The threshold policy in the M/G/1 queue with server vacations

This article deals with the M/G/1 queue with server vacations in which the return of the server to service depends on the number of customers present in the system. The main goal is optimization, which is done under the average cost criterion in the multiple- and single-vacation models as well as for the “total cost for one busy cycle” criterion in the multiple-vacation case. Expressions that characterize the optimal number of customers, below which the server should not start a new service period, are exhibited for the various cases. It is found that under the average cost criterion, the expression may be universal in the sense that it may hold for a general class of problems including such that arise in production planning and inventory theory (for the particular cost structure discussed).     

Opportunity-based age replacement: Exponentially distributed times between opportunities

This article gives a full analysis of a component-replacement model in which preventive replacements are only possible at maintenance opportunities. These opportunities arise according to a Poisson process, independently of failures of the component. Conditions for the existence of a unique average optimal control limit policy are established and an equation characterizing the optimal policy and minimal average costs is derived. An important result is that the optimal policy can be described as a so-called one-opportunity-look-ahead policy. Such policies play an important role as heuristics in more general models. It is shown that there is a correspondence with the well-known age-replacement model, which can be considered as an extreme case of the model. Finally, some numerical results are given.     

Robust shortest path planning and semicontractive dynamic programming

In this article, we consider shortest path problems in a directed graph where the transitions between nodes are subject to uncertainty. We use a minimax formulation, where the objective is to guarantee that a special destination state is reached with a minimum cost path under the worst possible instance of the uncertainty. Problems of this type arise, among others, in planning and pursuit‐evasion contexts, and in model predictive control. Our analysis makes use of the recently developed theory of abstract semicontractive dynamic programming models. We investigate questions of existence and uniqueness of solution of the optimality equation, existence of optimal paths, and the validity of various algorithms patterned after the classical methods of value and policy iteration, as well as a Dijkstra‐like algorithm for problems with nonnegative arc lengths.© 2016 Wiley Periodicals, Inc. Naval Research Logistics 66:15–37, 2019     

An optimum multiechelon repair policy and stockage model

Currently, sophisticated multiechelon models compute stockage quantities for spares and repair parts that will minimize total inventory investment while achieving a target level of weapon system operational availability. The maintenance policies to be followed are input to the stockage models. The Optimum Allocation of Test Equipment/Manpower Evaluated Against Logistics (OATMEAL) model will determine optimum maintenance as well as stockage policies for a weapon system. Specifically, it will determine at which echelon each maintenance function should be performed, including an option for component or module throwaway. Test equipment requirements to handle work load at each echelon are simultaneously optimized. Mixed-integer programming (MIP) combined with a Lagrangian approach are used to do the constrained cost minimization, that is, to minimize all costs dependent on maintenance and stockage policies while achieving a target weapons system operational availability. Real-life test cases are included.     

Stochastic framework for partially degradation systems with continuous component degradation‐rate‐interactions

Many conventional models that characterize the reliability of multicomponent systems are developed on the premise that for a given system, the failures of its components are independent. Although this facilitates mathematical tractability, it may constitute a significant departure from what really takes place. In many real‐world applications, system components exhibit various degrees of interdependencies, which present significant challenges in predicting degradation performance and the remaining lifetimes of the individual components as well as the system at large. We focus on modeling the performance of interdependent components of networked systems that exhibit interactive degradation processes. Specifically, we focus on how the performance level of one component affects the degradation rates of other dependent components. This is achieved by using stochastic models to characterize how degradation‐based sensor signals associated with the components evolve over time. We consider “Continuous‐Type” component interactions that occur continuously over time. This type of degradation interaction exists in many applications, in which interdependencies occur on a continuum. We use a system of stochastic differential equations to capture such “Continuous‐Type” interaction. In addition, we utilize a Bayesian approach to update the proposed model using real‐time sensor signals observed in the field and provide more accurate estimation of component residual lifetimes. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 286–303, 2014     

Optimal (τ, T) opportunistic maintenance of a k‐out‐of‐n:G system with imperfect PM and partial failure

