空中加油问题的递推模型与调度策略

首先对空中加油问题进行了分析,提取了相关性质,在此基础上建立了问题的递推模型.根据该模型,提出了一种启发式搜索算法.该算法计算复杂度低,适用性好.对应于辅机是否可以多次起飞,该算法分为两子算法.对这两种不同情况下的具体问题,设计了相关的优化函数.所有算法都在计算机中运行,并得到了相应结果.值得指出的是,提出的启发式搜索算法十分高效.对于问题1和问题2,该算法所得解是约束条件下的最优调度策略.对于问题3,问题4,问题5,该算法所得解逼近最优调度策略.     

基于遗传算法的大学课程表问题研究

课程表问题是时间表问题之一 ,也是 NP难问题 .根据大学授课形式的特点建立了大学课程表问题的数学模型 ,给出了求解该问题的遗传算法 .根据模型和大学课程表问题的特点设计了一种全新的编码 ,提出了一种新形式的交叉方式 .实验结果表明该方法是可行和有效的 .     

具有超抛物型极限方程的非线性奇摄动反应扩散问题

讨论了一类具有超抛物型方程的反应扩散问题.首先,证明了比较定理.其次,构造了形式渐近解.然后,利用微分不等式方法,研究了问题解的存在、唯一性和渐近性态.最后得到了原问题解的渐近展开式.     

求解椭圆方程柯西问题的修正吉洪诺夫正则化方法

研究了一类变系数椭圆方程的柯西问题,这类问题出现在很多实际问题领域.由于问题的不适定性,不可能通过经典的数值方法来求解上述问题,必须引入正则化手段.采用了一种修正吉洪诺夫正则化方法来求解上述问题.在一种先验和一种后验参数选取准则下,分别获得了问题的误差估计.数值例子进一步显示方法是稳定有效的.     

一类具有跳跃层的非线性反应扩散系统的渐近行为

讨论了一类具有跳跃层的反应扩散系统.首先,求出了问题的外部解.其次,引入伸长变量,构造了跳跃层校正项.最后,利用微分不等式理论,得到了原问题解的一致有效的渐近展开式.从而研究了相应问题的解的渐近性态.     

学生面试问题的一个解法

研究的是自主招生的面试安排问题.它与一个经典问题(Steiner System问题)有很紧密的联系.首先我们形式化地提出了这个问题,并针对问题提出了3种算法.值得一提的是,我们提出的同余构造算法在时间复杂度较低的情况下,具有很高的近似比(强于FPTAS).对于文理分科的情况,我们同样在形式化地提出问题之后,给出了相应的算法.我们编写程序实现了所述的算法.     

鲁棒信用风险优化的线性锥优化模型

考虑了具有强健性的信用风险优化问题. 根据最差条件在值风险度量信用风险的方法,建立了信用风险优化问题的模型. 由于信用风险的损失分布存在不确定性,考虑了两类不确定性区间,即箱子型区间和椭球型区间. 把具有强健性的信用风险优化问题分别转化成线性规划问题和二阶锥规划问题. 最后,通过一个信用风险问题的例子来说明此模型的有效性.     

两参数非线性发展方程的奇摄动尖层解

本文研究了一类具有非线性发展方程奇摄动问题.引入伸长变量和多重尺度,构造了初始边值问题外部解和尖层、边界层和初始层校正项,得到了问题形式解.利用不动点定理,证明了问题的解的一致有效性.推广了对两参数的奇摄动问题的研究结果.     

关于未解决的一个不等式问题的注记(英文)

文[6]中,F.Qi提出了一个未解决的不等式问题.本文给出了此问题的答案和进一步的拓广,同时也得到了该问题的反向不等式.     

一类具有转点的右端不连续奇摄动边值问题

研究了一类具有转点的右端不连续二阶半线性奇摄动边值问题解的渐近性.首先,在间断处将原问题分为左右两个问题,通过修正左问题退化问题的正则化方程,提高了左问题渐近解的精度,并利用Nagumo定理证明了左问题光滑解的存在性.其次,证明了右问题具有空间对照结构的解,并通过在间断点的光滑缝接,得到了原问题的渐近解.最后,通过一个算例验证了结果的正确性.     

A necessary and sufficient condition for Pareto-optimal security strategies in multicriteria matrix games

In this paper, a scalar game is derived from a zero-sum multicriteria matrix game, and it is proved that the solution of the new game with strictly positive scalarization is a necessary and sufficient condition for a strategy to be a Pareto-optimal security strategy (POSS) for one of the players in the original game. This is done by proving that a certain set, which is the extension of the set of security level vectors in the criterion function space, is convex and polyhedral. It is also established that only a finite number of scalarizations are necessary to obtain all the POSS for a player. An example is included to illustrate the main steps in the proof.This work was done while the author was a Research Associate in the Department of Electrical Engineering at the Indian Institute of Science and was financially supported by the Council of Scientific and Industrial Research, Delhi, India.The author wishes to express his gratefulness to Professor U. R. Prasad for helpful discussions and to two anonymous referees for suggestions which led to an improved presentation.     

