Two-machine flow-shop scheduling with rejection

We study a scheduling problem with rejection on a set of two machines in a flow-shop scheduling system. We evaluate the quality of a solution by two criteria: the first is the makespan and the second is the total rejection cost. We show that the problem of minimizing the makespan plus total rejection cost is NP-hard and for its solution we provide two different approximation algorithms, a pseudo-polynomial time optimization algorithm and a fully polynomial time approximation scheme (FPTAS). We also study the problem of finding the entire set of Pareto-optimal points (this problem is NP-hard due to the NP-hardness of the same problem variation on a single machine [20]). We show that this problem can be solved in pseudo-polynomial time. Moreover, we show how we can provide an FPTAS that, given that there exists a Pareto optimal schedule with a total rejection cost of at most R and a makespan of at most K, finds a solution with a total rejection cost of at most (1+?)R and a makespan value of at most (1+?)K. This is done by defining a set of auxiliary problems and providing an FPTAS algorithm to each one of them.     

Online scheduling with rejection and withdrawal

We study an online scheduling problem with rejection, in which some rearrangement of the solution is allowed. This problem is called scheduling with rejection and withdrawal. Each arriving job has a processing time and a rejection cost associated with it, and it needs to be either assigned to a machine or rejected upon arrival. At termination, it is possible to choose at most a fixed number of scheduled jobs and withdraw them (i.e., decide to reject them). We study the minimization version, where the goal is to minimize the sum of the makespan and the total rejection cost (which corresponds to the penalty), and the maximization problem, where the goal is to maximize the sum of the minimum load and the total rejection cost (which corresponds to profit). We study environments of machines, which are the case of m identical machines and the case of two uniformly related machines, and show a strong relation between these problems and the related classic online scheduling problems which they generalize, in contrast to standard scheduling with rejection, which typically makes the scheduling problems harder.     

A survey of multi-factory scheduling

Because of current globalization trend, production has shifted from the single factory production to multi-factory production network. To become competitive in today’s rapidly changing market requirements, factories have shifted from a centralized to a more decentralized structure, in many areas of decision making including scheduling. In multi-factory production network, each factory can be considered as an individual entity which has different efficiency and is subject to different constraints, for example, machine advances, worker cost, tax, close to suppliers, and transportation facilities, etc. Since limited resources make scheduling an important decision in the production, for several decades, researchers focused on determining an efficient schedule to improve the productivity. The recent remarkable attention in distributed production management in both academia and the industry has demonstrated the significance of multi-factory scheduling. For the first time, this paper provides a review on the multi-factory machine scheduling. For this, first, the paper classifies and reviews the literature according to shop environments, including single machine, parallel machines, flowshop, job shop, and open shop. Then the reviewed literature is quantified and measured. At the end, the paper concludes by presenting some problems receiving less attention than the others and proposes several research opportunities in the field.     

A survey of scheduling with deterministic machine availability constraints

Various deterministic scheduling problems with availability constraints motivated by preventive maintenance attract more and more researchers. Many results involving this constraint have been published in recent years. But there is no recent paper to summarize them. To be convenient for interested researchers, we make this survey. In this paper, complexity results, exact algorithms and approximation algorithms in single machine, parallel machine, flow shop, open shop, job shop scheduling environment with different criteria are surveyed briefly.     

基于离线利用率分析的混合关键级任务调度优化研究

现主流的混合关键级调度算法在系统高关键级状态下时主要通过抛弃低关键级任务来保证高关键级任务的执行,进而保证系统的正确性。此方法常常导致低关键级任务无法执行但系统资源却过剩的问题发生,故基于该问题提出复合型SDU（schedule depend on utilization）调度算法。该方法根据任务集对系统资源需求情况的不同进行利用率区间的划分,通过对各个区间实际使用情况的分析,设计相应的子算法进行调度,并提出了SDU算法对应的可调度性判据。仿真实验结果表明,相较于混合关键级任务调度领域主流的EDF-VD（earliest deadline first-virtual deadline）算法,所提SDU算法可将系统对任务集的调度率提升30%,并在相同情况下将系统对低关键级任务的执行率提升165%,证明了该算法可以极大地提高系统资源使用率,并保证系统服务完整性。     

A PTAS for parallel batch scheduling with rejection and dynamic job arrivals

In the parallel batch scheduling model, a group of jobs can be scheduled together as a batch while the processing time of this batch is the greatest processing time among its members; in the model of scheduling with rejection, any job can be rejected with a corresponding penalty cost added to the objective value. In this paper, we present a PTAS for the combined model of the above two scheduling models where jobs arrive dynamically. The objective is to minimize the sum of the makespan of the accepted jobs and the total penalty of the rejected ones. Our basic approaches are dynamic programming and roundings.     

