Problem Of Scheduling Jobs Research Articles

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.

Scheduling jobs using queries to interactively learn human availability times

The solution to a job scheduling problem that involves humans as well some other shared resource has to consider the humans’ availability times. For practical acceptance of a scheduling tool, it is crucial that the interaction with the humans is kept simple and to a minimum. It is rarely practical to ask users to fully specify their availability times or to let them enumerate all possible starting times for their jobs. In the scenario we are considering, users initially only propose a single starting time for each of their jobs and a feasible and optimized schedule shall then be found within a small number of interaction rounds. In each such interaction round, our scheduling approach may propose each user a small number of alternative time intervals for scheduling the user’s jobs, and then the user may accept or reject these. To make the best out of these limited interaction possibilities, we propose an approach that utilizes integer linear programming and an exact and computationally efficient probability calculation for the users’ availabilities assuming two different stochastic models. In this way, educated proposals of alternative time intervals for performing the jobs are determined based on the computed availability probabilities and the improvements these time intervals would enable. The approach is experimentally evaluated on a variety of artificial benchmark scenarios, and different variants are compared with each other and to diverse baselines. Results show that an initial schedule can usually be quickly improved over few interaction rounds even when assuming a quite simple stochastic model, and the final schedule may come close to the solution of the full-knowledge case despite the strongly limited interaction.

Minimizing Total Completion Time, Total Earliness Time, and Maximum Tardiness for a Single Machine scheduling problem

Machine scheduling problems (MSP) are considered as one of the most important classes of combinatorial optimization problems. In this paper, the problem of job scheduling on a single machine is studied to minimize the multiobjective and multiobjective objective function. This objective function is: total completion time, total lead time and maximum tardiness time, respectively, which are formulated as are formulated. In this study, a mathematical model is created to solve the research problem. This problem can be divided into several sub-problems and simple algorithms have been found to find the solutions to these sub-problems and compare them with efficient solutions. For this problem, some rules that provide efficient solutions have been proved and some special cases have been introduced and proved since the problem is an NP-hard problem to find some efficient solutions that are efficient for the discussed problem 1// and good or optimal solutions for the multi-objective functions 1// ,, and emphasize the importance of the dominance rule (DR), which can be applied to this problem to improve efficient solutions.

Logic-based Benders decomposition for bi-objective parallel machine selection and job scheduling with release dates and resource consumption

This work addresses a new bi-objective parallel machine selection and job scheduling problem with release dates and resource consumption. It consists in optimally selecting subcontractors (machines) from a set of geographically dispersed locations and scheduling the orders (jobs) to the selected subcontractors for processing while meeting the order release dates and resource consumption restrictions, so as to simultaneously minimize the maximum completion time, i.e., the makespan, and the total cost including machine usage cost and resource consumption cost. The problem is first formulated into a bi-objective mixed-integer linear program based on linear ordering (LO-MILP), and then valid inequalities are explored based on property analysis. To solve it, an ɛ-constraint method based on LO-MILP (ɛ-LO-MILP) is first proposed. To more efficiently solve it, we also develop a tailored logic-based Benders decomposition combined with ɛ-constraint method (ɛ-LBBD) where a novel method to obtain a tight lower bound of the identical parallel machine with machine-dependent release dates and some problem-specific cuts are proposed. Numerical experiments on an illustrative example are conducted to show the applicability of the model and algorithm and intuitively reveal the trade-off between production efficiency and cost. Experimental results on 200 instances with up to 100 orders demonstrate that ɛ-LBBD can reduce the computation time by about 28.92% compared to ɛ-LO-MILP and yields better Pareto solutions than ɛ-LO-MILP and the well-known non-dominated sorted genetic algorithm II do.

