A mathematical programming approach to identification and optimization of a class of unknown systems

There exists a class of decision problems for which: (1) models of input-output response functions are not available in a closed-form, functional representation; (2) informational costs associated with learning about the response function are significant. For these problems, combining identification with optimization using mathematical programming is potentially attractive. Three approaches to the identification-optimization problem are proposed: an outer-linearized approximation using relaxation (OLR); an inner-linearized approximation using restriction (ILR); and a sequential combination of inner- and outer-linearized subproblems (SIO). Algorithms based on each approach are developed and computational experience reported.     

Transportation problems with aggregated destinations when demands are uncertain

Transportation problems with uncertain demands are useful applied models themselves, and also they represent in a formal way the problem of estimating demands for use in deterministic models. We consider the effects of using a small, aggregate model of this type in place of a larger, more detailed one. Formulation of the aggregate objective function turns out to depend on how one chooses to use (disaggregate) the solution; several alternative methods are examined. Bounds are derived on the error induced by the approximation, thus facilitating comparison of alternative aggregations. We also consider the problem of estimating demands for an aggregate-level deterministic problem. In a specific sense, it is often not the case (as one might expect) that such aggregate demands are easier to estimate than the detailed demands. This is because aggregation and centralization are not the same thing.     

A computationally efficient approach for determining inventory levels in a capacitated multiechelon production‐distribution system

The system under study is a single item, two‐echelon production‐inventory system consisting of a capacitated production facility, a central warehouse, and M regional distribution centers that satisfy stochastic demand. Our objective is to determine a system base‐stock level which minimizes the long run average system cost per period. Central to the approach are (1) an inventory allocation model and associated convex cost function designed to allocate a given amount of system inventory across locations, and (2) a characterization of the amount of available system inventory using the inventory shortfall random variable. An exact model must consider the possibility that inventories may be imbalanced in a given period. By assuming inventory imbalances cannot occur, we develop an approximation model from which we obtain a lower bound on the per period expected cost. Through an extensive simulation study, we analyze the quality of our approximation, which on average performed within 0.50% of the lower bound. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 377–398, 2000     

Pricing bridges to cross a river

We consider a pricing problem in directed, uncapacitated networks. Tariffs must be defined by an operator, the leader, for a subset of m arcs, the tariff arcs. Costs of all other arcs in the network are assumed to be given. There are n clients, the followers, and after the tariffs have been determined, the clients route their demands independent of each other on paths with minimal total cost. The problem is to find tariffs that maximize the operator's revenue. Motivated by applications in telecommunication networks, we consider a restricted version of this problem, assuming that each client utilizes at most one of the operator's tariff arcs. The problem is equivalent to pricing bridges that clients can use in order to cross a river. We prove that this problem is APX‐hard. Moreover, we analyze the effect of uniform pricing, proving that it yields both an m approximation and a (1 + lnD)‐approximation. Here, D is upper bounded by the total demand of all clients. In addition, we consider the problem under the additional restriction that the operator must not reject any of the clients. We prove that this problem does not admit approximation algorithms with any reasonable performance guarantee, unless P = NP, and we prove the existence of an n‐approximation algorithm. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

C^3I/M＆S互操作性研究

结合C^3I/M＆S互操作性的主要问题,总结了互操作性技术参考模型,在此基础上对C^3I/M＆S互操作性的数据模型及标准、接口标准进行了详细论述,介绍了北约C^3I/SIM互操作性试验情况,并指出了未来C^3I/M＆S互操作性研究的发展趋势,对军队C^3I系统和仿真系统的建设有一定的指导意义。     

A class of inventory models with customer impatience

Classical inventory models generally assume either no backlogging of demands or unlimited backlogging. This paper treats the case wherein backlogged customers are willing to wait for a random period of time for service. A broad class of such models is discussed, with a more complete analysis performed on a simple subclass. Steady state equations are derived and solved assuming exponentially distributed interarrival times of customers, order delivery lead times, and customer patience.     

