Analysis of a machine repair problem with an unreliable server and phase type repairs and services

In this paper we study a machine repair problem in which a single unreliable server maintains N identical machines. The breakdown times of the machines are assumed to follow an exponential distribution. The server is subject to failure and the failure times are exponentially distributed. The repair times of the machine and the service times of the repairman are assumed to be of phase type. Using matrix‐analytic methods, we perform steady state analysis of this model. The time spent by a failed machine in service and the total time in the repair facility are shown to be of phase type. Several performance measures are evaluated. An optimization problem to determine the number of machines to be assigned to the server that will maximize the expected total profit per unit time is discussed. An illustrative numerical example is presented. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 462–480, 2003     

互补问题中无SLC限制的内点算法

针对互补问题提出了一种无SLC限制的内点算法,仅要求线性函数F(x)=Hx q中的F是一个P*(τ)函数,不需要满足范数Lipschitz条件.并对该算法的全局收敛性做了证明。     

消防部队基层干部心理问题分析与对策研究

消防部队基层干部面临个体需求与现实满足存在较大差距时出现的心理问题,受个体与周围环境因素的影响。面对心理问题,在重视部队传统教育的基础上,大胆借鉴现代企业管理经验和理念,充分利用压力的正效应,结合物质鼓励和精神激励,合理疏导,妥善处理。     

二次型极小化问题带误差的迭代算法

证明了二次型极小化问题带误差的迭代算法的有效性,所得结果推广了关于二次型极小化问题迭代的收敛性。     

快速解命中的一种有效方法

基于对命中函数的考察,提出了一种新的命中解解算方法,实际应用及仿真计算结果表明,该方法能明显提高解算精度和缩短迭代时间。     

A generalized assignment model for dynamic supply chain capacity planning

We consider a generalization of the well‐known generalized assignment problem (GAP) over discrete time periods encompassed within a finite planning horizon. The resulting model, MultiGAP, addresses the assignment of tasks to agents within each time period, with the attendant single‐period assignment costs and agent‐capacity constraint requirements, in conjunction with transition costs arising between any two consecutive periods in which a task is reassigned to a different agent. As is the case for its single‐period antecedent, MultiGAP offers a robust tool for modeling a wide range of capacity planning problems occurring within supply chain management. We provide two formulations for MultiGAP and establish that the second (alternative) formulation provides a tighter bound. We define a Lagrangian relaxation‐based heuristic as well as a branch‐and‐bound algorithm for MultiGAP. Computational experience with the heuristic and branch‐and‐bound algorithm on over 2500 test problems is reported. The Lagrangian heuristic consistently generates high‐quality and in many cases near‐optimal solutions. The branch‐and‐bound algorithm is also seen to constitute an effective means for solving to optimality MultiGAP problems of reasonable size. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012     

A branch‐and‐price approach for the stochastic generalized assignment problem

In this article, we address a stochastic generalized assignment machine scheduling problem in which the processing times of jobs are assumed to be random variables. We develop a branch‐and‐price (B&P) approach for solving this problem wherein the pricing problem is separable with respect to each machine, and has the structure of a multidimensional knapsack problem. In addition, we explore two other extensions of this method—one that utilizes a dual‐stabilization technique and another that incorporates an advanced‐start procedure to obtain an initial feasible solution. We compare the performance of these methods with that of the branch‐and‐cut (B&C) method within CPLEX. Our results show that all B&P‐based approaches perform better than the B&C method, with the best performance obtained for the B&P procedure that includes both the extensions aforementioned. We also utilize a Monte Carlo method within the B&P scheme, which affords the use of a small subset of scenarios at a time to estimate the “true” optimal objective function value. Our experimental investigation reveals that this approach readily yields solutions lying within 5% of optimality, while providing more than a 10‐fold savings in CPU times in comparison with the best of the other proposed B&P procedures. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 131–143, 2014     

奇型抛物问题的有限元误差估计

本文引入带权的 Sobolev 空间,讨论了奇型线性问题:(?)((?)u)/((?)t)-1/x~(?)(x~aa(x)u′)′=f(t,x) (x,t)∈1×J(?)/((?)x)u(t,0)=u(t,1)=0 t∈Ju(0,x)=φ(x) x∈I式中 I=(0,1),J=[0,T],0<α<3的有限元方法,并在适当条件下,给出了最佳估计:‖u_(?)-u‖_(0,2,a)≤ch~2{‖φ‖_(2,2,a)+[integral 0 to t (‖u‖~2_(2,2,a)+‖u_(?)‖~2_(2,2,a)dt]~(1/2)}‖u_(?)-u‖_(1,2,a)≤ch~2{‖φ‖_(2,2,a)+[integral 0 to t (‖u‖~2_(2,2,a)+‖u_(?)‖~2_(2,2,a)dt]~(1/2)}     

一类m-点边值问题的正解

研究一类二阶m-点边值问题u″ f(t,u,u)′=0,00,i=1,…,m-2,ζi满足0=ζ0<ζ1<ζ2<…<ζm-2<ζm-1=1和i∑=1aiζi<1。应用推广的Krasnosel-skii′s不动点定理,给出了上述边值问题至少存在一个正解的充分条件。     

陆基常规导弹武器系统射击效率评估

现行的陆基常规导弹武器射击效率的算法原理滞后于导弹作战实际需要.针对毁伤律问题、积累毁伤效应问题、相关性问题、目标毁伤的模糊性问题进行了探讨,指出应用当代新的数学理论方法改造现行陆基常规导弹射击效率算法理论的必要性和迫切性.