Application of Markov renewal theory and semi-Markov decision processes in maintenance modeling and optimization of multi-unit systems

In this paper, a condition-based maintenance model for a multi-unit production system is proposed and analyzed using Markov renewal theory. The units of the system are subject to gradual deterioration, and the gradual deterioration process of each unit is described by a three-state continuous time homogeneous Markov chain with two working states and a failure state. The production rate of the system is influenced by the deterioration process and the demand is constant. The states of the units are observable through regular inspections and the decision to perform maintenance depends on the number of units in each state. The objective is to obtain the steady-state characteristics and the formula for the long-run average cost for the controlled system. The optimal policy is obtained using a dynamic programming algorithm. The result is validated using a semi-Markov decision process formulation and the policy iteration algorithm. Moreover, an analytical expression is obtained for the calculation of the mean time to initiate maintenance using the first passage time theory.     

On efficient algorithms for finding efficient salvo policies

We consider the salvo policy problem, in which there are k moments, called salvos, at which we can fire multiple missiles simultaneously at an incoming object. Each salvo is characterized by a probability p_i: the hit probability of a single missile. After each salvo, we can assess whether the incoming object is still active. If it is, we fire the missiles assigned to the next salvo. In the salvo policy problem, the goal is to assign at most n missiles to salvos in order to minimize the expected number of missiles used. We consider three problem versions. In Gould's version, we have to assign all n missiles to salvos. In the Big Bomb version, a cost of B is incurred when all salvo's are unsuccessful. Finally, we consider the Quota version in which the kill probability should exceed some quota Q. We discuss the computational complexity and the approximability of these problem versions. In particular, we show that Gould's version and the Big Bomb version admit pseudopolynomial time exact algorithms and fully polynomial time approximation schemes. We also present an iterative approximation algorithm for the Quota version, and show that a related problem is NP-complete.     

警卫部队基层建设研究

部队建设的基础在基层，基层建设是警卫部队建设与发展的重要内容，也是警卫事业全面发展的重要保证。在新世纪新阶段，只有以科学发展观为指导，把科学发展观贯穿于警卫部队基层建设的全过程，落实到各项具体工作中，才能使部队建设在安全、有序的环境下得以全面、持续、和谐、健康地发展，才能真正提升部队战斗力，履行好警卫部队肩负的历史使命。     

公共场所人员安全疏散评价方法探讨

公共场所安全疏散评价对于确保火灾中人员的生命安全具有重要意义。基于“性能化”防火设计的思想，对影响公共场所安全疏散的因素进行了分析，并对安全疏散的必要性能和评价程序进行了较为全面的探讨，其中包括烟气的评价、人员疏散能力的评价、疏散路线合理性的评价、疏散对策的评价等，目的在于通过合理的评价方法得出合理的疏散性能，为减少公共场所火灾造成的人员伤亡和财产损失提供帮助。     

基于灰色系统理论的目标方位估算及应用

针对潜艇作战过程中依据目标方位变化判断战场态势的军事需求,根据灰色系统理论,以实测目标方位序列为原始数据,建立GM(1,1)模型,深入挖掘其内在规律性,对目标方位序列的变化趋势进行科学分析,并估算未来时刻目标方位,用于战术态势判断、检验目标运动要素解算和战术绘算的准确性,以及干预目标运动要素解算,以期望利用有限的数据,获得最大限度的信息,为潜艇指挥员提供决策支持。     

Adjacency‐based local top‐down search method for finding maximal efficient faces in multiple objective linear programming

It is well‐known that the efficient set of a multiobjective linear programming (MOLP) problem can be represented as a union of the maximal efficient faces of the feasible region. In this paper, we propose a method for finding all maximal efficient faces for an MOLP. The new method is based on a condition that all efficient vertices (short for the efficient extreme points and rays) for the MOLP have been found and it relies on the adjacency, affine independence and convexity results of efficient sets. The method uses a local top‐down search strategy to determine maximal efficient faces incident to every efficient vertex for finding maximal efficient faces of an MOLP problem. To our knowledge, the proposed method is the first top‐down search method that uses the adjacency property of the efficient set to find all maximal efficient faces. We discuss this and other advantages and disadvantages of the algorithm. We also discuss some computational experience we have had with our computer code for implementing the algorithm. This computational experience involved solving several MOLP problems with the code.     

Optimal switchover times between two activities utilizing the same resource

The “gold‐mining” decision problem is concerned with the efficient utilization of a delicate mining equipment working in a number of different mines. Richard Bellman was the first to consider this type of a problem. The solution found by Bellman for the finite‐horizon, continuous‐time version of the problem with two mines is not overly realistic since he assumed that fractional parts of the same mining equipment could be used in different mines and this fraction could change instantaneously. In this paper, we provide some extensions to this model in order to produce more operational and realistic solutions. Our first model is concerned with developing an operational policy where the equipment may be switched from one mine to the other at most once during a finite horizon. In the next extension we incorporate a cost component in the objective function and assume that the horizon length is not fixed but it is the second decision variable. Structural properties of the optimal solutions are obtained using nonlinear programming. Each model and its solution is illustrated with a numerical example. The models developed here may have potential applications in other areas including production of items requiring the same machine or choosing a sequence of activities requiring the same resource. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 186–203, 2002; DOI 10.1002/nav.10008     

公安高校计算机基础课程关联性分析

对＂1＋X＂双层课程体系下的计算机基础课程之间的关联性进行初步分析,揭示了教学目标一致性、教学内容互相渗透、人才培养逐层连续性等特点。     

A partial characterization of the optimal ordering/rationing policy for a periodic review system with two demand classes and backordering

We consider a finite horizon periodic review, single product inventory system with a fixed setup cost and two stochastic demand classes that differ in their backordering costs. In each period, one must decide whether and how much to order, and how much demand of the lower class should be satisfied. We show that the optimal ordering policy can be characterized as a state dependent (s,S) policy, and the rationing structure is partially obtained based on the subconvexity of the cost function. We then propose a simple heuristic rationing policy, which is easy to implement and close to optimal for intensive numerical examples. We further study the case when the first demand class is deterministic and must be satisfied immediately. We show the optimality of the state dependent (s,S) ordering policy, and obtain additional rationing structural properties. Based on these properties, the optimal ordering and rationing policy for any state can be generated by finding the optimal policy of only a finite set of states, and for each state in this set, the optimal policy is obtained simply by choosing a policy from at most two alternatives. An efficient algorithm is then proposed. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

Analytic solution for the nucleolus of a three‐player cooperative game

The nucleolus solution for cooperative games in characteristic function form is usually computed numerically by solving a sequence of linear programing (LP) problems, or by solving a single, but very large‐scale, LP problem. This article proposes an algebraic method to compute the nucleolus solution analytically (i.e., in closed‐form) for a three‐player cooperative game in characteristic function form. We first consider cooperative games with empty core and derive a formula to compute the nucleolus solution. Next, we examine cooperative games with nonempty core and calculate the nucleolus solution analytically for five possible cases arising from the relationship among the value functions of different coalitions. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010