlines and prevents bottlenecks in the assembly cell. Results: The proposed mathematical model generates optimal solutions to the job scheduling problem in the assembly cell, which serves as a case study. This addresses the need to minimize tardiness to meet delivery deadlines or minimize earliness while avoiding an increase in work-in-process inventories. The model ensures that optimal scheduling decisions are made to optimize both delivery performance and inventory levels. Conclusions: Due to the NP-hard complexity of the scheduling problem under study, the proposed mathematical model demonstrates computational efficiency in solving scheduling problems with fewer than 20 jobs. The model is designed to handle such smaller-scale problems within a reasonable computational time frame, considering the inherent complexity of the scheduling problem.

Dynamic scheduling mechanism for intelligent workshop with deep reinforcement learning method based on multi-agent system architecture

With the development and changes of industry and market demand, the personalized customization production mode with small batch and multiple batches has gradually become a new production mode. This makes production environment become more complex and dynamic. However, traditional production workshops cannot effectively adapt to this environment. Combining with new technologies, transforming traditional workshops into intelligent workshop to cope with new production mode become an urgent problem. Therefore, this paper proposes a multi-agent manufacturing system based on IoT for intelligent workshop. Meanwhile, this paper takes flexible job shop scheduling problem (FJSP) as a specific production scenario and establishes relevant mathematics model. To build the agent in intelligent workshop, this paper proposes a data-based with combination of virtual and physical agent (DB-VPA) which has information layer, software layer and physical layer. Then, based on the manufacturing system, this paper designs a dynamic scheduling mechanism with deep reinforcement learning (DRL) for intelligent workshop. This method contains three aspects: (1) Modeling production process based on Markov decision process (MDP). (2) Designing communication mechanism for DB-VPAs. (3) Designing scheduling model combining with improved genetic programming and proximal policy optimization (IGP-PPO) which is a DRL method. Finally, relevant experiments are executed in a prototype experiment platform. The experiments indicate that the proposed method has superiority and generality in solving scheduling problem with dynamic events.

Adaptive fuzzy-genetic algorithm operators for solving mobile robot scheduling problem in job-shop FMS environment

Flexible Manufacturing Systems (FMS) is known as one of the recurring themes that possess these promising characteristics with a synergistic combination of productivity-efficiency transport and flexibility through a number of machine tools alongside other material handling devices. In FMS, mobile robots are commonly deployed in material handling system for the purpose of increasing the efficiency and productivity of the manufacturing process. A reliable, efficient, and optimal scheduling is the most important in manufacturing system. The scheduling problems can become highly complex, especially in large-scale systems with numerous tasks and constraints. Thus, schedule optimization becomes crucial to enhance target performance by determining the best allocations and sequences of resources under specified constraints. Recently, Genetic Algorithm (GA) is a remarkably applicable search algorithm to solve scheduling problems to the way that near optimal could be found. While the performance of GA much depends on the selection of the main parameters, a standard GA may suffer from the issue of premature convergence due to the lack of control on its parameters especially crossover and mutation operators. As there is no specific method or way to tune these parameters, the algorithm is prone to converge on the local optimum, thereby leading to performance degradation. To overcome such flaw, this paper proposed an improved Genetic Algorithm using an adaptive Fuzzy Logic to control crossover and mutation operators (FGAOC) for the solution to the NP-hard problem of scheduling mobile robot within Job-Shop FMS environment. The proposed algorithm has been evaluated in several case studies such as small and large-scale problem, various numbers of mobile robots and the 40-test benchmark problem. The results have demonstrated that the proposed FGAOC has delivered a good performance in exploration-exploitation activities with better solution quality.