Collaborative algorithm of workpiece scheduling and AGV operation in flexible workshop

PurposeThis study aims to solve the problem of job scheduling and multi automated guided vehicle (AGV) cooperation in intelligent manufacturing workshops.Design/methodology/approachIn this study, an algorithm for job scheduling and cooperative work of multiple AGVs is designed. In the first part, with the goal of minimizing the total processing time and the total power consumption, the niche multi-objective evolutionary algorithm is used to determine the processing task arrangement on different machines. In the second part, AGV is called to transport workpieces, and an improved ant colony algorithm is used to generate the initial path of AGV. In the third part, to avoid path conflicts between running AGVs, the authors propose a simple priority-based waiting strategy to avoid collisions.FindingsThe experiment shows that the solution can effectively deal with job scheduling and multiple AGV operation problems in the workshop.Originality/valueIn this paper, a collaborative work algorithm is proposed, which combines the job scheduling and AGV running problem to make the research results adapt to the real job environment in the workshop.

Job-Deadline-Guarantee-Based Joint Flow Scheduling and Routing Scheme in Data Center Networks.

Many emerging Internet of Things (IoT) applications deployed on cloud platforms have strict latency requirements or deadline constraints, and thus meeting the deadlines is crucial to ensure the quality of service for users and the revenue for service providers in these delay-stringent IoT applications. Efficient flow scheduling in data center networks (DCNs) plays a major role in reducing the execution time of jobs and has garnered significant attention in recent years. However, only few studies have attempted to combine job-level flow scheduling and routing to guarantee meeting the deadlines of multi-stage jobs. In this paper, an efficient heuristic joint flow scheduling and routing (JFSR) scheme is proposed. First, targeting maximizing the number of jobs for which the deadlines have been met, we formulate the joint flow scheduling and routing optimization problem for multiple multi-stage jobs. Second, due to its mathematical intractability, this problem is decomposed into two sub-problems: inter-coflow scheduling and intra-coflow scheduling. In the first sub-problem, coflows from different jobs are scheduled according to their relative remaining times; in the second sub-problem, an iterative coflow scheduling and routing (ICSR) algorithm is designed to alternately optimize the routing path and bandwidth allocation for each scheduled coflow. Finally, simulation results demonstrate that the proposed JFSR scheme can significantly increase the number of jobs for which the deadlines have been met in DCNs.

Models and algorithms for the preventive maintenance optimization of railway vehicles

The motivation of this paper follows strictly from industrial needs to improve competitiveness in railway companies by the efficient rolling stock utilization affected by the obligatory preventive maintenances of vehicles, which cause their temporary unavailability. Nevertheless, it is economically essential to minimize the total time on maintenances of vehicles, which can be achieved in a certain range by the scheduling of transport tasks taking into account maintenance policies of the vehicles, their mileage and date since the last maintenance, and the workload related to the tasks. Therefore, to face the problem, we model the consider issue as the job scheduling problem to maximize the availability of railway vehicles under preventive maintenances. We prove that the problem is strongly NP-hard and we propose efficient heuristic and metaheuristic algorithms that are characterized by a low computational complexity and they are able to find solutions satisfying from the perspective of industrial practice. The simulations based on real-life data reveal that our approach can provide schedules, which significantly improve availability of locomotives resulting in high potential financial benefits for railway companies.

A Comparative Study of Evolutionary and Swarm Intelligence Algorithms for Job Scheduling on Identical Parallel Machines

In parallel computing systems, job scheduling plays a crucial role in enhancing system efficiency and minimizing the makespan. In recent years, evolutionary and swarm intelligence algorithms have gained prominence as effective approaches for solving combinatorial optimization problems. In the present work, we have considered genetic algorithm (GA) for evolutionary algorithms and particle swarm optimization (PSO) for swarm intelligence algorithms. Evolutionary algorithms (EA) and swarm intelligence algorithms (SIA) have shown promising results in solving job scheduling challenges. In this study, we collate the performance of EA and SIA approaches for job scheduling on parallel machines. We use different benchmark instances to evaluate the algorithms' makespan and computational time performance. The results show that SIA algorithms outperform EA algorithms regarding makespan and computational time for all benchmark instances. Furthermore, the study provides insights into the strengths and weaknesses of EA and SIA algorithms for job scheduling on parallel machines. Our findings provide useful insights for researchers and practitioners interested in applying optimization techniques to solve job scheduling problems on parallel machines.