The opportunistic maintenance of a k‐out‐of‐n:G system with imperfect preventive maintenance (PM) is studied in this paper, where partial failure is allowed. In many applications, the optimal maintenance actions for one component often depend on the states of the other components and system reliability requirements. Two new (τ, T) opportunistic maintenance models with the consideration of reliability requirements are proposed. In these two models, only minimal repairs are performed on failed components before time τ and the corrective maintenance (CM) of all failed components are combined with PM of all functioning but deteriorated components after τ; if the system survives to time T without perfect maintenance, it will be subject to PM at time T. Considering maintenance time, asymptotic system cost rate and availability are derived. The results obtained generalize and unify some previous research in this area. Application to aircraft engine maintenance is presented. © 2000 John Wiley & Sons;, Inc. Naval Research Logistics 47: 223–239, 2000     

Scheduling with earliest start and due date constraints

We consider the scheduling of n tasks on a single resource. Each task becomes available for processing at time a_i, must be completed by time b_i, and requires d_i time units for processing. The aim is to find a schedule that minimizes the elapsed time to complete all jobs. We present solution algorithms for this problem when job splitting is permitted and when job splitting is not permitted. Then we consider several scheduling situations which arise in practice where these models may apply.     

复杂系统复合维修间隔期优化模型

采用组合策略对复杂系统辅以功能检测的定期更换维修工作进行综合优化.在分析复杂系统维修费用结构和组成的基础上,建立了其无限使用期条件下单位时间期望费用的数学模型,从而获得系统最佳的功能检测间隔期、定期更换周期内的检测次数和最优总费用.最后通过一个算例验证了该策略和模型的有效性.     

装甲装备使用可用度与维修保障费用的优化模型

维修保障费用是影响装甲装备使用可用度的重要因素之一。要在有限的保障经费下实现高可用度要求,就必须建立装甲装备的使用可用度与维修保障费用的优化模型。根据装甲装备实际维修特点,在分析装甲装备预防性维修过程中故障类型多样的基础上,构建了装甲装备在给定维修周期内的使用可用度模型和维修保障费用模型,进而建立了使用可用度与维修保障费用的优化模型,提出了模型的解法和模型的改进建议。     

Dual criteria preemptive open-shop problems with minimum makespan

In this article we present an algorithm for the minimum makespan preemptive open shop, which is superior to existing algorithms in both space and time requirements. We define the more complex generalized open shop and flexible open shop and address the minimum makespan problem on these shops. We show how we can use the algorithm for the minimum makespan open shop to achieve load balancing in simple and generalized open shops without increasing the complexity of the algorithm. Load balancing dictates that the number of busy machines in each period is as even as possible. We also consider preventive maintenance issues in the open shop, and makespan retains its minimum value. In particular we consider the scenario where a machine can be maintained during any period that it happens to be idle. Also we consider the case that a maintenance schedule is prespecified. We show that this problem can be solved via a linear programming formulation that can also take into account release times for the jobs and ready times for the machines. Faster algorithms are presented for open shops with three machines or less. © 1995 John Wiley & Sons, Inc.     

Scheduling with variable time slot costs

In this article, we study a class of new scheduling models where time slot costs have to be taken into consideration. In such models, processing a job will incur certain cost which is determined by the time slots occupied by the job in a schedule. The models apply when operational costs vary over time. The objective of the scheduling models is to minimize the total time slot costs plus a traditional scheduling performance measure. We consider the following performance measures: total completion time, maximum lateness/tardiness, total weighted number of tardy jobs, and total tardiness. We prove the intractability of the models under general parameters and provide polynomial‐time algorithms for special cases with non‐increasing time slot costs.© 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Monotone optimal preventive maintenance policies for stochastically failing equipment

This paper examines various models for maintenance of a machine operating subject to stochastic deterioration. Three alternative models are presented for the deterioration process. For each model, in addition to the replacement decision, the option exists of performing preventive maintenance. The effect of this maintenance is to “slow” the deterioration process. With an appropriate reward structure imposed on the processes, the models are formulated as continuous time Markov decision processes. the optimality criterion being the maximization of expected discounted reward earned over an infinite time horizon. For each model conditions are presented under which the optimal maintenance policy exhibits the following monotonic structure. First, there exists a control limit rule for replacement. That is, there exists a number i* such that if the state of machine deterioration exceeds i* the optimal policy replaces the machine by a new machine. Secondly, prior to replacement the optimal level of preventive maintenance is a nonincreasing function of the state of machine deterioration. The conditions which guarantee this result have a cost/benefit interpretation.     

