When is model complexity too much? Illustrating the benefits of simple models with Hughes' salvo equations

The simulations that many defense analysts rely upon in their studies continue to grow in size and complexity. This paper contrasts the guidance that the authors have received—from some of the giants of military operations research—with the current practice. In particular, the analytic utility of Hughes' simple salvo equations is compared with that of the complex Joint Warfighting System (JWARS), with respect to JWARS' key performance parameters. The comparison suggests that a family of analytic tools supports the best analyses. It follows that smaller, more agile, and transparent models, such as Hughes' salvo equations, are underutilized in defense analyses. We believe that these models should receive more attention, use, and funding. To illustrate this point, this paper uses two very simple models (by modern standards) to rapidly generate insights on the value of information relative to force strength. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2003     

Competition under time‐varying demands and dynamic lot sizing costs

We develop a competitive pricing model which combines the complexity of time‐varying demand and cost functions and that of scale economies arising from dynamic lot sizing costs. Each firm can replenish inventory in each of the T periods into which the planning horizon is partitioned. Fixed as well as variable procurement costs are incurred for each procurement order, along with inventory carrying costs. Each firm adopts, at the beginning of the planning horizon, a (single) price to be employed throughout the horizon. On the basis of each period's system of demand equations, these prices determine a time series of demands for each firm, which needs to service them with an optimal corresponding dynamic lot sizing plan. We establish the existence of a price equilibrium and associated optimal dynamic lotsizing plans, under mild conditions. We also design efficient procedures to compute the equilibrium prices and dynamic lotsizing plans.© 2008 Wiley Periodicals, Inc. Naval Research Logistics 2009     

A two‐echelon inventory‐location problem with service considerations

We study the problem of designing a two‐echelon spare parts inventory system consisting of a central plant and a number of service centers each serving a set of customers with stochastic demand. Processing and storage capacities at both levels of facilities are limited. The manufacturing process is modeled as a queuing system at the plant. The goal is to optimize the base‐stock levels at both echelons, the location of service centers, and the allocation of customers to centers simultaneously, subject to service constraints. A mixed integer nonlinear programming model (MINLP) is formulated to minimize the total expected cost of the system. The problem is NP‐hard and a Lagrangian heuristic is proposed. We present computational results and discuss the trade‐off between cost and service. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009     

Single‐warehouse multi‐retailer inventory systems with full truckload shipments

We consider a multi‐stage inventory system composed of a single warehouse that receives a single product from a single supplier and replenishes the inventory of n retailers through direct shipments. Fixed costs are incurred for each truck dispatched and all trucks have the same capacity limit. Costs are stationary, or more generally monotone as in Lippman (Management Sci 16, 1969, 118–138). Demands for the n retailers over a planning horizon of T periods are given. The objective is to find the shipment quantities over the planning horizon to satisfy all demands at minimum system‐wide inventory and transportation costs without backlogging. Using the structural properties of optimal solutions, we develop (1) an O(T²) algorithm for the single‐stage dynamic lot sizing problem; (2) an O(T³) algorithm for the case of a single‐warehouse single‐retailer system; and (3) a nested shortest‐path algorithm for the single‐warehouse multi‐retailer problem that runs in polynomial time for a given number of retailers. To overcome the computational burden when the number of retailers is large, we propose aggregated and disaggregated Lagrangian decomposition methods that make use of the structural properties and the efficient single‐stage algorithm. Computational experiments show the effectiveness of these algorithms and the gains associated with coordinated versus decentralized systems. Finally, we show that the decentralized solution is asymptotically optimal. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009     

Approximation algorithms for general one‐warehouse multi‐retailer systems

Logistical planning problems are complicated in practice because planners have to deal with the challenges of demand planning and supply replenishment, while taking into account the issues of (i) inventory perishability and storage charges, (ii) management of backlog and/or lost sales, and (iii) cost saving opportunities due to economies of scale in order replenishment and transportation. It is therefore not surprising that many logistical planning problems are computationally difficult, and finding a good solution to these problems necessitates the development of many ad hoc algorithmic procedures to address various features of the planning problems. In this article, we identify simple conditions and structural properties associated with these logistical planning problems in which the warehouse is managed as a cross‐docking facility. Despite the nonlinear cost structures in the problems, we show that a solution that is within ε‐optimality can be obtained by solving a related piece‐wise linear concave cost multi‐commodity network flow problem. An immediate consequence of this result is that certain classes of logistical planning problems can be approximated by a factor of (1 + ε) in polynomial time. This significantly improves upon the results found in literature for these classes of problems. We also show that the piece‐wise linear concave cost network flow problem can be approximated to within a logarithmic factor via a large scale linear programming relaxation. We use polymatroidal constraints to capture the piece‐wise concavity feature of the cost functions. This gives rise to a unified and generic LP‐based approach for a large class of complicated logistical planning problems. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

陆基导弹武器系统生存能力研究

导弹武器系统的生存能力是一个关键的战技指标.国内外对导弹武器系统生存能力的分析评估十分重视,已开展了许多研究工作.介绍了研究陆基导弹武器系统生存能力的重要性,对其概念、定性评估模型、解析评估模型、仿真评估模型和提高生存能力的途径等几方面的研究进行了综述和分析,并就相关问题提出了一些看法.     

联合补充博弈的费用分摊

就一个仓库、多个零售商,对联合订货费用函数的模型进行分析,给出了一个求解最佳订货周期的多项式时间的算法,且算法的时间复杂性为O（nlogn）。利用文献[8]中的技巧,给出了该库存博弈的核。     

陆军战斗决心方案评估方法研究

战斗决心方案评估是陆军指挥员及指挥机关组织战斗过程中的一项重要工作。研究评估方法为陆军部队行动选择战斗决心方案提供依据。对战斗决心方案的评估,根据决心方案的战术手段、作战目标选择、战斗部署等三项主要内容,建立评估指标体系和评估数学模型,得出综合评估结果。该量化分析的评估方法提高了决策的精确性。     

航空随队支援干扰掩护区仿真建模研究

干扰暴露区及干扰扇面等传统评估指标对静态干扰部署可以进行有效评估分析,对机动干扰掩护难以进行准确描述分析。为有效评估电子对抗航空兵随队支援干扰能力,以及准确进行航空兵突防编队配置及干扰力量需求分析,引入了干扰掩护区的概念,并建立相关模型进行仿真计算,得出3条电子对抗随队支援航空兵突防的运用启示。     

高功率微波弹的杀伤效果分析与仿真

根据高功率微波弹微波脉冲的攻击入射角,给出了高功率微波弹杀伤区域模型,结合高功率微波损坏和干扰电子元器件的能量阈值,提出了高功率微波弹对目标的失效区、干扰区及安全区的概念,并建立相应的数学模型进行了仿真分析,为高功率微波弹攻击参数的设定及实际的作战运用提供了理论依据。