Job Scheduling By Using Swarm Intelligent Algorithms: survey

The job scheduling problem is used in industry, manufacturing, job planning, and the network environment to manage users’ jobs on the right machines with different limitations. There are three types of job scheduling problems. Firstly, job shop scheduling means each job is executed on a determined sequence of machines specified previously. While in the flow shop scheduling problem, each job can be carried on one idle sequencing using a job queue. The third type, open shop, the sequence of jobs can be carried out on any free machine. This paper describes the various types of job scheduling problems and the various swarm intelligence algorithms, particularly cuckoo search algorithm, that can used to solve them.

Approaches Used In Adapting Metaheuristic Optimization Algorithms Developed For Continuous Problems to Discrete Problems

Many real-world problems such as determining the type and number of wind turbines, facility placement problems, job scheduling problems, are in the category of combinatorial optimization problems in terms of the type of decision variables. However, since many of the evolutionary optimization algorithms are developed for solving continuous optimization problems, they cannot be directly applied to optimization problems with discrete decision variables. Therefore, the continuous decision variable values generated by these metaheuristics need to be converted to binary values using some techniques. In other words, to apply such algorithms to discrete optimization problems, it is necessary to adapt the candidate solution vectors of the algorithms to discrete values and make changes in their working structures. In this study, firstly, adaptation methods that are frequently used in previous studies in transforming metaheuristic optimization algorithms designed for the solution of continuous optimization problems into discrete optimization algorithms are explained. Then, the popular location update strategies used in solving discrete optimization problems are explained. The presented work summarizes the process of adapting continuous optimization algorithms to solve combinatorial problems step by step.

A Reinforcement Learning Approach for Scheduling Problems with Improved Generalization through Order Swapping

The scheduling of production resources (such as associating jobs to machines) plays a vital role for the manufacturing industry not only for saving energy, but also for increasing the overall efficiency. Among the different job scheduling problems, the Job Shop Scheduling Problem (JSSP) is addressed in this work. JSSP falls into the category of NP-hard Combinatorial Optimization Problem (COP), in which solving the problem through exhaustive search becomes unfeasible. Simple heuristics such as First-In, First-Out, Largest Processing Time First and metaheuristics such as taboo search are often adopted to solve the problem by truncating the search space. The viability of the methods becomes inefficient for large problem sizes as it is either far from the optimum or time consuming. In recent years, the research towards using Deep Reinforcement Learning (DRL) to solve COPs has gained interest and has shown promising results in terms of solution quality and computational efficiency. In this work, we provide an novel approach to solve the JSSP examining the objectives generalization and solution effectiveness using DRL. In particular, we employ the Proximal Policy Optimization (PPO) algorithm that adopts the policy-gradient paradigm that is found to perform well in the constrained dispatching of jobs. We incorporated a new method called Order Swapping Mechanism (OSM) in the environment to achieve better generalized learning of the problem. The performance of the presented approach is analyzed in depth by using a set of available benchmark instances and comparing our results with the work of other groups.

Hybridizing local searching with genetic algorithms for the job sequencing and tool switching problem with non-identical parallel machines

The job sequencing and tool switching problem (SSP) is an old and highly studied problem. However, the SSP with non-identical parallel machines (SSP-NPM) is a new generalization of this problem. Since the SSP-NPM has been very recently introduced, the number of solution methods for this problem is low. Additionally, exact solution methods are mostly insufficient to find a good solution within a reasonable computational time since this problem is NP-hard. Therefore, heuristic approaches are more appropriate, especially when solving large-size problems. Thus, this study presents a new hybrid algorithm that is a combination of a genetic algorithm (GA) and a local search (LS) technique. Both of these methods are greatly preferred by authors for solving job scheduling problems. Thereby, this study combines their strengths to solve the SSP-NPM. Two versions of the proposed method are tested with benchmark instances. These versions differ in terms of their tool optimization policies: the first uses the well-known “keep tool needed soonest” (KTNS) policy, while the second uses the “randomly remove tool” (RRT) policy. Computational experiments showed that combining some of the features of GA and LS methods for the SSP-NPM contributed greatly to the quality of the solution. Two versions of the proposed hybrid method were compared to a mixed-integer programming model and several schemes of an iterated local search algorithm. Our computational results show that both versions of the proposed hybrid method were significantly better than the other methods, and were able to find the solutions within a reasonable computational time.