A survey of offline algorithms for energy minimization under deadline constraints

Modern computers allow software to adjust power management settings like speed and sleep modes to decrease the power consumption, possibly at the price of a decreased performance. The impact of these techniques mainly depends on the schedule of the tasks. In this article, a survey on underlying theoretical results on power management, as well as offline scheduling algorithms that aim at minimizing the energy consumption under real-time constraints, is given.     

Bounded single-machine parallel-batch scheduling with release dates and rejection

We consider the bounded single-machine parallel-batch scheduling problem with release dates and rejection. A job is either rejected, in which case a certain penalty has to be paid, or accepted and then processed on the machine. The objective is to minimize the sum of the makespan of the accepted jobs and the total penalty of the rejected jobs. When the jobs have identical release dates, we present a polynomial-time algorithm. When the jobs have a constant number of release dates, we give a pseudo-polynomial-time algorithm. For the general problem, we provide a 2-approximation algorithm and a polynomial-time approximation scheme.     

时间约束混合流水车间调度问题综述

车间调度是智能制造领域中的核心问题之一,在经典流水车间调度中,所有工件按照相同的加工顺序在指定机床上加工.混合流水车间调度(HFS)作为流水车间调度的特例,相比前者增加了机床选择的灵活性,可以显著优化系统目标,但同时也增加了问题求解的难度.由于时间约束HFS相比基本HFS问题更贴近实际生产过程,近年来,综合考虑各类时间相关约束的HFS问题得到了深入研究.因此,本文围绕基本HFS、有限等待时间HFS、带准备时间HFS、模糊/随机加工时间HFS、多时间约束HFS、时间约束相关多目标HFS等问题开展研究.针对每一类时间约束HFS问题,按照问题规模对当前研究成果进行分类描述,按照确定性算法、启发式方法、元启发式方法、算法混合对相关成果进行算法分类,按照实际工业应用对文献进行归类分析.另一方面,围绕交货期、能耗、成本等3类性能指标,分析了在各类时间约束HFS问题中的多目标优化相关成果.最后详细分析了带时间约束HFS问题在问题层面、算法层面和应用层面存在的挑战性问题和未来研究的方向.     

Distributed job scheduling based on Swarm Intelligence: A survey

Scientists and engineers need computational power to satisfy the increasing resource intensive nature of their simulations. For example, running Parameter Sweep Experiments (PSE) involve processing many independent jobs, given by multiple initial configurations (input parameter values) against the same program code. Hence, paradigms like Grid Computing and Cloud Computing are employed for gaining scalability. However, job scheduling in Grid and Cloud environments represents a difficult issue since it is basically NP-complete. Thus, many variants based on approximation techniques, specially those from Swarm Intelligence (SI), have been proposed. These techniques have the ability of searching for problem solutions in a very efficient way. This paper surveys SI-based job scheduling algorithms for bag-of-tasks applications (such as PSEs) on distributed computing environments, and uniformly compares them based on a derived comparison framework. We also discuss open problems and future research in the area.     

A nature inspired intelligent water drops evolutionary algorithm for parallel processor scheduling with rejection

Scheduling has become a popular area for artificial intelligence and expert system researchers during last decade. In this paper, a new metaheuristic algorithm entitled intelligent water drops (IWD) is adapted for solving a generalized kind of order scheduling problem where rejection of received orders is allowed with a penalty cost. At the beginning of production period, a set of orders are received by manufacturer. Due to capacity limit, the manufacturer can only process a subset of orders and has to decide to reject some of undesirable orders. The accepted orders are proceed to be scheduled by a set of identical parallel processors in shop floor. The objective is to select the best set of orders with high contribution in manufacturer's benefit and then find the appropriate schedule of accepted orders minimizing the number of tardy orders. To effectively solve the suggested problem, the Lexicographic utility function is customized to address different objectives and then an IWD algorithm, which is based on the process of the natural rivers and the interactions among water drops in a river, is devised. To further enhance the performance of basic IWD, an Iterated Local Search (ILS) heuristic is also incorporated into the main algorithm. To demonstrate the applicability of suggested problem and also show the effectiveness of enhanced IWD with ILS, a real-world application in commercial printing industry is presented and the performance of algorithm is compared with traditional algorithms like GA, DE and ACO.     

