Optimal job splitting on a multi‐slot machine with applications in the printing industry

In this article, we define a scheduling/packing problem called the Job Splitting Problem, motivated by the practices in the printing industry. There are n types of items to be produced on an m‐slot machine. A particular assignment of the types to the slots is called a “run” configuration and requires a setup cost. Once a run begins, the production continues according to that configuration and the “length” of the run represents the quantity produced in each slot during that run. For each unit of production in excess of demand, there is a waste cost. Our goal is to construct a production plan, i.e., a set of runs, such that the total setup and waste cost is minimized. We show that the problem is strongly NP‐hard and propose two integer programming formulations, several preprocessing steps, and two heuristics. We also provide a worst‐case bound for one of the heuristics. Extensive tests on real‐world and randomly generated instances show that the heuristics are both fast and effective, finding near‐optimal solutions. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

基于目标威胁度的相控阵雷达自适应调度方法

对时间资源的合理安排是相控阵雷达发挥自身优势的关键。将目标威胁度引入调度算法中,与工作方式和任务截止期共同进行综合优先级规划。通过构建目标威胁度的量化模型,使雷达在调度跟踪任务时依目标威胁度大小分配时间。提出了修正价值率和执行威胁率的概念,完善了性能评估指标。通过仿真,全面评价了新算法性能,验证了引入目标威胁度的合理性。结果表明,新算法可以有效提升相控阵雷达对高威胁度目标的处理能力。     

多向嵌套循环的 FMS并行执行模式

基于小粒度并行结构的分类,提出了结构范式的概念。在此基础上,探讨了多向嵌套循环的并行执行问题,提出了父、母、子进程的概念以及面向多向嵌套循环的FMS 处理机调度策略     

挠性航天器变幅值输入成形姿态机动策略

针对变参数挠性航天器的姿态机动问题,在变幅值零振动成形器的基础上,提出了鲁棒性较强的变幅值零振动和零微分成形器设计方法,设计了鲁棒姿态机动策略.该机动策略的控制目标是,将航天器机动到期望状态的同时,消除挠性结构的残余振动.以含转动挠性太阳翼的航天器进行三轴姿态机动为例,进行数值仿真.仿真结果表明,该机动策略对挠性结构频...     

Two-agent scheduling with linear resource-dependent processing times

This paper considers a two-agent scheduling problem with linear resource-dependent processing times, in which each agent has a set of jobs that compete with that of the other agent for the use of a common processing machine, and each agent aims to minimize the weighted number of its tardy jobs. To meet the due date requirements of the jobs of the two agents, additional amounts of a common resource, which may be in discrete or continuous quantities, can be allocated to the processing of the jobs to compress their processing durations. The actual processing time of a job is a linear function of the amount of the resource allocated to it. The objective is to determine the optimal job sequence and resource allocation strategy so as to minimize the weighted number of tardy jobs of one agent, while keeping the weighted number of tardy jobs of the other agent, and the total resource consumption cost within their respective predetermined limits. It is shown that the problem is -hard in the ordinary sense, and there does not exist a polynomial-time approximation algorithm with performance ratio unless ; however it admits a relaxed fully polynomial time approximation scheme. A proximal bundle algorithm based on Lagrangian relaxation is also presented to solve the problem approximately. To speed up convergence and produce sharp bounds, enhancement strategies including the design of a Tabu search algorithm and integration of a Lagrangian recovery heuristic into the algorithm are devised. Extensive numerical studies are conducted to assess the effectiveness and efficiency of the proposed algorithms.     

Approximation schemes for single‐machine scheduling with a fixed maintenance activity to minimize the total amount of late work

We consider the problem of scheduling n independent and simultaneously available jobs without preemption on a single machine, where the machine has a fixed maintenance activity. The objective is to find the optimal job sequence to minimize the total amount of late work, where the late work of a job is the amount of processing of the job that is performed after its due date. We first discuss the approximability of the problem. We then develop two pseudo‐polynomial dynamic programming algorithms and a fully polynomial‐time approximation scheme for the problem. Finally, we conduct extensive numerical studies to evaluate the performance of the proposed algorithms. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 172–183, 2016     

A note on efficient sequences with respect to total flow time and number of tardy jobs

For the single‐machine scheduling problem with the objective of simultaneously minimizing total flow time and number of tardy jobs, a lower bound on the number of efficient sequences is known. However, the proof thereof, which makes use of a modified version of Smith's algorithm, is unduly lengthy and sophisticated. Adopting a totally new point of view, we present in this short article a much simpler proof based on the naive idea of pairwise interchange. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 346–348, 2016     

Multiple common due dates

Common due date problems have been extensively discussed in the scheduling literature. Initially, these problems discussed finding a common due date for a set of jobs on a single machine. These single machine problems were later extended to finding the common due date on a set of parallel machines. This paper further extends the single machine problem to finding multiple common due dates on a single machine. For a basic and important class of penalty functions, we show that this problem is comparable to the parallel machine problem. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 293–298, 2001     

A heuristic for the two‐machine no‐wait openshop scheduling problem

In this paper the problem of minimizing makespan in a two‐machine openshop is examined. A heuristic algorithm is proposed, and its worst case performance ratio and complexity are analyzed. The average case performance is evaluated using an empirical study. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 129–145, 1999