On excess-, current-, and total-life distributions of phase-type renewal processes

Consider a renewal process whose interrenewal-time distribution is phase type with representation (α, T). We show that the (time-dependent) excess-life distribution is phase type with representation (α′, T), where α′ is an appropriately modified initial probability vector. Using this result, we derive the (time-dependent) distributions for the current life and the total life of the phase-type renewal process. They in turn enable us to obtain the equilibrium distributions for the three random variables. These results simplify the computation of the respective distribution functions and consequently enhance the potential use of renewal theory in stochastic modeling—particularly in inventory, queueing, and reliability applications. © 1992 John Wiley & Sons, Inc.     

The parallel replacement problem with demand and capital budgeting constraints

A generalized parallel replacement problem is considered with both fixed and variable replacement costs, capital budgeting, and demand constraints. The demand constraints specify that a number of assets, which may vary over time, are required each period over a finite horizon. A deterministic, integer programming formulation is presented as replacement decisions must be integer. However, the linear programming relaxation is shown to have integer extreme points if the economies of scale binary variables are fixed. This allows for the efficient computation of large parallel replacement problems as only a limited number of 0–1 variables are required. Examples are presented to provide insight into replacement rules, such as the “no‐splitting‐rule” from previous research, under various demand scenarios. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 40–56, 2000     

低雷诺数壁面约束流动皮托管测速误差分析与校正

针对低雷诺数壁面约束流动中皮托管测速误差产生的两大主要影响因素——剪切速度与近壁效应,采用计算流体力学技术分别对其进行数值模拟,并研究各自引起的误差变化规律。数值模拟结果表明:虽然剪切速度引起的流线偏移规律与相关文献结论基本一致,但是数值结果预测的流线偏移量并不是一个渐近函数;近壁距离在5倍管径即出现较为明显的测量误差,并且发现近壁距离在1倍管径处出现误差的非单调性变化。最后通过将数值模拟结果与现有的修正方法进行对比,提出了更为合理的修正方程。     

Inventory policies for a make‐to‐order system with a perishable component and fixed ordering cost

We consider a make‐to‐order production system where two major components, one nonperishable (referred to as part 1) and one perishable (part 2), are needed to fulfill a customer order. In each period, replenishment decisions for both parts need to be made jointly before demand is realized and a fixed ordering cost is incurred for the nonperishable part. We show that a simple (s_n,S,S) policy is optimal. Under this policy, S along with the number of backorders at the beginning of a period if any and the availability of the nonperishable part (part 1) determines the optimal order quantity of the perishable part (part 2), while (s_n,S) guide when and how much of part 1 to order at each state. Numerical study demonstrates that the benefits of using the joint replenishment policy can be substantial, especially when the unit costs are high and/or the profit margin is low. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

Probability inequalities via negative dependence for random variables conditioned on order statistics

Distributions are studied which arise by considering independent and identically distributed random variables conditioned on events involving order statistics. It is shown that these distributions are negatively dependent in a very strong sense. Furthermore, bounds are found on the distribution functions. The conditioning events considered occur naturally in reliability theory as the time to system failure for k-out-of-n systems. An application to systems formed with “second-hand” components is given.     

A decomposition procedure for convex quadratic programs

This article deals with the solution of convex quadratic programs by iteratively solving a master problem and a subproblem as proposed previously by Sacher. The approach has the advantage that the subproblems are linear programs so that advantage can be taken of existing schemes for solving large linear problems. At each step in solving the master problem, a closed-form solution can be specified so that the procedure is well suited for solving large quadratic programs and can take advantage of the constraint structure.     

On estimating population characteristics from record-breaking observations II. Nonparametric results

Consider an experiment in which only record-breaking values (e.g., values smaller than all previous ones) are observed. The data available may be represented as X₁,K₁,X₂,K₂, …, where X₁,X₂, … are successive minima and K₁,K₂, … are the numbers of trials needed to obtain new records. Such data arise in life testing and stress testing and in industrial quality-control experiments. When only a single sequence of random records are available, efficient estimation of the underlying distribution F is possible only in a parametric framework (see Samaniego and Whitaker [9]). In the present article we study the problem of estimating certain population quantiles nonparametrically from such data. Furthermore, under the assumption that the process of observing random records can be replicated, we derive and study the nonparametric maximum-likelihood estimator F̂ of F. We establish the strong uniform consistency of this estimator as the number of replications grows large, and identify its asymptotic distribution theory. The performance of F̂ is compared to that of two possible competing estimators.     

Production lot sizing under setup and worker learning

Previous lot-sizing models incorporating learning effects focus exclusively on worker learning. We extend these models to include the presence of setup learning, which occurs when setup costs exhibit a learning curve effect as a function of the number of lots produced. The joint worker/setup learning problem can be solved to optimality by dynamic programming. Computational experience indicates, however, that solution times are sensitive to certain problem parameters, such as the planning horizon and/or the presence of a lower bound on worker learning. We define a two-phase EOQ-based heuristic for the problem when total transmission of worker learning occurs. Numerical results show that the heuristic consistently generates solutions well within 1% of optimality.     

French Arms Exports and Intrastate Conflicts: An Empirical Investigation

The aim of this article is to evaluate how French Major Conventional Weapons (MCW) exports impact on the conflict intensity of recipient countries. The recent increase in French arms exports seems to contradict the French political discourse on the promotion of regional stability. We run zero-inflated ordered probit model in order to analyze the role of the arms trade on the intensity of civil conflicts in 144 countries from 1992 to 2014, using SIPRI and UCDP/PRIO data. Our results suggest that French MCW exports tended not to exacerbate intrastate conflicts during this period. This finding is robust to changes in the empirical framework. We propose two lines of explanations: France seems to be prone to choosing partners that respect human rights and selling more ‘defense-oriented’ MCW than the rest of the world.