Response surface analysis of two‐stage stochastic linear programming with recourse

We apply the techniques of response surface methodology (RSM) to approximate the objective function of a two‐stage stochastic linear program with recourse. In particular, the objective function is estimated, in the region of optimality, by a quadratic function of the first‐stage decision variables. The resulting response surface can provide valuable modeling insight, such as directions of minimum and maximum sensitivity to changes in the first‐stage variables. Latin hypercube (LH) sampling is applied to reduce the variance of the recourse function point estimates that are used to construct the response surface. Empirical results show the value of the LH method by comparing it with strategies based on independent random numbers, common random numbers, and the Schruben‐Margolin assignment rule. In addition, variance reduction with LH sampling can be guaranteed for an important class of two‐stage problems which includes the classical capacity expansion model. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 753–776, 1999     

Hook 技术及其在软件研发中的应用

介绍了Hook技术的基本概念和方法 ,对常用的几类Hook技术重点进行了分析 ,并举例说明了在进行软件研发时 ,这些Hook技术可以应用的场合 ,最后介绍了在电子字典 ,带滚轮的鼠标驱动程序等实际软件开发项目过程中 ,如何应用Hook技术的详细方法和步骤     

Balancing a one‐way corridor capacity and safety‐oriented reliability: A stochastic optimization approach for metro train timetabling

In urban rail transit systems of large cities, the headway and following distance of successive trains have been compressed as much as possible to enhance the corridor capacity to satisfy extremely high passenger demand during peak hours. To prevent train collisions and ensure the safety of trains, a safe following distance of trains must be maintained. However, this requirement is subject to a series of complex factors, such as the uncertain train braking performance, train communication delay, and driver reaction time. In this paper, we propose a unified mathematical framework to analyze the safety‐oriented reliability of metro train timetables with different corridor capacities, that is, the train traffic density, and determine the most reliable train timetable for metro lines in an uncertain environment. By employing a space‐time network representation in the formulations, the reliability‐based train timetabling problem is formulated as a nonlinear stochastic programming model, in which we use 0‐1 variables to denote the time‐dependent velocity and position of all involved trains. Several reformulation techniques are developed to obtain an equivalent mixed integer programming model with quadratic constraints (MIQCP) that can be solved to optimality by some commercial solvers. To improve the computational efficiency of the MIQCP model, we develop a dual decomposition solution framework that decomposes the primal problem into several sets of subproblems by dualizing the coupling constraints across different samples. An exact dynamic programming combined with search space reduction strategies is also developed to solve the exact optimal solutions of these subproblems. Two sets of numerical experiments, which involve a relatively small‐scale case and a real‐world instance based on the operation data of the Beijing subway Changping Line are implemented to verify the effectiveness of the proposed approaches.     

加权模糊C均值聚类算法实现BDS三频组合观测值优选

在对BDS三频载波相位组合观测值进行误差分析的基础上,确定了优选载波相位线性组合系数的筛选标准。针对传统聚类算法在高维多频混合数据集分类中存在的不足,采用一种基于加权的模糊C均值聚类算法,通过对同一维度在不同簇上赋予不同的权重值,对传统遍历搜索法所获得的部分BDS三频载波相位组合观测值进行了优化分类选取,有效解决了传统全球导航卫星系统载波相位观测值选取方法效率低的问题,同时为多系统多频数据组合观测值系数的优化选取提供了一种新的思路。对分类结果进行分析,确定了各类组合观测量的适用范围,并结合实测数据,利用无几何层叠模糊度解算方法对优选组合进行了整周模糊度的解算,结果验证了该方法的可行性。     

基于最坏情况下的稳健波束形成自适应方向图副瓣控制方法

针对最坏情况下性能优化的稳健自适应波束形成,提出一种自适应方向图的副瓣控制方法。该方法通过在副瓣任意区域设置多个二次不等式约束,对副瓣增益进行控制,从而可将方向图副瓣电平严格控制在期望值以下。该方法的优化模型可转化为凸二阶锥规划问题,利用内点法可有效求解实现。计算机仿真结果表明存在波束指向误差情况下,该方法既能获得指定的较低副瓣电平,又不带来干扰抑制性能的损失。     

The one‐warehouse multiretailer problem with an order‐up‐to level inventory policy

We consider a two‐level system in which a warehouse manages the inventories of multiple retailers. Each retailer employs an order‐up‐to level inventory policy over T periods and faces an external demand which is dynamic and known. A retailer's inventory should be raised to its maximum limit when replenished. The problem is to jointly decide on replenishment times and quantities of warehouse and retailers so as to minimize the total costs in the system. Unlike the case in the single level lot‐sizing problem, we cannot assume that the initial inventory will be zero without loss of generality. We propose a strong mixed integer program formulation for the problem with zero and nonzero initial inventories at the warehouse. The strong formulation for the zero initial inventory case has only T binary variables and represents the convex hull of the feasible region of the problem when there is only one retailer. Computational results with a state‐of‐the art solver reveal that our formulations are very effective in solving large‐size instances to optimality. © 2010 Wiley Periodicals, Inc. Naval Research Logistics, 2010     

支持向量顺序回归机的线性规划算法

支持向量顺序回归机是标准支持向量分类机的一个推广,它是一个凸的二次规划问题。本文根据l1范数与l2范数等价关系和优化问题的对偶原理,把凸的二次规划转化成线性规划。由此提了支持向量顺序回归机的线性规划算法,进一步用数值实验验证了此算法的可行性和有效性。并与支持向量顺序回归机相比,它的运行时间缩短了,而且误差i不超过支持向量顺序回归机;     

Production planning with resources subject to congestion

A fundamental difficulty in developing effective production planning models has been accurately reflecting the nonlinear dependency between workload and lead times. We develop a mathematical programming model for production planning in multiproduct, single stage systems that captures the nonlinear dependency between workload and lead times. We then use outer linearization of this nonlinear model to obtain a linear programming formulation and extend it to multistage systems. Extensive computational experiments validate the approach and compare its results to conventional models that assume workload‐independent planning lead times. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009     

Coordination of pricing and inventory control across products

We consider the joint pricing and inventory‐control problem for a retailer who orders, stocks, and sells two products. Cross‐price effects exist between the two products, which means that the demand of each product depends on the prices of both products. We derive the optimal pricing and inventory‐control policy and show that this policy differs from the base‐stock list‐price policy, which is optimal for the one‐product problem. We find that the retailer can significantly improve profits by managing the two products jointly as opposed to independently, especially when the cross‐price demand elasticity is high. We also find that the retailer can considerably improve profits by using dynamic pricing as opposed to static pricing, especially when the demand is nonstationary. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009