Reentrant hybrid flow shop scheduling with stockers in automated material handling systems using deep reinforcement learning

In smart factories, automated material handling system (AMHSs) replace manual material handling to increase production efficiency, in which stockers serve as the temporary storage for work-in-process inventories. Furthermore, costly machines and complex processes in advanced manufacturing lead to the need for multiple reentrant processes of the same workstation. However, previous works on scheduling problems rarely considered the function of stockers and reentrant processes, and their approaches were mostly based on metaheuristic algorithms. Recent advances in artificial intelligence enable the possibility of solving scheduling problems using deep reinforcement learning (DRL). Therefore, this work investigates the reentrant hybrid flow shop scheduling problem with stockers (RHFS2) inspired by AMHSs, and solves it by DRL. Firstly, the states, actions, and rewards of the Markov decision process for this problem are designed; and then, two deep Q network (DQN) approaches based on the actions for determining machines and jobs, respectively, are proposed. Simulation results demonstrate that our proposed DQN approaches outperform for finding better solutions of different-scale problems than classical metaheuristic algorithms.

A two-stage iterated greedy algorithm and a multi-objective constructive heuristic for the mixed no-idle flowshop scheduling problem to minimize makespan subject to total completion time

Advanced production systems usually are complex in nature and aim to deal with multiple performance measures simultaneously. Therefore, in most cases, the consideration of a single objective function is not sufficient to properly solve scheduling problems. This paper investigates the multi-objective mixed no-idle flowshop scheduling problem. The addressed optimization case is minimizing makespan subject to an upper bound on total completion time. To solve this problem, we proposed a two-stage iterated greedy and a multi-objective constructive heuristic. Moreover, we developed a new multi-objective improvement procedure focusing on increasing the performance of the developed methods in solving the addressed problem. and a new initialization procedure. We performed several computational tests in order to compare our developed methods with the main algorithms from similar scheduling problems in the literature. It was revealed that the proposed approaches give the best results compared with other state-of-the-art performing methods.

An intelligent and interpretable rule-based metaheuristic approach to task scheduling in cloud systems

Metaheuristic algorithms can be very successful in solving scheduling problems. However, these methods can be slow for time-critical applications due to the iterative stochastic processes they perform. This problem becomes even more pronounced in dynamic environments such as cloud systems. This paper proposes an interpretable rule-based solution to minimize this problem. Combining metaheuristic task scheduling solutions and machine learning techniques, this method uses a two-phase mechanism, semi-offline and online. In the semi-offline phase, we first archive metaheuristic solutions to previously randomly generated or encountered task-scheduling problems. The basic idea of the proposed method is to reuse these previously obtained successful metaheuristic solution patterns for future similar problems. Finding similar solution patterns from this extensive archive dataset is done by automatically extracting rule sets through machine learning techniques. These interpretable rule sets are used to identify the type of task scheduling problem encountered in the online phase and to find the optimal solution pattern. The performance of this method, which dramatically reduces execution time and enables the use of metaheuristics in time-critical applications, has been tested and proven for various cloud task-scheduling scenarios.

A Monte Carlo simulation approach to the gap-time relationship in solving scheduling problem

This article presents a study on the job shop problem, a combinatorial optimization problem that models scheduling and resource allocation in industrial settings. The article aims to investigate the relationship between optimality gap and required computational resources, considering various optimality gap levels that are applicable in real-life situations. The study uses a Monte Carlo simulation to analyze the behavior of solvers in solving different sizes of random-generated scheduling problems. The findings of the study offer insights into the worthiness of reaching an optimal solution versus implementing a near-optimal solution and starting the work. The codes used in the study are accessible on the author's GitHub account.

Minimizing Makespan in a Permutation Flow Shop Environment: Comparison of Scatter Search, Genetic Algorithm and Greedy Randomized Adaptive Search Procedures

Solving scheduling problems enables more efficient use of production capacity. It involves defining the sequence of operations, determining the capacity of resources, and balancing workloads. Different methods, especially metaheuristics, have been used to solve these problems. This study presents the application of Scatter Search (SS), Genetic Algorithm (GA), and Greedy Randomized Adaptive Search Procedures (GRASP) for minimizing makespan in a permutation flow shop environment. In this study, the performances of these methods are compared through various test problems in the literature and a real-life problem of a company operating in the automotive sector. Study comprises 48 jobs that must be planned within a day for eight consecutive operations. In cellular manufacturing, the sequence in which each job is processed in eight operations is the same. In solving permutation flow shop scheduling problems (PFSP), one of the NP-hard problems, meta-heuristic methods are widely applied due to their successful results. From this point of view, SS, GA, and GRASP are employed in this study, and their performances are compared.

