A three‐stage procurement optimization problem under uncertainty

This article examines a problem faced by a firm procuring a material input or good from a set of suppliers. The cost to procure the material from any given supplier is concave in the amount ordered from the supplier, up to a supplier‐specific capacity limit. This NP‐hard problem is further complicated by the observation that capacities are often uncertain in practice, due for instance to production shortages at the suppliers, or competition from other firms. We accommodate this uncertainty in a worst‐case (robust) fashion by modeling an adversarial entity (which we call the “follower”) with a limited procurement budget. The follower reduces supplier capacity to maximize the minimum cost required for our firm to procure its required goods. To guard against uncertainty, the firm can “protect” any supplier at a cost (e.g., by signing a contract with the supplier that guarantees supply availability, or investing in machine upgrades that guarantee the supplier's ability to produce goods at a desired level), ensuring that the anticipated capacity of that supplier will indeed be available. The problem we consider is thus a three‐stage game in which the firm first chooses which suppliers' capacities to protect, the follower acts next to reduce capacity from unprotected suppliers, and the firm then satisfies its demand using the remaining capacity. We formulate a three‐stage mixed‐integer program that is well‐suited to decomposition techniques and develop an effective cutting‐plane algorithm for its solution. The corresponding algorithmic approach solves a sequence of scaled and relaxed problem instances, which enables solving problems having much larger data values when compared to standard techniques. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

New results on rendezvous search on the interval

In a rendezvous search problem, two players are placed in a network and must try to meet each other in the least possible expected time. We look at rendezvous search on a discrete interval in which the players are initially placed using independent draws (usually assumed to be from the same distribution). Some optimal solutions are known if this distribution is uniform, and also for certain other special types of distribution. In this article, we present two new results. First, we characterize the complete set of solutions for the uniform case, showing that all optimal strategies must have two specific properties (namely, of being swept and strictly geodesic). Second, we relate search strategies on the interval to proper binary trees, and use this correspondence to derive a recurrence relation for solutions to the symmetric rendezvous problem for any initial distribution. This relation allows us to solve any such problem computationally by dynamic programming. Finally, some ideas for future research are discussed. © Wiley Periodicals, Inc. Naval Research Logistics 60: 454–467, 2013     

Strategic Defense and Attack for Series and Parallel Reliability Systems: Reply to Rejoinder

Kovenock and Roberson's (2012a, b) replication of Hausken’s (2008a) equations and parameter restrictions do not enhance our insight into the defense and attack of reliability systems. This reply intends to fill the remaining understanding gaps.     

THE SUPPLY PRICE OF COMMITMENT: EVIDENCE FROM THE AIR FORCE ENLISTMENT BONUS PROGRAM

In fiscal year 1999, the US Air Force introduced a bonus program designed to encourage longer enlistment terms. This regime shift provides a unique opportunity to estimate the elasticity of labor supply at a new margin: the length of the employment contract. A $5000 bonus differential is estimated to increase the probability that a recruit will choose a 6‐year enlistment over a 4‐year enlistment by 30 percentage points. The program is found to be cost‐effective relative to other policies to increase man‐years.     

混合对策无人战机空战决策

在混合对策理论的基础上,将空战过程看作是由一系列离散的状态组成的离散事件动态系统,建立了空战过程的离散状态子模型,利用空战态势指数和战机空战能力指数构造了战术评估函数,以完成对战术动作的筛选工作,并结合3DOF质点模型设计了机动指令生成器,实现对无人机运动状态的控制,并在Matlab环境下对机动实例进行了仿真.     

基于保障场的装备保障力量配置优化研究

根据电场的作用机理,提出保障场的概念,从场思维的角度构建装备保障力量配置分析的优化模型;并进一步定量分析与定性判断相结合,提出装备保障力量配置优化的流程,最后结合实例具体分析。研究结果对装备保障的部署决策具有一定参考价值和指导意义。     

基于敌后侦察与诱骗博弈的远程火力打击战法

对敌后侦察反军事诱骗的远程火力打击战法的定量分析是战役研究中尚未解决的关键问题之一,根据信息作战原理,运用仿真和统计学分析的混合方法,建立基于概率的二人非零和(TPNZS)非合作博弈模型,设计基于侦察与诱骗博弈的远程火力打击战法,定量分析我方的敌后侦察和敌方的军事诱骗对远程信息与火力联合打击能力的影响,并对一个典型实例的初步试验及分析结果表明:与敌后侦察和军事诱骗有关的正确识别目标和错误识别目标的概率以及远程火力命中目标的概率是评估远程信息与火力联合打击能力的关键,而对评估结果进行博弈分析则是远程火力打击战法设计的关键,用识别正确目标和错误目标能力以及远程火力命中目标能力描述的基于敌后侦察与诱骗博弈的远程火力最优打击战法为Δ*=(0,Δ2*,1-Δ2*)=(0.0000,0.7727,0.2273),被打击方对远程火力打击的最优战法为π*=(π1*,0,1-π1*)=(0.8511,0.0000,0.1489)。     

云模型在雷达干扰资源多目标优化配置中的应用

鉴于干扰效果/效益评估在雷达干扰资源优化分配中的重要地位,提出了一种基于云模型和匈牙利算法的雷达干扰资源优化分配模型。利用一维云模型单条件单规则发生器和逆向云发生器构建了评估指标干扰效果推理器,利用基于风险态度因子的云模型映射函数定义了云模型之间距离的度量方法。提出了一种基于云模型与逼近理想解法的雷达干扰效益矩阵求解方法,最后运用匈牙利算法实现了干扰资源优化分配。将所建模型应用到干扰资源分配中,结果表明该模型能够较好的处理评估中的不确定性知识,是合理、可行的。     

The SSA-BP-based potential threat prediction for aerial target considering commander emotion

The target's threat prediction is an essential procedure for the situation analysis in an aerial defense system. However, the traditional threat prediction methods mostly ignore the effect of commander's emotion. They only predict a target's present threat from the target's features itself, which leads to their poor ability in a complex situation. To aerial targets, this paper proposes a method for its potential threat prediction considering commander emotion (PTP-CE) that uses the Bi-directional LSTM (BiLSTM) network and the backpropagation neural network (BP) optimized by the sparrow search algorithm (SSA). Furthermore, we use the BiLSTM to predict the target's future state from real-time series data, and then adopt the SSA-BP to combine the target's state with the commander's emotion to establish a threat prediction model. Therefore, the target's potential threat level can be obtained by this threat prediction model from the predicted future state and the recognized emotion. The experimental results show that the PTP-CE is efficient for aerial target's state prediction and threat prediction, regardless of commander's emotional effect.     

A cooperative game in search theory

Search theory originates from the military research efforts of WWII. Most researchers of that period modeled their search games in noncooperative games, where players are enemies or compete against each other. In this article, we deal with a cooperative search game, where multiple searchers behave cooperatively. First we describe several search problems and discuss the possibility of a coalition or cooperation among searchers. For the cooperative search game, we define a function named quasi‐characteristic function, which gives us a criterion similar to the so‐called characteristic function in the general coalition game with transferable utility. The search operation includes a kind of randomness with respect to whether the searchers can detect a target and get the value of the target. We also propose a methodology to divide the obtained target value among members of the coalition taking account of the randomness. As a concrete problem of the cooperative search game, we take the so‐called search allocation game, where searchers distribute their searching resources to detect a target in a cooperative way and the target moves in a search space to evade the searchers. Lastly, we discuss the core of the cooperative search allocation game. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009