基于复杂排队系统的TOC服务模型与性能分析

三值光学计算机的运算请求处理过程缺乏合理、系统的性能评价标准与体系。基于M/M/1、M/M/n、MX/M/1和M/MB/1构成的复杂排队系统,构建了三值光学计算机的四阶段服务模型,同时建立了立即调度和结束时调度两种不同策略与算法。基于不同排队系统讨论了运算请求的接收时间、预处理时间、运算时间和发送时间的计算方法,进而得到最终响应时间。最后,通过仿真实验对两种策略的模型进行验证,结果表明结束时调度策略明显优于立即调度策略。     

Forecasting Civil Conflict with Zero-Inflated Count Models

Advances in the study of civil war have led to the proliferation of event count data, and to a corresponding increase in the use of (zero-inflated) count models for the quantitative analysis of civil conflict events. Our ability to effectively use these techniques is met with two current limitations. First, researchers do not yet have a definitive answer as to whether zero-inflated count models are a verifiably better approach to civil conflict modeling than are ‘less assuming’ approaches such as negative binomial count models. Second, the accurate analysis of conflict-event counts with count models – zero-inflated or otherwise – is severely limited by the absence of an effective framework for the evaluation of predictive accuracy, which is an empirical approach that is of increasing importance to conflict modelers. This article rectifies both of these deficiencies. Specifically, this study presents count forecasting techniques for the evaluation and comparison of count models' predictive accuracies. Using these techniques alongside out-of-sample forecasts, it then definitively verifies – for the first time – that zero-inflated count models are superior to comparable non-inflated models for the study of intrastate conflict events.     

弹道跟踪数据处理中的几个计算问题

结合弹道跟踪数据建模和数据处理的实践 ,提出了几个有典型应用价值的测量数据模型 ,在应用这些数学模型解决实际问题时 ,涉及统计、优化、函数逼近等几方面的理论和计算问题。这些问题和模型的研究 ,对解决许多相关的实际问题有重要意义。     

The effect of prior assumptions on the expected cost of m/m/1 queueing systems with unknown arrival rate

In this study we deal with the determination of optimal service rate in an M/M/1 queue. The arrival rate is unknown and assumed to be a random variable with a known distribution function. Holding and operating costs are considered and service rate is determined to minimize total expected discounted costs for infinite horizon. The effects of the arrival rate's distribution properties on the characteristics of the system are examined.     

Modelling international conflict under conditions of state level economic and political uncertainty

Formal models of international conflict have tended to concentrate on change across the security dimension, assuming that the state level economic and political dimensions are constant. However, the conclusion of the Cold War suggests that over the long run these dimensions are not constant; indeed, the development of economic power, state level limits on defence expenditures, structural impediments to economic change, and several other ‘constants’ clearly do have an endogenous role in international conflict. This paper suggests one strategy for their inclusion as a causal factor in conflict modelling.     

基于混合矩的多输出模型确认指标研究

针对随机不确定性条件下多输出计算模型与物理实验数据之间一致性难以量化度量这一问题,本文提出一组新的基于混合矩的多输出模型确认指标。在不确定情况下,同时考虑到多维输出之间的相关关系和单输出的均值,构建了由多输出数学期望列阵和协方差矩阵组成的多输出模型确认局部混合矩指标和全局混合矩指标。其中局部混合矩指标包括绝对指标(LA-3M)和相对指标(LR-3M),它们适合固定位置的多输出局部模型确认;全局混合矩指标也包括绝对指标(GA-3M)和相对指标(GR-3M),它们适合多点位置的多输出全局模型确认。通过数字算例和工程算例,并与PIT和t-pooling 面积指标进行对比,结果表明本文所提指标可行有效,能够方便地度量计算模型和物理实验之间的差异程度。     

Heuristic modeling of supply availabilities in large networks

The objective of this article is to describe heuristic solutions to the problem of modeling inventories at each node of a large network in the context of a computer simulation model of that network. The heuristic solutions are compared with the mathematical solution which is too unwieldy for use in a simulation model. The Weibull cumulative distribution is used as an approximation for the heuristic models. We question whether the good performance of the Weibull is coincidence or perhaps mathematically justifiable.     

Bayesian analysis of queues with impatient customers: Applications to call centers

Queuing models have been extensively used in the literature for obtaining performance measures and developing staffing policies. However, most of this work has been from a pure probabilistic point of view and has not addressed issues of statistical inference. In this article, we consider Bayesian queuing models with impatient customers with particular emphasis on call center operations and discuss further extensions. We develop the details of Bayesian inference for queues with abandonment such as the M/M/s + M model (Erlang‐A). In doing so, we discuss the estimation of operating characteristics and its implications on staffing. We illustrate the implementation of the Bayesian models using actual arrival, service, and abandonment data from call centers. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