ИНТЕГРИРОВАННАЯ МОДЕЛЬ РЕШЕНИЯ ЗАДАЧИ ДИСПЕТЧЕРИЗАЦИИ ЗАЯВОК

The paper considers the problem of scheduling. The paradigm of organization of distributedcomputing based on Grid-computing is considered. The classification of task scheduling systems isgiven. Various approaches to solving the scheduling problem are described. A model of the task ofservicing applications based on the principles of the theory of queuing systems is presented. Thetask statement is formulated on the basis of Grid-scheduling. The concept of a resource rectangleis proposed. The environment for scheduling resource rectangles is defined. A model is proposedthat allows formalizing the user's request for service by the concept of a resource (non-Euclidean)rectangle. Instead of the principle of optimization based on the machine search for the best distributionof the array of resource rectangles, a heuristic principle was proposed, which made it possibleto reduce the amount of necessary calculations. The proposed heuristic scheduling algorithmmakes it possible to take into account the properties of the array and evaluate the quality of solutions.Models of the demand environment in the form of single cubic faces are constructed.The model of cubic faces is generalized to the experiment of cubic layers. The description of thedemand model used is given. A model of the resource supply environment in the form of a canonicalpyramid is constructed and the concept of a canonical demand-supply experiment for modelhomogeneous resource elements is introduced. A truncation of the supply-demand experiment hasbeen introduced. A hybrid model based on a combination of evolutionary search principles andfuzzy control methods is proposed. To solve scheduling problems, it is proposed to use evolutionaryalgorithms. A modified solution coding technique and new modifications of genetic operatorsfor solving scheduling problems have been developed. A block diagram of the algorithm for solvingthe problem under consideration is presented, taking into account the use of a fuzzy logic controller.Computer simulation has been performed and the results of computational experimentshave been presented. The features of the proposed method are revealed, its advantages and disadvantagesare formulated.

An Open-Source Simulation Model for Solving Scheduling Problems

In this study, an open-source simulation model is presented for solving scheduling problems. The model is capable of solving different benchmarks. The methods involved in the simulation are mainly based on generating dispatching rules or using them to solve problems, but there are other heuristics as well. Dispatching rules in an evolutionary process are generated using Gene Expression Programming. For this aim, a coding method, which has not been described in the literature before, is explained. Along with the explanation of the properties of the source code, information about deterministic, dynamic models, buffer states, machine breakdown states, and the methods used to deal with them is presented. Concepts are explained with visual examples. In addition, a subject that has not been investigated in the literature before is analyzed by using the simulation model. This topic is to examine the results of solving machine assignment and operation sequencing sub-problems in flexible job shop scheduling problems with different rules. Moreover, objective functions that the source code can handle are discussed. Unlike many studies in the literature, the codes are presented to the readers as open source. Also, it is open to development and can be easily modified by users to solve other types of problems. Finally, in the study, experimental results are presented on the basis of some benchmarks available in the literature, and the limits of the study and source code are explained.

Decomposition Strategies for Solving Scheduling Problems in Industrial Applications

This article presents an overview of a research study of a crucial optimization problem in the Computer Science/Operations research field: The Job-shop Scheduling Problem (JSP). The JSP is a challenging task in which a set of operations must be processed using a set of scarce machines to optimize a particular objective. The main purpose of the JSP is to determine the execution order of the processes assigned to each machine to optimize an objective. Our main interest in this study is to investigate developing decomposition strategies using logic programming to solve the JSP. We split our goal into two main phases. The first phase is to apply the decomposition approach and evaluate the proposed model by solving a set of known benchmark instances. The second phase is to apply the successful decomposition methods obtained from the first phase to solve a scheduling problem in the real-life application. In the current state, we finished the first phase and started the second one aiming to have a model that can provide a schedule of a factory for a short-time period.