基于状态的检查与修理综合决策模型

分析了单部件系统退化过程的特点,建立了基于状态的检查与修理决策模型。该模型根据系统的当前状态来决定检查与修理,通过分析计算系统在一个更新周期内平均检查次数、预防性维修及修复性故障的概率,建立维修费用与检查问隔及预防性维修阈值的关系,以平均维修费用最小为目标,优化检查间隔及预防性维修阈值。最后运用Matlab对模型进行数值计算,结果表明,模型能有效地降低维修费用。     

Inventory models of future supply uncertainty with single and multiple suppliers

We consider order-quantity/reorder-point inventory models where the availability of supply is subject to random fluctuations. We use concepts from renewal reward processes to develop average cost objective function models for single, two, and multiple suppliers. Identifying the regenerative cycle for each problem aids the development of the cost function. In the case of two suppliers, spectral theory is used to derive explicit expressions for the transient probabilities of a four-state continuous-time Markov chain representing the status of the system. These probabilities are used to compute the exact form of the average cost expression. For the multiple-supplier problem, assuming that all the suppliers have similar availability characteristics, we develop a simple model and show that as the number of suppliers becomes large, the model reduces to the classical EOQ model. © 1996 John Wiley & Sons, Inc.     

New maximum entropy methods for modeling lifetime distributions

This article introduces two new maximum entropy (ME) methods for modeling the distribution of time to an event. One method is within the classical ME framework and provides characterizations of change point models such as the piecewise exponential distribution. The second method uses the entropy of the equilibrium distribution (ED) for the objective function and provides new characterizations of the exponential, Weibull, Pareto, and uniform distributions. With the same moment constraints, the classical ME and the maximum ED entropy algorithms generate different models for the interarrival time. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 427–434, 2014     

An optimum group maintenance policy

In this article we present an optimum maintenance policy for a group of machines subject to stochastic failures where the repair cost and production loss due to the breakdown of machines are minimized. A nomograph was developed for machines with exponential failure time distributions. The optimal schedule time for repair as well as the total repair cost per cycle can be obtained easily from the nomograph. Conditions for the existence of a unique solution for the optimum schedule and the bounds for the schedule are discussed.     

栅格数据处理中邻域型算法的并行优化方法

随着并行计算的成熟,众多数据密集型的栅格处理算法亟需利用并行计算来缩减执行时间.针对其中一类邻域型算法,构建了用于估计是时间代价的串行/并行时域模型,分析了各个组成的代价影响因素,提出了降低数据I/O代价的并行I/O方法和降低数据通信代价的光圈预测方法.实验证明,所提的两个优化方法可以使邻域型栅格处理算法的并行程序更加充分地利用并行计算资源,进而在一般并行化的基础上进一步提升其并行性能.     

Multiperiod resource allocation with a smoothing objective

We consider a multiperiod resource allocation problem, where a single resource is allocated over a finite planning horizon of T periods. Resource allocated to one period can be used to satisfy demand of that period or of future periods, but backordering of demand is not allowed. The objective is to allocate the resource as smoothly as possible throughout the planning horizon. We present two models: the first assumes that the allocation decision variables are continuous, whereas the second considers only integer allocations. Applications for such models are found, for example, in subassembly production planning for complex products in a multistage production environment. Efficient algorithms are presented to find optimal allocations for these models at an effort of O(T²). Among all optimal policies for each model, these algorithms find the one that carries the least excess resources throughout the planning horizon. © 1995 John Wiley & Sons, Inc.     

What you should know about the vehicle routing problem

In the Vehicle Routing Problem (VRP), the aim is to design a set of m minimum cost vehicle routes through n customer locations, so that each route starts and ends at a common location and some side constraints are satisfied. Common applications arise in newspaper and food delivery, and in milk collection. This article summarizes the main known results for the classical VRP in which only vehicle capacity constraints are present. The article is structured around three main headings: exact algorithms, classical heuristics, and metaheuristics. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

舵减横摇研究综述

舵减横摇系统是当今世界新发展起来的一种减摇系统,它具有结构简单,成本低廉,应用广泛等优点。本文就舵减横摇系统的可行性、数学模型和控制方法以及国内外研究和应用前景作了综合介绍和评价。