A set-processing algorithm for scheduling staff on 4-day or 3-day work weeks

This paper presents an efficient algorithm for scheduling a single-category work force on 4-day or 3-day work weeks. Employees work 4 or 3 days each week, have A out of every B weekends off, and work no more than 5 consecutive days in a work stretch on 4-day work weeks and no more than 4 days in a work stretch on 3-day work weeks. Such conditions often prevail in 7-day-a-week organizations such as hospitals, manufacturing plants, and retail stores. We determine the minimum number of workers required to satisfy the scheduling constraints under any pattern of daily requirements. Then we present the algorithm for assigning days off for each worker, thereby determining the work schedules. We show that the algorithm, by construction, will necessarily satisfy the scheduling constraints. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 839–853, 1998     

Reformulating linear programs with transportation constraints—With applications to workforce scheduling

We study linear programming models that contain transportation constraints in their formulation. Typically, these models have a multistage nature and the transportation constraints together with the associated flow variables are used to achieve consistency between consecutive stages. We describe how to reformulate these models by projecting out the flow variables. The reformulation can be more desirable since it has fewer variables and can be solved faster. We apply these ideas to reformulate two well‐known workforce staffing and scheduling problems: the shift scheduling problem and the tour scheduling problem. We also present computational results. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

Bounded flexibility in days‐on and days‐off scheduling

This article presents a flexible days‐on and days‐off scheduling problem and develops an exact branch and price (B&P) algorithm to find solutions. The main objective is to minimize the size of the total workforce required to cover time‐varying demand over a planning horizon that may extend up to 12 weeks. A new aspect of the problem is the general restriction that the number of consecutive days on and the number of consecutive days off must each fall within a predefined range. Moreover, the total assignment of working days in the planning horizon cannot exceed some maximum value. In the B&P framework, the master problem is stated as a set covering‐type problem whose columns are generated iteratively by solving one of three different subproblems. The first is an implicit model, the second is a resource constrained shortest path problem, and the third is a dynamic program. Computational experiments using both real‐word and randomly generated data show that workforce reductions up to 66% are possible with highly flexible days‐on and days‐off patterns. When evaluating the performance of the three subproblems, it was found that each yielded equivalent solutions but the dynamic program proved to be significantly more efficient. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 60: 678–701, 2013     

成像卫星任务周规划模型与算法

作为卫星运控系统中的一个重要模块,卫星任务短期规划对充分发挥卫星系统效能有着重要影响。与卫星任务的日规划的作用和特点不同,它既涉及到任务规划的技术问题又涉及到卫星管理问题。针对周规划任务,本文分析周规划的需求和特点,兼顾周规划的四项主要作用,构造周规划的分层框架;分析周规划优化目标及约束条件,建立卫星任务的负载度周规划模型;针对模型求解属于高维离散组合优化问题,仿真实验评价了几种基本智能优化求解算法,并应用引入分布式并行技术的遗传模拟退火算法求解。     

One-facility location with rectilinear tour distances

This article concerns the location of a facility among n points where the points are serviced by “tours” taken from the facility. Tours include m points at a time and each group of m points may become active (may need a tour) with some known probability. Distances are assumed to be rectilinear. For m ≤ 3, it is proved that the objective function is separable in each dimension and an exact solution method is given that involves finding the median of numbers appropriately generated from the problem data. It is shown that the objective function becomes multimodal when some tours pass through four or more points. A bounded heuristic procedure is suggested for this latter case. This heuristic involves solving an auxiliary three-point tour location problem.     

A multiple‐shift workforce scheduling model under annualized hours

Many manufacturing and service organizations in Europe have used annualized hours, also known as flexiyear, to successfully tackle seasonal demand. Under annualized hours, the employer has a certain number of labor hours available in a year and the employer can allocate the hours over the year according to manpower need. A problem in planning for annualized hours is the scheduling of the workforce over the year. We present an algorithm to generate an annual schedule for a scenario in which a facility operates one or more shifts and manpower need may vary from week to week. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 726–736, 1999     

Priority and dynamic scheduling in a make‐to‐stock queue with hyperexponential demand

We consider the scheduling problem in a make‐to‐stock queue with two demand classes that can be differentiated based on their variability. One class experiences Poisson arrivals and the other class experiences hyperexponential renewal arrivals. We provide an exact analysis of the case where the demand class with higher variability is given non‐preemptive priority. The results are then used to compare the inventory cost performance of three scheduling disciplines, first‐come first‐serve and priority to either class. We then build on an existing dynamic scheduling heuristic to propose a modification that works well for our system. Extensions of the heuristic to more than two classes and to the case where demand state is known are also discussed. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006.     