The SoftCumulative Constraint with Quadratic Penalty

The Cumulative constraint greatly contributes to the success of constraint programming at solving scheduling problems. The SoftCumulative, a version of the Cumulative where overloading the resource incurs a penalty is, however, less studied. We introduce a checker and a filtering algorithm for the SoftCumulative, which are inspired by the powerful energetic reasoning rule for the Cumulative. Both algorithms can be used with classic linear penalty function, but also with a quadratic penalty function, where the penalty of overloading the resource increases quadratically with the amount of the overload. We show that these algorithms are more general than existing algorithms and vastly outperform a decomposition of the SoftCumulative in practice.

An enhanced two phase estimation of distribution algorithm for solving scheduling problem

ABSTRACT Scheduling is one critical issue both in the field of industry engineering and combinatorial optimization research. In order to solve multi-objective scheduling problem with uncertainty, this paper presents a method of enhanced hybrid Estimation of Distribution Algorithm (EDA) with Teaching and Learning-Based Optimization Algorithm (TLBO). First, in order to concentrate their respective advantages, two algorithms of EDA and TLBO are integrated to enhance the capability of both global and local search. Second, scenario-based simulation is adopted to deal with uncertainty, and an adaptive sampling strategy is involved to dynamically adjust the number of scenarios during the evolving process. Third, a problem-specific local search is designed to further improve the optimality of candidate solutions. By comparing with existing algorithms on the benchmark problems of flexible job shop scheduling problem (FJSP), it is to demonstrate that our proposal can obtain better solutions in the aspects of optimality and computational efficiency.

A Greedy heuristic for solving scheduling problems with bounded rejection cost

We study single machine scheduling problems with the option of job rejection. The scheduling measures considered are: makespan, total completion time, total tardiness and number of tardy jobs. Following many real-life settings, the total permitted rejection cost is assumed to be bounded. All the problems are known to be NP-hard. The paper focuses on the introduction of an efficient greedy-type heuristic, and performing an extensive numerical study. For makespan minimization, the heuristic is proved to be asymptotically optimal under very general conditions. For each of the problems, a pseudo-polynomial dynamic programming algorithm is introduced, and consequently, the results obtained by the greedy heuristic are compared to the optimum. We show that the greedy heuristic leads to very small optimality gaps in all our tests, and that the dynamic programming algorithms can solve medium and large size instances in reasonable times.

Optimization approaches for solving production scheduling problem: A brief overview and a case study for hybrid flow shop using genetic algorithms

The aim of this paper is to investigate scheduling problems in manufacturing. After a brief introduction to the modelling approach to the scheduling problem, the study focuses on the optimization approach to the scheduling problem. Firstly, the different optimization approaches are categorised and their respective advantages and disadvantages are shown. This is followed by a detailed analysis of the characteristics and applicability of each of the commonly used optimization approaches. Finally, a case study is presented. A mathematical model is developed with the objective of minimising the maximum completion time for a mixed flow shop scheduling problem, and a genetic algorithm is used to solve the problem. The validity of the model is verified through the case study, which can provide a reasonable scheduling solution for actual manufacturing. This provides a reference for the selection and use of methods for solving scheduling problems in practical production.

Optimization of Genetic Algorithm in Courses Scheduling

Scheduling courses is an intricate and pivotal part of a university as it impacts the teaching and learning process. The problem frequently occurs is the struggle of placing schedules which is manual, takes a long time, and inaccurate. This paper explores the process and how effective the genetic algorithm method is in solving scheduling problems in lecture environment. The selection of genetic algorithms owes to it produces an optimal scheduling solution. To build a scheduling optimization system, it is essential to collect room data, lecturers, courses, days and hours of teaching. The data collection comes from field studies by observations and interviews. Literature studies are also needed to acquire the basic course scheduling, optimization, genetic algorithms, PHP, MySQL, Bootstrap, and Visual Studio Code. The test outcomes attained the preeminent one with the highest fitness value in the number of generations, populations, the crossover combination and mutation rates. The final result showed that the first chromosome is the finest chromosome produces scheduling with the highest fitness value. The outcomes of the whole algorithm process are consistent with the original predicted data, and the same lecturer is not scheduled to teach more than once at the same time. It is expected that the application of the genetic algorithm method optimizes course scheduling with great outcome.