A survey of dynamic scheduling in manufacturing systems

In most real-world environments, scheduling is an ongoing reactive process where the presence of a variety of unexpected disruptions is usually inevitable, and continually forces reconsideration and revision of pre-established schedules. Many of the approaches developed to solve the problem of static scheduling are often impractical in real-world environments, and the near-optimal schedules with respect to the estimated data may become obsolete when they are released to the shop floor. This paper outlines the limitations of the static approaches to scheduling in the presence of real-time information and presents a number of issues that have come up in recent years on dynamic scheduling. The paper defines the problem of dynamic scheduling and provides a review of the state-of-the-art of currently developing research on dynamic scheduling. The principles of several dynamic scheduling techniques, namely, heuristics, meta-heuristics, multi-agent systems, and other artificial intelligence techniques are described in detail, followed by a discussion and comparison of their potential.     

VSA: An offline scheduling analyzer for Xen virtual machine monitor

Nowadays, it is an important trend in the system domain to use the software-based virtualization technology to build the execution environments (e.g., the Clouds). After introducing the virtualization layer, there exist two schedulers: One in the hypervisor and the other inside the Guest Operating System (GOS). To fully understand the virtualized system and identify the possible reasons for performance problems incurred by the virtualization technology, it is very important for the system administrators and engineers to know the scheduling behavior of the hypervisor, in addition to understanding the scheduler inside the GOS. In this paper, we develop a virtualization scheduling analyzer, called VSA, to analyze the trace data of the Xen virtual machine monitor. With VSA, one can easily obtain the scheduling data associated with virtual processors (i.e., VCPUs) and physical processors (i.e., PCPUs), and further conduct the scheduling analysis for a group of interacting VCPUs running in the same domain.     

Weak-restriction bi-objective optimization algorithm for scheduling with rejection on non-identical batch processing machines

We investigate the problem of scheduling a set of jobs with arbitrary sizes and unequal weights on a set of parallel batch machines with non-identical capacities. The objective is to minimize the makespan of the accepted jobs and the total rejection penalty of the rejected jobs, simultaneously. To address the studied problem, a Pareto-based ant colony optimization algorithm with the first job selection probability (FPACO) is proposed. A weak-restriction selection strategy is proposed to obtain the desirability of candidate jobs. Two objective-oriented heuristic information and pheromone matrices are designed, respectively, to record the experience in different search dimensions. Moreover, a local optimization algorithm is incorporated to improve the solution quality. Finally, the proposed algorithm is compared with four existing algorithms through extensive simulation experiments. The experimental results indicate that the proposed algorithm outperforms all of the compared algorithms within a reasonable time.     

Preemptive online scheduling with rejection of unit jobs on two uniformly related machines

We consider preemptive online and semi-online scheduling of unit jobs on two uniformly related machines. Jobs are presented one by one to an algorithm, and each job has a rejection penalty associated with it. A new job can either be rejected, in which case the algorithm pays its rejection penalty, or it can be scheduled preemptively on the machines, in which case it may increase the maximum completion time of any machine in the schedule, also known as the makespan of the constructed schedule. The objective is to minimize the sum of the makespan of the schedule of all accepted jobs and the total penalty of all rejected jobs. We study two versions of the problem. The first one is the online problem where the jobs arrive unsorted, and the second variant is the semi-online case, where the jobs arrive sorted by a non-increasing order of penalties. We also show that the variant where the jobs arrive sorted by a non-decreasing order of penalties is equivalent to the unsorted one. We design optimal online algorithms for both cases. These algorithms have smaller competitive ratios than the optimal competitive ratio for the more general problem with arbitrary processing times (except for the case of identical machines), but larger competitive ratios than the optimal competitive ratio for preemptive scheduling of unit jobs without rejection.     

Markov models for offline handwriting recognition: a survey

Since their first inception more than half a century ago, automatic reading systems have evolved substantially, thereby showing impressive performance on machine-printed text. The recognition of handwriting can, however, still be considered an open research problem due to its substantial variation in appearance. With the introduction of Markovian models to the field, a promising modeling and recognition paradigm was established for automatic offline handwriting recognition. However, so far, no standard procedures for building Markov-model-based recognizers could be established though trends toward unified approaches can be identified. It is therefore the goal of this survey to provide a comprehensive overview of the application of Markov models in the research field of offline handwriting recognition, covering both the widely used hidden Markov models and the less complex Markov-chain or n-gram models. First, we will introduce the typical architecture of a Markov-model-based offline handwriting recognition system and make the reader familiar with the essential theoretical concepts behind Markovian models. Then, we will give a thorough review of the solutions proposed in the literature for the open problems how to apply Markov-model-based approaches to automatic offline handwriting recognition.