基于约束满足的多目标对地观测卫星成像调度

EOS(对地观测卫星)成像调度需要根据用户提出的成像任务需求确定卫星成像序列,是一个复杂的组合优化问题。考虑到成像侧视约束条件,建立EOS成像调度的多目标有向无环约束图模型。在此模型的基础上提出了基于SPEA2(strength pareto evolutionary algorithm 2)的多目标成像调度算法,采用约束控制技术设计遗传算子处理成像约束。经过三个实际的多目标成像调度问题测试,表明该算法可以有效地解决EOS成像调度问题。     

Maintenance and flight scheduling of low observable aircraft

In this article, we focus on relatively new maintenance and operational scheduling challenges that are faced by the United States Air Force concerning low‐observable (LO) or stealth aircraft. The LO capabilities of an aircraft degrade stochastically as it flies, making it difficult to make maintenance scheduling decisions. Maintainers can address these damages, but must decide, which aircraft should be put into maintenance, and for how long. Using data obtained from an active duty Air Force F‐22 wing and interviews with Air Force maintainers and program specialists, we model this problem as a generalization of the well‐known restless multiarmed bandit superprocess. Specifically, we use an extension of the traditional model to allow for actions that require varying lengths of time, and generate two separate index policies from a single model; one for maintenance actions and one for the flying action. These index policies allow maintenance schedulers to intuitively, quickly, and effectively rank a fleet of aircraft based on each aircraft's LO status and decide, which aircraft should enter into LO maintenance and for how long, and which aircraft should be used to satisfy daily sortie requirements. Finally, we present extensive data‐driven, detailed simulation results, where we compare the performance of the index policies against policies currently used by the Air Force, as well as some other possible more naive heuristics. The results indicate that the index policies significantly outperform existing policies in terms of fully mission capable (FMC) rates. In particular, the experiments highlight the importance of coordinated maintenance and flying decisions. © 2015 Wiley Periodicals, Inc. 62:60–80, 2015     

Batch scheduling with step‐deteriorating processing times to minimize flowtime

Both topics of batch scheduling and of scheduling deteriorating jobs have been very popular among researchers in the last two decades. In this article, we study a model combining these two topics. We consider a classical batch scheduling model with unit‐jobs and batch‐independent setup times, and a model of step‐deterioration of processing times. The objective function is minimum flowtime. The optimal solution of the relaxed version (allowing non‐integer batch sizes) is shown to have a unique structure consisting of two consecutive decreasing arithmetic sequences of batch sizes. We also introduce a simple and efficient rounding procedure that guarantees integer batch sizes. The entire solution procedure requires an effort of O(n) (where nis the number of jobs.) © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

基于SOA的防空指挥信息系统体系框架研究

针对各军兵种开发的指挥信息系统各自孤立,不能有效集成以满足未来网络中心战要求的问题,研究了基于SOA的系统集成技术及防空指挥信息系统的基本组成和结构,提出了一个可实现的基于SOA的防空指挥信息系统的分层结构模型,并应用SCA技术设计了一个防空指挥信息系统的原型系统。结果表明采用SCA可以实现防空指挥信息系统内子系统之间的基于SOA的无缝集成,提高了系统的可重用性、可扩展性。     

SpaceFibre星载数据网络低延时确定性调度算法

针对超高速SpaceFibre星载网络中多源数据传输的确定性和实时性应用需求,提出一种分类细粒度低延时确定性调度算法。该算法基于差异化调度策略的思想,将数据流划分为三类。为实现网络资源的细粒度分配,引入扩展时隙。该算法采用无冲突均匀调度方法,降低了数据包的平均排队延时。为适应有效载荷组网的航天应用场景,该算法兼顾网络拓扑结构生成调度方案。为验证算法有效性,在OPNET仿真平台下利用自定义建模技术搭建网络仿真模型。仿真结果表明:相比优先权调度和无冲突连续调度机制,该算法实现了时间敏感数据流的确定性传输;随着时隙数目的增加,网络的延时性能和抗抖动性能显著提升,吞吐量性能得到保证;该算法具有一定的航天工程实用价值。     

Dual sourcing: Responsive hedging against correlated supply and demand uncertainty

This article analyzes dual sourcing decisions under stochastically dependent supply and demand uncertainty. A manufacturer faces the trade‐off between investing in unreliable but high‐margin offshore supply and in reliable but low‐margin local supply, where the latter allows for production that is responsively contingent on the actual demand and offshore supply conditions. Cost thresholds for both types of supply determine the optimal resource allocation: single offshore sourcing, single responsive sourcing, or dual sourcing. Relying on the concept of concordance orders, we study the effects of correlation between supply and demand uncertainty. Adding offshore supply to the sourcing portfolio becomes more favorable under positive correlation, since offshore supply is likely to satisfy demand when needed. Selecting responsive capacity under correlated supply and demand uncertainty is not as straightforward, yet we establish the managerially relevant conditions under which responsive capacity either gains or loses in importance. Our key results are extended to the broad class of endogenous supply uncertainty developed by Dada et al. [Manufact Serv Operat Mange 9 (2007), 9–32].© 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

Hu's precedence tree scheduling algorithm: A simple proof

This article presents a simple proof of Hu's algorithm for scheduling in minimum time a set of tasks constrained by precedence tree constraints, each task requiring a unit time to complete, and where m processors are available.     