Formal scheduling method for zero-defect manufacturing

A defect prevention is a part of manufacturing company practice. Paper proposes a formal approach for solving scheduling problems with unexpected events as extension of general frameworks for Zero-Defect Manufacturing (ZDM) strategy. ZDM aims to improve the process efficiency and the product quality while eliminating defects and minimizing process errors. However, most of ZDM applications focus on using the technological achievements of Industry 4.0 to detect and predict defects, forgetting to optimize the schedule on the production line. We propose formal method to create predictive-reactive schedule for problems with defect detection and repair. Our proposal is based on the formal Algebraic-Logical Meta-Model (ALMM). In particular, it uses the model switching method and combines defect detection, heuristics construction and decision support containing predictions of disturbances in the production process and enabling their prevention. Production defects are detected and repaired, and consequently, production delivers components without defects, and in the shortest possible time. Moreover, the collection and analysis of data related to the occurrence of disturbances in the production process helps the management board in making decisions based on analysis gathered and stored data. Thus, the proposed method includes strategies such as detection, repair, prediction and prevention for defect-free production. We illustrate the proposed method on the example of a flow-shop system with different types of product defect problem.

Energy-aware task scheduling in cloud compting based on discrete pathfinder algorithm

Task scheduling is one of the fundamental issues that attract the attention of lots of researchers to enhance cloud performance and consumer satisfaction. Task scheduling is an NP–hard problem that is challenging due to the several conflicting objectives of users and service providers. Therefore, meta-heuristic algorithms are the more preferred option for solving scheduling problems in a reasonable time. Although many task scheduling algorithms are proposed, existing strategies mainly focus on minimizing makespan or energy consumption while ignoring other performance factors. In this paper, we propose a new task scheduling algorithm based on the Discrete Pathfinder Algorithm (DPFA) that is inspired by the collective movement of the animal group and mimics the guidance hierarchy of swarms to find hunt. The proposed scheduler considers five objectives (i.e., makespan, energy consumption, throughput, tardiness, and resource utilization) as cost functions. Finally, different algorithms such as Firefly Algorithm (FA), Particle Swarm Optimization (PSO), Grasshopper Optimization Algorithm (GOA), and Bat Algorithm (BA), are used for comparison. The experimental results indicate that the proposed scheduling algorithm can improve up to 9.16%, 38.44%, 3.59%, and 3.44% the makespan in comparison with FA, BA, PSO, and GOA, respectively. Moreover, the results show dramatic improvements in terms of resource utilization, throughput, and energy consumption.

A Hybrid Quantum-Classical Approach to Solving Scheduling Problems

An effective approach to solving complex problems is to decompose them and integrate dedicated solvers for those subproblems. We introduce a hybrid decomposition that incorporates: (1) a quantum annealer that samples from the configuration space of a relaxed problem to obtain strong candidate solutions, and (2) a classical processor that maintains a global search tree and enforces constraints on the relaxed components of the problem. Our framework is the first to use quantum annealing as part of a complete search. We consider variants of our approach with differing amounts of guidance from the quantum annealer. We empirically test our algorithm and compare the variants on problems from three scheduling domains: graph-coloring-type scheduling, simplified Mars Lander task scheduling, and airport runway scheduling. While we were only able to test on problems of small sizes, due to the limitation of currently available quantum annealing hardware, the empirical results show that results obtained from the quantum annealer can be used for more effective search node pruning and to improve node selection heuristics when compared to a standard classical approach.