Reallocation Problems with Minimum Completion Time

Reallocation scheduling is one of the most fundamental problems in various areas such as supply chain management, logistics, and transportation science. In this paper, we introduce the reallocation problem that models the scheduling in which products are with fixed cost (e.g., transition time), non-fungible, and reallocated among warehouses in parallel, and comprehensively study the complexity of the problem under various settings of the transition time, product size, and capacities. We show that the problem can be solved in polynomial time for a fundamental setting where the product size and transition time are both uniform. We also show that the feasibility of the problem is NP-complete even for little more general settings, which implies that no polynomial-time algorithm constructs a feasible schedule of the problem unless P \(=\) NP. We then consider to solve the problem by relaxing capacity constraints, which we call the capacity augmentation, and derive a reallocation schedule feasible with the augmentation such that the completion time is at most the optimal of the original problem. When the warehouse capacity is sufficiently large, we design constant-factor approximation algorithms. We also show the relationship between the reallocation problem and the bin packing problem when the warehouse and carry-in capacities are sufficiently large.KeywordsAlgorithmNP-hardnessCapacity augmentationApproximationSchedulingBin packing

The way the processes in a parallel program are scheduled on the processors of a multiprocessor system affects the performance significantly. Finding a schedule of processes to processors which results in minimum completion time is NP-hard. Therefore, one has to resort to heuristic schedules. However, it is often difficult to determine if a specific schedule is close to the optimal case or if it is worthwhile to look for other schedules. Based on information from previous executions of the parallel program, we present a formula for an upper bound on the minimum completion time of the program. The bound is a function of a set of parameters. Some of these parameters are obtained from the previous executions of the program and the others describe the target multiprocessor architecture for which we want to bound the minimum completion time. The bound is optimal when it is based on information from one previous execution. Using these results, we are able to decide if a certain schedule is close to optimal or if it is worthwhile to look for other schedules. This is demonstrated by evaluating the completion time of a specific schedule of a particular program. The proofs used for obtaining the bound are based on program transformations and combinatorial mathematics.

Serial and within-stage independent parallel model equivalence on the minimum completion time

Fog computing (FC) is an emerging paradigm that extends computation, communication, and storage facilities towards the edge of a network. In this heterogeneous and distributed environment, resource allocation is very important. Hence, scheduling will be a challenge to increase productivity and allocate resources appropriately to the tasks. We schedule tasks in fog computing devices based on classification data mining technique. A key contribution is that a novel classification mining algorithm I‐Apriori is proposed based on the Apriori algorithm. Another contribution is that we propose a novel task scheduling model and a TSFC (Task Scheduling in Fog Computing) algorithm based on the I‐Apriori algorithm. Association rules generated by the I‐Apriori algorithm are combined with the minimum completion time of every task in the task set. Furthermore, the task with the minimum completion time is selected to be executed at the fog node with the minimum completion time. We finally evaluate the performance of I‐Apriori and TSFC algorithm through experimental simulations. The experimental results show that TSFC algorithm has better performance on reducing the total execution time of tasks and average waiting time.

In this paper we present algorithms for the problem of scheduling n independent jobs on m identical machines. As a generalization of the classical multiprocessor scheduling problem each machine is available only at a machine dependent release time. Two objective functions are considered. To minimize the makespan, we develop a dual approximation algorithm with a worst case bound of 5/4. For the problem of maximizing the minimum completion time, we develop an algorithm, such that the minimum completion time in the schedule produced by this algorithm is at least 2/3 times the minimum completion time in the optimum schedule. The paper closes with some numerical results.

Cloud computing technology is getting more advanced these days. Cloud computing is a pay-as-you-go service since it allows for variable resource allocation for services. Task scheduling and resource allocation are becoming major requirements for efficient and effective load balancing among cloud resources. For scheduling resources in cloud environment, different tasks need to be executed simultaneously by the available resources in order to minimize the completion time. To achieve this, we proposed a new technique called Enhanced Max-Min Algorithm (EMM). This algorithm takes less time to complete all the tasks with minimum completion time. In the proposed algorithm, small size tasks are concurrently executed and resource allocation is done accordingly. When compared to Min-Min algorithm the Enhanced Max-Min algorithm provides high resource utilization and reduces the makespan.

Quantum-based predictive fog scheduler for IoT applications

Task scheduling is one of the key technology of cloud computing, its main goal is to satisfy the fairness of the system resources and tasks more effectively, and at the same time as much as possible to realize the load balance of system resources and reduce the completion time. Combined with the advantages of genetic Algorithm, we put forward a Fair and Balanced and effective genetic Scheduling Algorithm FBEGSA (Fair Balanced Efficient Genetic Scheduling Algorithm).The experimental results show that the algorithm is useful to task scheduling.

Fog computing has emerged as a viable framework for processing delay sensitive applications. Modern applications consist of latency‐sensitive and latency‐tolerant jobs, leading to fog architectures that are often multi‐tiered/hierarchical. FiFSA (hierarchical first fog scheduling algorithm) and EFSA (hierarchical elected fog scheduling algorithm) are capable of scheduling both online and batch jobs on hierarchical fog‐cloud architectures. We consider heterogeneity in computing capacity—both among fog devices in separate layers, and among fog devices in the same layers. In general, online jobs with modest cpu requirements are scheduled on lower tier fog devices, and batch jobs with significant cpu requirements are scheduled on higher tier‐fog nodes, or the cloud data center (cdc). FiFSA assigns jobs to the first fog device with sufficient spare capacity. EFSA employs a MinMin heuristic that assigns jobs to the fog device that results in minimum completion time, while considering fog load. The performance of the proposed algorithms has been evaluated on a real‐life workload trace, using both simulation scenarios and a prototype testbed. FiFSA and EFSA offer an improvement of 19% to 70% in completion times and an improvement of 42% to 72% in system cost over other comparable algorithms.