基于动态罚函数遗传算法的电磁探测卫星多星规划方法

针对电磁探测卫星的特点,考虑其主要约束条件,建立了多星联合规划数学模型,提出了基于遗传算法的电磁探测卫星多星规划算法.为处理遗传算法迭代过程中产生的不可行解,引入了基于罚函数法的约束处理方法.针对罚函数法中惩罚系数难以确定的特点,设计了惩罚系数自适应调整的动态罚函数机制.根据模拟的数据进行实验及分析,表明该方法能有效解决电磁探测卫星多星规划问题.     

基于预定作业周期的航母作战部署调度研究

为科学筹划航母作战部署调度,优化航母作战兵力的运用,对航母作战部署调度问题进行建模研究。介绍航母预定作业周期,重点阐述航母综合训练期、维修保障期和人员/作战节奏等相关内容;在此基础上,分析航母作战部署调度的约束条件,在满足对作战区域有效时间覆盖条件下,以最小化航母作战兵力数量为目标函数,构建航母作战部署调度优化模型,并通过实例进行验证。结果表明,该模型是有效、实用的,可为科学决策航母作战部署调度提供依据和方法。     

Balancing perfectly periodic service schedules: An application from recycling and waste management

A national recycling and waste management company provides periodic services to its customers from over 160 service centers. The services are performed periodically in units of weeks over a planning horizon. The number of truck‐hours allocated to this effort is determined by the maximum weekly workload during the planning horizon. Therefore, minimizing the maximum weekly workload results in minimum operating expenses. The perfectly periodic service scheduling (PPSS) problem is defined based on the practices of the company. It is shown that the PPSS problem is strongly NP‐hard. Attempts to solve large instances by using an integer programming formulation are unsuccessful. Therefore, greedy BestFit heuristics with three different sorting schemes are designed and tested for six real‐world PPSS instances and 80 randomly generated data files. The heuristics provide effective solutions that are within 2% of optimality on average. When the best found BestFit schedules are compared with the existing schedules, it is shown that operational costs are reduced by 18% on average. © 2012 Wiley Periodicals, Inc. Naval Research Logistics 59: 160–171, 2012     

A dynamic,nonstationary inventory problem for a price/quantity setting firm

A dynamic and nonstationary model is formulated for a firm which attempts to minimize total expected costs over a finite planning horizon. The control variables are price and production. The price p and the demand ζ are linked through the relationship ζ = g(p) + η, where g(p) is the riskless demand curve and η is a random variable. The general model allows for proportional ordering costs, convex holding and stockout costs, downward sloping riskless demand curve, backlogging, partial backlogging, lost sales, partial spoilage of inventory, and two modes of collecting revenue. Sufficient conditions are developed for this problem to have an optimal policy which resembles the single critical number policy known from stochastic inventory theory. It is also shown what set of parameters will satisfy these sufficiency conditions.     

Stochastic call center staffing with uncertain arrival,service and abandonment rates: A Bayesian perspective

In this article, we introduce staffing strategies for the Erlang‐A queuing system in call center operations with uncertain arrival, service, and abandonment rates. In doing so, we model the system rates using gamma distributions that create randomness in operating characteristics used in the optimization formulation. We divide the day into discrete time intervals where a simulation based stochastic programming method is used to determine staffing levels. More specifically, we develop a model to select the optimal number of agents required for a given time interval by minimizing an expected cost function, which consists of agent and abandonment (opportunity) costs, while considering the service quality requirements such as the delay probability. The objective function as well as the constraints in our formulation are random variables. The novelty of our approach is to introduce a solution method for the staffing of an operation where all three system rates (arrival, service, and abandonment) are random variables. We illustrate the use of the proposed model using both real and simulated call center data. In addition, we provide solution comparisons across different formulations, consider a dynamic extension, and discuss sensitivity implications of changing constraint upper bounds as well as prior hyper‐parameters. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 460–478, 2016     

On‐line algorithms for minimizing makespan on batch processing machines

We consider problem of scheduling jobs on‐line on batch processing machines with dynamic job arrivals to minimize makespan. A batch machine can handle up to B jobs simultaneously. The jobs that are processed together from a batch, and all jobs in a batch start and complete at the same time. The processing time of a batch is given by the longest processing time of any job in the batch. Each job becomes available at its arrival time, which is unknown in advance, and its processing time becomes known upon its arrival. In the first part of this paper, we address the single batch processing machine scheduling problem. First we deal with two variants: the unbounded model where B is sufficiently large and the bounded model where jobs have two distinct arrival times. For both variants, we provide on‐line algorithms with worst‐case ratio (the inverse of the Golden ratio) and prove that these results are the best possible. Furthermore, we generalize our algorithms to the general case and show a worst‐case ratio of 2. We then consider the unbounded case for parallel batch processing machine scheduling. Lower bound are given, and two on‐line algorithms are presented. © 2001 John Wiley & Sons, Inc. Naval Research Logistics 48: 241–258, 2001