Generalized orienteering problem with resource dependent rewards

We introduce a generalized orienteering problem (OP) where, as usual, a vehicle is routed from a prescribed start node, through a directed network, to a prescribed destination node, collecting rewards at each node visited, to maximize the total reward along the path. In our generalization, transit on arcs in the network and reward collection at nodes both consume a variable amount of the same limited resource. We exploit this resource trade‐off through a specialized branch‐and‐bound algorithm that relies on partial path relaxation problems that often yield tight bounds and lead to substantial pruning in the enumeration tree. We present the smuggler search problem (SSP) as an important real‐world application of our generalized OP. Numerical results show that our algorithm applied to the SSP outperforms standard mixed‐integer nonlinear programming solvers for moderate to large problem instances. We demonstrate model enhancements that allow practitioners to represent realistic search planning scenarios by accounting for multiple heterogeneous searchers and complex smuggler motion. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

UUV编队协同搜索静止目标的准最优方法

考虑到操作的简单性且实际执行搜索任务时搜索力不是无限可分,将连续空间的搜索问题转换为离散空间的最优搜索问题。通过划分网格,将连续的目标位置分布离散化。根据最优搜索理论,提出了单个无人水下航行器的准最优随机搜索方法,较好地逼近理论最优值。并以此为基础,分析了无人水下航行器编队的3种协同搜索方法:集中最优搜索、分散最大概率搜索和准最优搜索。最后通过实例仿真,得出了编队准最优搜索策略的有效性、优越性和可操作性。此方法将对无人水下航行器编队的战法研究具有参考借鉴意义。     

基于搜索论的远程反舰导弹搜捕概率建模方法

针对传统捕捉概率模型难以满足远程反舰导弹机动搜捕概率建模计算的问题,提出利用搜索论进行导弹机动搜捕概率计算的建模方法。该方法根据目标机动规律建立其分布概率密度函数,并依据末制导雷达发现目标概率的"倒四次方律"及弹目相对运动轨迹,构建其探测函数,通过求取两者之积的积分实现搜捕概率计算。计算结果显示:若远程反舰导弹不采取机动搜捕策略,目标指示误差增加1km时搜捕概率降低0.47,目标速度增加10节时搜捕概率降低0.3,末制导雷达搜索半径减小50%时搜捕概率降低0.3;若采取平行搜捕策略,上述因素对其影响大幅下降。可见,该方法综合考虑了目标机动规律、传感器探测规律、导弹搜捕策略,可实现远程反舰导弹机动搜捕概率的解算。     

Using a birth‐and‐death process to estimate the steady‐state distribution of a periodic queue

If the number of customers in a queueing system as a function of time has a proper limiting steady‐state distribution, then that steady‐state distribution can be estimated from system data by fitting a general stationary birth‐and‐death (BD) process model to the data and solving for its steady‐state distribution using the familiar local‐balance steady‐state equation for BD processes, even if the actual process is not a BD process. We show that this indirect way to estimate the steady‐state distribution can be effective for periodic queues, because the fitted birth and death rates often have special structure allowing them to be estimated efficiently by fitting parametric functions with only a few parameters, for example, 2. We focus on the multiserver M_t/GI/s queue with a nonhomogeneous Poisson arrival process having a periodic time‐varying rate function. We establish properties of its steady‐state distribution and fitted BD rates. We also show that the fitted BD rates can be a useful diagnostic tool to see if an M_t/GI/s model is appropriate for a complex queueing system. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 664–685, 2015     

Inventory models with nonlinear shortage costs and stochastic lead times; applications of shape properties of randomly stopped counting processes

In this article, we study generalizations of some of the inventory models with nonlinear costs considered by Rosling in (Oper. Res. 50 (2002) 797–809). In particular, we extend the study of both the periodic review and the compound renewal demand processes from a constant lead time to a random lead time. We find that the quasiconvexity properties of the cost function (and therefore the existence of optimal (s, S) policies), holds true when the lead time has suitable log‐concavity properties. The results are derived by structural properties of renewal delayed processes stopped at an independent random time and by the study of log‐concavity properties of compound distributions. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 345–356, 2015     

Integrated scheduling of loading and transportation with tractors and semitrailers separated