Advances in network technologies and computing resources have led to the possibility of deploying large scale computational systems, such as those following a Grid architecture (or related architectures). The scheduling problem is a significant issue in the Grid environment. In practice, a scheduling algorithm should consider multiple objectives. Typically, there are two kinds of objectives. The first is the performance of the system in terms of quantities related to the completion time of tasks, the second is the amount of state information required, which is often measured in terms of quantities such as communications costs. These two objectives are often in tension with one another. For example, gathering large amounts of state information can lead to low completion times. In this work, we introduce a scheduling algorithm which simultaneously addresses the objectives listed above namely, minimizing completion times, while requiring zero dynamic state information. Using simulation, we show the promising performance of our algorithm, and its robustness with respect to errors in parameter estimates. Keywords-Grid Scheduling; Scheduling Algorithms; Shadow Routing Approach

Every flexible manufacturing system demands minimization of production completion time, which reduces the constraints and minimize the production quality with increase in final cost and efficiency. Minimization of production completion time basically deals with two objectives i.e. minimizing machine idle time and minimizing earliness-tardiness penalties. The minimization of these two objectives must be done by considering all constraints i.e. precedence, available machines, machine transition, machine set up, machine capacity, large inventories, etc. This can be achieved through Advanced Planning and Scheduling (APS). A multiobjective genetic algorithm with iterative search is presented to find the optimal solutions for APS problem. This algorithm minimize above two objectives with satisfaction of all constraints. APS mixed integer programming model is developed using Matlab 12 which uses an iterative search technique to improve an efficiency of the system and produces the optimal solution within a short period of time.

Evaluation of Level of Confidence and Optimization of Roll-back Recovery with Checkpointing for Real-Time Systems

Objectives: In this paper various task scheduling algorithm along with load distribution techniques investigated to ensure efficient mapping of tasks to resources and for coherent resource utilization in heterogeneous environment. Statistical Analysis: A detailed comparative approach is conferred for different job scheduling and load balancing algorithm available in the literature. Considered parameters for comparisons are scheduling approaches, techniques, findings, benefits, pros and cons. This study facilitates to identify the efficient scheduling and load balancing approach which optimizes resource use, minimizes completion time as well as task waiting time and balanced load among resources. Findings: Make span time and flow time are two important parameters to compute and minimize job execution time. This paper explores an intense survey of minimization of task execution time with minimum make span time and flow time. Apart from this a joint review on job scheduling, load balancing and minimizing job completion time using Expected Time to Compute (ETC) matrix is presented. At the end of this paper a research model is proposed which is a novel and hybrid approach with a combination of the efficiency of scheduling and load balancing. Application: The Load Balancing (LB) is an important feature of the grid environment. The efficient LB algorithm assures cost effective resource usage by the provisioning of resources to users on demand schedule in pay-as-you-say-manner.

The problem of scheduling of tasks in distributed, heterogeneous, and multiprocessing computing environment like grid and cloud computing is considered as one of the most important issue from research perspective. As the performance of such kind of systems is highly depends upon the way, how tasks are allocated among the multiple processing units for their efficient execution. The underlying objective of any task scheduling mechanism is to minimize the overall makespan for the execution of given set of jobs/tasks and computing machines. Scheduling of tasks in cloud computing falls in the class of NP-hard optimization problem. As a result, many meta-heuristic algorithms have been applied and tested to solve this problem but still lot of scope is there for the better strategies. The characteristic of the good algorithm is that it must be adaptable to the dynamic environment. Through this paper, we are proposing task scheduling mechanism based on particle swarm optimization (PSO) in which opposition-based learning technique is used to avoid premature convergence and to accelerate the convergence of standard PSO and compared same with the well-established task scheduling strategies based on PSO, mPSO (modified PSO), genetic algorithm GA, max–min, minimum completion time and minimum execution time. The results obtained for the various class of experiments clearly establish that the proposed opposition-based learning inspired particle swarm optimization based scheduling strategy performs better in comparison to its peers which are taken into the consideration.

This paper presents a hybrid approach based discrete Particle Swarm Optimization (PSO) and chaotic strategies for solving multi-objective task scheduling problem in cloud computing. The main purpose is to allocate the summited tasks to the available resources in the cloud environment with minimum makespan (i.e. schedule length) and processing cost while maximizing resource utilization without violating Service Level Agreement (SLA) among users and cloud providers. The main challenges faced by Particle Swarm Optimization (PSO) when used to solve scheduling problems are premature convergence and trapping into local optimum. This paper presents an enhanced Particle Swarm Optimization algorithm hybridized with Chaotic Map strategies. The proposed approach is called Enhanced Particle Swarm Optimization based Chaotic Strategies (EPSOCHO) algorithm. Our proposed approach suggests two Chaotic Map strategies: sinusoidal iterator and Lorenz attractor to enhanced PSO algorithm in order to get good convergence and diversity for optimizing the task scheduling in cloud computing. The proposed approach is simulated and implemented in Cloudsim simulator. The performance of the proposed approach is compared with the standard PSO algorithm, the improved PSO algorithm with Longest job to fastest processor (LJFP-PSO), and the improved PSO algorithm with minimum completion time (MCT-PSO) using different sizes of tasks and various benchmark datasets. The results clearly demonstrate the efficiency of the proposed approach in terms of makespan, processing cost and resources utilization.