Online job scheduling scheme for low-carbon data center operation: An information and energy nexus perspective

As the digitalization of the economy and society accelerates, the enormous and fast-growing energy consumption of data centers is becoming a global concern. With the unique power consumption flexibility introduced by computing job scheduling, data centers could play an important role in enhancing the capability to integrate renewable generation as a demand-side resource. In this paper, we propose an online job scheduling scheme for low-carbon data center operation from an information and energy nexus perspective. We formulate the job scheduling problem as a Markov decision process in which job dependencies, job heterogeneity, and quality of service are considered comprehensively. To address the challenges of large-scale heterogeneous computing jobs, we propose a deep reinforcement learning-based approach to solve the energy-aware scheduling problem and achieve an optimal online policy. The case study results based on real-world data illustrate that the proposed scheme can effectively reduce the carbon footprint and energy cost of a data center while maintaining the quality of service for cloud products.

A NOTE ON HARDNESS OF MULTIPROCESSOR SCHEDULING WITH SCHEDULING SOLUTION SPACE TREE

We study the computational complexity of the non-preemptive scheduling problem of a listof independent jobs on a set of identical parallel processors with a makespan minimizationobjective. We make a maiden attempt to explore the combinatorial structure showing theexhaustive solution space of the problem by defining the Scheduling Solution Space Tree(SSST) data structure. The properties of the SSST are formally defined and characterizedthrough our analytical results. We develop a unique technique to show the problemNP using the SSST and the Weighted Scheduling Solution Space Tree (WSSST) datastructures. We design the first non-deterministic polynomial-time algorithm named MagicScheduling (MS) for the problem based on the reduction framework. We also define anew variant of multiprocessor scheduling by including the user as an additional inputparameter. We formally establish the complexity class of the variant by the reductionprinciple. Finally, we conclude the article by exploring several interesting open problemsfor future research investigation.

Nonmonotonically job scheduling

This paper describes new model of job scheduling problem generalized for nonmonotonical reward functions. Importance of informational asymmetry is shown for conflict in consideration, leading to connection with <<theory of conspiracies>>. Structurally consistent equilibria is demostrated to be acceptable as solution concept.

Enhancing the job scheduling procedure to develop an efficient cloud environment using near optimal clustering algorithm

In this internet era, cloud computing and there are various problems in the cloud computing, where the consumers as well as the service providers facing in their day to day cloud activities. Job scheduling problem plays a vital role in the cloud environment. To provide an efficient job scheduling environment, it is necessary to perform efficient resource clustering. In this regard, the proposed system, concentrated on the resource clustering methodology by proposing an efficient resource clustering algorithm named identicalness split up periodic node size (ISPNS) in the cloud environment. The algorithm proposed helps in forming resource clusters with the help of cloud environment. The proposed system is compared with the existing systems to justify the performance of the proposed resource clustering algorithm and it produces near optimal solution for the resource clustering problem which helps to provide an efficient job scheduling in cloud environment.

Design of reservation model of teaching equipment in NC laboratory based on BS mode

In order to solve the jobscheduling problem of CNC laboratory equipment concurrent reservation, the design method of CNC laboratory teaching equipment reservation model based on BS mode is proposed. By using BS mode, the equipment management structure of numerical control laboratory is designed hierarchically. The reservation time series model to realise the load transmission and information estimation in the process of reservation is then built. According to the statistical results, the reservation fitness function, reservation scheduling and reservation algorithm are designed. Based on this, the database security storage function and SMS processing function of the model are designed to realise the construction of teaching equipment reservation model in CNC laboratory. Experimental results show that compared with the traditional equipment design model, the model designed in this paper has higher reservation success rate and better application performance.

