Maximizing the ratio of two convex functions over a convex set

The purpose of this article is to present an algorithm for globally maximizing the ratio of two convex functions f and g over a convex set X. To our knowledge, this is the first algorithm to be proposed for globally solving this problem. The algorithm uses a branch and bound search to guarantee that a global optimal solution is found. While it does not require the functions f and g to be differentiable, it does require that subgradients of g can be calculated efficiently. The main computational effort of the algorithm involves solving a sequence of subproblems that can be solved by convex programming methods. When X is polyhedral, these subproblems can be solved by linear programming procedures. Because of these properties, the algorithm offers a potentially attractive means for globally maximizing ratios of convex functions over convex sets. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Selecting T for a periodic review inventory model with staggered deliveries

Consider a single‐item, periodic review, infinite‐horizon, undiscounted, inventory model with stochastic demands, proportional holding and shortage costs, and full backlogging. Orders can arrive in every period, and the cost of receiving them is negligible (as in a JIT setting). Every T periods, one audits the current stock level and decides on deliveries for the next T periods, thus incurring a fixed audit cost and—when one schedules deliveries—a fixed order cost. The problem is to find a review period T and an ordering policy that satisfy the average cost criterion. The current article extends an earlier treatment of this problem, which assumed that the fixed order cost is automatically incurred once every T periods. We characterize an optimal ordering policy when T is fixed, prove that an optimal review period T** exists, and develop a global search algorithm for its computation. We also study the behavior of four approximations to T** based on the assumption that the fixed order cost is incurred during every cycle. Analytic results from a companion article (where μ/σ is large) and extensive computational experiments with normal and gamma demand test problems suggest these approximations and associated heuristic policies perform well when μ/σ ≥ 2. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 329–352, 2000     

Minimizing sums and products of linear fractional functions over a polytope

In this paper, we develop efficient deterministic algorithms for globally minimizing the sum and the product of several linear fractional functions over a polytope. We will show that an elaborate implementation of an outer approximation algorithm applied to the master problem generated by a parametric transformation of the objective function serves as an efficient method for calculating global minima of these nonconvex minimization problems if the number of linear fractional terms in the objective function is less than four or five. It will be shown that the Charnes–Cooper transformation plays an essential role in solving these problems. Also a simple bounding technique using linear multiplicative programming techniques has remarkable effects on structured problems. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 583–596, 1999     

优序法在舰艇编队导弹攻击效能评估中的应用

导弹攻击是舰艇编队海上行动的主要作战样式,其导弹攻击效能的评估十分重要。首先建立了舰艇编队导弹攻击作战效能评价指标体系,然后介绍了评估舰艇编队导弹攻击效能的一种新方法——优序法,该方法应用简单,既可以处理定性问题,又能处理定量问题。最后给出了应用实例,验证了优序法比较适合于对舰艇编队导弹攻击效能进行评估。通过对舰艇编队导弹攻击效能的评估,可以有效地选用合适的舰艇编队样式。     

Volume discount decisions: Wealth maximization or EOQ approach?

A recent paper finds that when volume discounts are available, in some cases, reliance on the Economic Order Quantity (EOQ) model can induce purchasers to make wealth reducing decisions, and the Present Value (PV) approach should be preferred. While this finding is theoretically correct, the magnitudes of wealth reductions suggested by the paper's numerical examples seem to be questionable. Furthermore, the paper also finds that, in some other cases, a purchaser using the EOQ approach realizes a net increase in current wealth compared to a purchaser using the PV approach. Logic suggests that such a finding cannot be correct, since by its very definition, it is the PV approach that seeks to maximize the current wealth. We offer an alternative frame of comparison and a modified model to show that, under the paper's assumptions, the EOQ approach can never realize a net increase in current wealth compared to the current wealth generated by the PV approach. On the other hand, we also show that when typical values of the relevant parameters prevail, the additional costs imposed by the EOQ approach are not significant. Finally, we suggest that insofar as the PV approach requires greater administrative costs to implement, it may even be counterproductive to the goal of wealth maximization. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 377–389, 1998     

On lifetimes in random environments

For a component operating in random environment, whose hazard rate is assumed to be the realization of a suitable increasing stochastic process, conditions are found such that its lifetime is increasing in likelihood ratio (ILR). For the lifetimes of two components of the same kind some comparisons based on partial stochastic orders are presented. Some applications to the case of repairable components are finally provided. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 365–375, 1998     

Estimating reliability of components with increasing failure rate using series system data

The maximum likelihood estimator (MLE) for a distribution function with increasing failure rate is derived, based on a collection of series system data. Applications can arise in industries where operating environments make available only such system-level data, due to system configuration or type-II censoring. The estimator can be solved using isotonic regression. For the special case in which systems contain one component, the estimator is equivalent to the restricted maximum likelihood estimator of Marshall and Proschan [9]. The MLE is illustrated using emergency diesel generator failure data from the nuclear industry. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 115–123, 1998     

复Banach空间的凸性及 Hp 鞅

本文系统地讨论了复Ｂａｎａｃｈ空间的各种凸性,以及取值于复Ｂａｎａｃｈ空间的Ｈｐ鞅,得到了关于凸性及Ｈｐ鞅之间的各种等价性命题。     

几何凸集中一个递归关系的建立与求解

几何凸集中递归关系的建立是求解问题的关键。本文对一个定理中递归关系的建立给出了容易理解的详细表述,然后利用生成函数法求其解。     

变窗长秩排序统计滤波器与噪声图象滤波

基于信号分解理论,在非线性秩排序统计滤波器基础上,提出一种新型的非线性滤波器结构——二值秩排序统计滤波器。主要工作包括:(1)提出了滤波器的定义和实现结构;(2)实现算法;(3)滤波特性分析;(4)噪声图象滤波的计算机仿真。理论分析和实验结果表明,本文提出的滤波器具有良好的脉冲干扰抑制能力和边缘保持特性,硬件实现简单。