Motivated by some practical applications, we study a new integrated loading and transportation scheduling problem. Given a set of jobs, a single crane is available to load jobs, one by one, onto semitrailers with a given capacity. Loaded semitrailers are assigned to tractors for transportation tasks. Subject to limited resources (crane, semitrailers, and tractors), the problem is to determine (1) an assignment of jobs to semitrailers for loading tasks, (2) a sequence for the crane to load jobs onto semitrailers, (3) an assignment of loaded semitrailers to tractors for transportation tasks, and (4) a transportation schedule of assigned tractors such that the completion time of the last transportation task is minimized. We first formulate the problem as a mixed integer linear programming model (MILPM) and prove that the problem is strongly NP‐hard. Then, optimality properties are provided which are useful in establishing an improved MILPM and designing solution algorithms. We develop a constructive heuristic, two LP‐based heuristics, and a recovering beam search heuristic to solve this problem. An improved procedure for solutions by heuristics is also presented. Furthermore, two branch‐and‐bound (B&B) algorithms with two different lower bounds are developed to solve the problem to optimality. Finally, computational experiments using both real data and randomly generated data demonstrate that our heuristics are highly efficient and effective. In terms of computational time and the number of instances solved to optimality in a time limit, the B&B algorithms are better than solving the MILPM. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 416–433, 2015     

Optimal FCFS allocation rules for periodic‐review assemble‐to‐order systems

In Assemble‐To‐Order (ATO) systems, situations may arise in which customer demand must be backlogged due to a shortage of some components, leaving available stock of other components unused. Such unused component stock is called remnant stock. Remnant stock is a consequence of both component ordering decisions and decisions regarding allocation of components to end‐product demand. In this article, we examine periodic‐review ATO systems under linear holding and backlogging costs with a component installation stock policy and a First‐Come‐First‐Served (FCFS) allocation policy. We show that the FCFS allocation policy decouples the problem of optimal component allocation over time into deterministic period‐by‐period optimal component allocation problems. We denote the optimal allocation of components to end‐product demand as multimatching. We solve the multi‐matching problem by an iterative algorithm. In addition, an approximation scheme for the joint replenishment and allocation optimization problem with both upper and lower bounds is proposed. Numerical experiments for base‐stock component replenishment policies show that under optimal base‐stock policies and optimal allocation, remnant stock holding costs must be taken into account. Finally, joint optimization incorporating optimal FCFS component allocation is valuable because it provides a benchmark against which heuristic methods can be compared. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 158–169, 2015     

The dynamic and stochastic knapsack Problem with homogeneous‐sized items and postponement options

This article generalizes the dynamic and stochastic knapsack problem by allowing the decision‐maker to postpone the accept/reject decision for an item and maintain a queue of waiting items to be considered later. Postponed decisions are penalized with delay costs, while idle capacity incurs a holding cost. This generalization addresses applications where requests of scarce resources can be delayed, for example, dispatching in logistics and allocation of funding to investments. We model the problem as a Markov decision process and analyze it through dynamic programming. We show that the optimal policy with homogeneous‐sized items possesses a bithreshold structure, despite the high dimensionality of the decision space. Finally, the value (or price) of postponement is illustrated through numerical examples. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 267–292, 2015     

基于SF-REM的齿轮箱剩余寿命预测方法研究

剩余寿命预测是视情维修决策的重点和难点.针对工程实践中历史数据少、模型参数估计精度低的问题,建立一种基于随机滤波(SF)的齿轮箱剩余寿命预测模型.该方法采用递归期望最大化(REM)算法对模型参数进行递归更新,推导极大似然估计方法的参数递归更新过程,最后经实例验证模型的有效性和实用性.     

Model Versions and Fast Algorithms for Network Epidemiology

Network epidemiology has become a core framework for investigating the role of human contact patterns in the spreadingof infectious diseases. In network epidemiology, one represents the contact structure as a network of nodes（individuals） connected bylinks（sometimes as a temporal network where the links are not continuously active） and the disease as a compartmental model（whereindividuals are assigned states with respect to the disease and follow certain transition rules between the states）. In this paper, we discussfast algorithms for such simulations and also compare two commonly used versions,one where there is a constant recovery rate（the numberof individuals that stop being infectious per time is proportional to the number of such people）;the other where the duration of the diseaseis constant. The results show that, for most practical purposes, these versions are qualitatively the same.