Job scheduling problem in fog-cloud-based environment using reinforced social spider optimization

Fog computing is an emerging research domain to provide computational services such as data transmission, application processing and storage mechanism. Fog computing consists of a set of fog server machines used to communicate with the mobile user in the edge network. Fog is introduced in cloud computing to meet data and communication needs for Internet of Things (IoT) devices. However, the vital challenges in this system are job scheduling, which is solved by examining the makespan, minimizing energy depletion and proper resource allocation. In this paper, we introduced a reinforced strategy Dynamic Opposition Learning based Social Spider Optimization (DOLSSO) Algorithm to enhance individual superiority and schedule workflow in Fog computing. The extensive experiments were conducted using the FogSim simulator to generate the dataset and an energy-efficient open-source tool utilized to model and simulate resource management in fog computing. The performance of the formulated model is ratified using two test cases. The proposed algorithm attained the optimized schedule with minimized cost function concerning the CPU processing period and assigned memory. Our simulation outcomes show the efficacy of the introduced technique in handling job scheduling issues, and the results are contrasted with five existing metaheuristic techniques. The results show that the proposed method achieves 10% - 15% better CPU utilization and 5%-10% less energy consumption than the other techniques.

FINDING THE OPTIMAL SOLUTION FOR A SPECIAL CASE OF THE FIXED INTERVAL JOB SCHEDULING PROBLEM WITH DIFFERENT PROCESSOR SIZE REQUIREMENTS AND A HIERARCHICAL STRUCTURE

ABSTRACT In many operational scheduling problems, we encounter situations wherein a resource with a higher capacity can undertake a job that requires a resource with a lower capacity, but not vice versa. For example, a crane with a lifting capacity of 40 tons can be used, if necessary, to lift a load of 27 tons at a construction site, but a crane with a lifting capacity of only 30 tons cannot be used to lift a load of 35 tons. Another familiar example is the assignment of airplanes to different flights. In almost all such cases, a resource that has a higher capacity is a lot more expensive than the one with a lower capacity. Further, each task has to be completed in a time interval that may be fixed or flexible. In the literature, job scheduling problems like these are called Hierarchical Class Scheduling Problems (HCSP), because of the hierarchical structure of their capacity requirements. For problems like these, currently no viable algorithmic techniques are available to determine the optimal mix of resources or processors needed to complete all the jobs on schedule, in spite of the availability of modern powerful computers. Scheduling problems of this type, among many others, are categorized as NP-hard problems in the specialized field of computer science that deals with the subject of computational complexity and solvability of problems. In this paper, we consider a special case of the Hierarchical Class Scheduling Problem (HCSP) and present some propositions that help us find the optimal solution for the special case. Keywords Fixed Interval Scheduling, Hierarchical Class Scheduling, NP-hard Problems

Solving job scheduling problems in a resource preemption environment with multi-agent reinforcement learning

In smart manufacturing, robots gradually replace traditional machines as new processing units, which have significantly liberated laborers and reduced manufacturing expenditure. However, manufacturing resources are usually limited so that the preemption relationship exists among robots. Under this circumstance, job scheduling puts forward higher requirements on accuracy and generalization . To this end, this paper proposes a scheduling algorithm to solve job scheduling problems in a resource preemption environment with multi-agent reinforcement learning. The resource preemption environment is modeled as a decentralized partially observable Markov decision process , where each job is regarded as an intelligent agent that chooses an available robot according to its current partial observation. Based on this modeling, a multi-agent scheduling architecture is constructed to handle the high-dimension action space issue caused by multi-task simultaneous scheduling. Besides, multi-agent reinforcement learning is employed to learn both the decision-making policy of each agent and the cooperation between job agents. This paper is novel in addressing the scheduling problem in a resource preemption environment and solving the job shop scheduling problem with multi-agent reinforcement learning. The experiments of the case study indicate that our proposed method outperforms the traditional rule-based methods and the distributed-agent reinforcement learning method in total makespan, training stability, and model generalization. • We solved the job shop scheduling problem with the MARL algorithm. • We solved the scheduling problem in a resource preemption environment. • Algorithms QMIX and PPO are applied to address scheduling problems. • Our proposal outperforms others in terms of accuracy and generalization.