Aggregating courier deliveries

We consider the problem of efficiently scheduling deliveries by an uncapacitated courier from a central location under online arrivals. We consider both adversary‐controlled and Poisson arrival processes. In the adversarial setting we provide a randomized (3βΔ/2δ ? 1) ‐competitive algorithm, where β is the approximation ratio of the traveling salesman problem, δ is the minimum distance between the central location and any customer, and Δ is the length of the optimal traveling salesman tour overall customer locations and the central location. We provide instances showing that this analysis is tight. We also prove a 1 + 0.271Δ/δ lower‐bound on the competitive ratio of any algorithm in this setting. In the Poisson setting, we relax our assumption of deterministic travel times by assuming that travel times are distributed with a mean equal to the excursion length. We prove that optimal policies in this setting follow a threshold structure and describe this structure. For the half‐line metric space we bound the performance of the randomized algorithm in the Poisson setting, and show through numerical experiments that the performance of the algorithm is often much better than this bound.     

Replacing continuous demand with discrete demand in a competitive location model

Location models commonly represent demand as discrete points rather than as continuously spread over an area. This modeling technique introduces inaccuracies to the objective function and consequently to the optimal location solution. In this article this inaccuracy is investigated by the study of a particular competitive facility location problem. First, the location problem is formulated over a continuous demand area. The optimal location for a new facility that optimizes the objective function is obtained. This optimal location solution is then compared with the optimal location obtained for a discrete set of demand points. Second, a simple approximation approach to the continuous demand formulation is proposed. The location problem can be solved by using the discrete demand algorithm while significantly reducing the inaccuracies. This way the simplicity of the discrete approach is combined with the approximated accuracy of the continuous-demand location solution. Extensive analysis and computations of the test problem are reported. It is recommended that this approximation approach be considered for implementation in other location models. © 1997 John Wiley & Sons, Inc.     

Optimal disposal policies for a single-item inventory system with returns

We consider a single-item inventory system in which the stock level can increase due to items being returned as well as decrease when demands occur. Returned items can be repaired and then used to satisfy future demand, or they can be disposed of. We identify those inventory levels where disposal is the best policy. It is shown that this problem is equivalent to a problem of controlling a single-server queue. When the return and demand processes are both Poisson, we find the optimal policy exactly. When the demand and return processes are more general, we use diffusion approximations to obtain an approximate model, which is then solved. The approximate model requires only mean and variance data. Besides the optimal policy, the output of the models includes such characteristics as the operating costs, the purchase rate for new items, the disposal rate for returned items and the average inventory level. Several numerical examples are given. An interesting by-product of our investigation is an approximation for the steady-state behavior of the bulk GI/G/1 queue with a queue limit.     

A queuing process with bilevel hysteretic service-rate control

The purpose of this paper is to analyze the effect of a particular control doctrine applied to the service mechanism of a queuing process. A bilevel hysteretic control based on queue length control levels is employed in an M/M/1 queuing system. Expressions are obtained for queue length probabilities, the first two factorial moments of queue length and two figures of merit for describing control performance under the assumption of statistical equilibrium. Computational examples illustrate the effects on queuing processes subject to this type of control. Several cost formulae are considered for comparison of costs when the queue control doctrine is varied. Situations in which hysteretic control is useful are discussed.     

Estimation in single server queues

Moment and maximum likelihood estimates (m.l.e.'s) arc investigated for nonparametric and parametric models for a single server queue observed over a random time horizon, namely, up to the nth departure epoch. Also. m.l.e's of the mean interarrival time and mean service time in anM/M/1 queue observed over a fixed time-interval are studied Limit distributions of these estimates are obtained Without imposing steady state assumptions on the queue-size or waiting time processes.     

线-面传输线Taylor与Agrawal模型解的比较

基于Maxwell方程推导描述外电磁场对导线的耦合传输线模型有Taylor,Agrawal和Rachidi三种模型,每个耦合公式给出相同的传输线响应,但是它们之间又有细微的差别,Nucci和Rachidi通过数值方法验证在圆柱形雷电电磁场激励下这三种线-面传输线模型在负载终端具有相同的全电压解。本文采用解析的方法对线-面传输线Taylor模型和Agrawal模型进行研究,获得了这两个模型基于平面电磁波激励下的终端负载响应的解析解,证明了它们的解析解是相同的。也就是说,线-面传输线Taylor模型和Agrawal模型其实是对同一个解的不同描述。因此,在实际应用时,可以根据具体情况来选择不同的传输线模型进行求解。