离散多时滞广义不确定系统的变结构控制

研究了线性离散多时滞广义不确定系统的变结构控制的综合与设计问题.首先引入了一种新的受限系统等价分解形式,把所给的系统分解成两个低维的子系统:一个是不带控制项的差分系统;一个是带有控制项的差分系统.其次,根据上面的分解形式及离散时滞广义系统鲁棒稳定性的有关结果,设计了带有差分补偿器的切换函数,使得系统在准切换流形上的运动渐近稳定.然后在不确定项有界的条件下,设计了离散变结构控制律,使得在此控制律的作用下,系统从状态空间中任意一点出发的解的轨迹,于有限步内或者到达准切换流形,此后在准切换流形上渐近滑向原点;或者进入准切换流形的一个小邻域内,并稳定于原点邻域内的一个小的抖振.最后给出了数值例子以说明该综合设计方法的可行性与简便性.     

格中两类分配等式的关系研究

针对离散数学经典教材中提出的"交运算对并运算的分配等式和并运算对交运算的分配等式是等价的"这一结论,分析了一种常见的错误证明,通过一个反例说明该结论在一般的格中不一定成立,进一步证明这两个分配等式在且仅在模格中是等价的,并提出利用定义判断一个模格是否是分配格的简便算法.作为一个应用,重新证明了该教材中的一条定理.     

Bidding under price uncertainty in multi-unit pay-as-bid procurement auctions for power systems reserve

In this paper a methodology for profit maximized bidding under price uncertainty in a day-ahead, multi-unit and pay-as-bid procurement auction for power systems reserve is proposed. Within this novel methodology a bidder is considered to follow a Bayes-strategy. Thereby, one bidder is assumed to behave strategically and the behavior of the remaining is summarized in a probability distribution of the market price and a reaction function to price dumping by the strategic bidder. With this approach two problems arise: First, as a pay-as-bid auction is considered, no uniform price and therefore no single probability distribution of the market price is readily available. Second, if historic bidding data of all participants are used to estimate such a distribution and market power is a relevant factor, the bid of the strategically behaving bidder is likely to influence the distribution. Within this paper for both of the problems solutions are presented. It is shown that by estimating a probability of acceptance the optimal bidding price with respect to a given capacity can be calculated by maximizing a stochastic non-linear objective function of expected profit. Taking the characteristics of recently established markets in Germany into account, the methodology is applied using exemplary data. It is shown that the methodology helps to manage existing price uncertainties and hence supports the trading decisions of a bidder. It is inferred that the developed methodology may also be used for bidding on other auction markets with a similar market design.     

Extended optimal inspection policies for a system in storage

A system such as missiles and spare parts of aircraft has to perform a normal operation in a severe environment at any time when it is used. However, the system is in storage for a long time from the delivery to the usage and its reliability goes down with time. Thus, a system in storage should be inspected and maintained at periodic times to hold a higher reliability than is prespecified.The following inspection model is considered: A system has three types of units, where unit 1 is maintained, unit 21 is not maintained but is replaced and unit 22 is neither maintained nor replaced. The system is overhauled if its reliability becomes lower than a prespecified probability. The number of replacements and time until overhaul are derived. Using these results, the average cost is obtained and both an optimal inspection time and an optimal replacement time to minimize it are numerically discussed.     

A Friedrichs–Maz'ya inequality for functions of bounded variation

The aim of this short note is to give an alternative proof, which applies to functions of bounded variation in arbitrary domains, of an inequality by Maz'ya that improves Friedrichs inequality. A remarkable feature of such a proof is that it is rather elementary, if the basic background in the theory of functions of bounded variation is assumed. Nevertheless, it allows to extend all the previously known versions of this fundamental inequality to a completely general version. In fact the inequality presented here is optimal in several respects. As already observed in previous proofs, the crucial step is to provide conditions under which a function of bounded variation on a bounded open set, extended to zero outside, has bounded variation on the whole space. We push such conditions to their limits. In fact, we give a sufficient and necessary condition if the open set has a boundary with σ‐finite surface measure and a sufficient condition if the open set is fully arbitrary. Via a counterexample we show that such a general sufficient condition is sharp.     

Optimal inventory threshold for a dynamic service make‐to‐stock system with strategic customers

We consider a make‐to‐stock production system with one product type, dynamic service policy, and delay‐sensitive customers. To balance the waiting cost of customers and holding cost of products, a dynamic production policy is adopted. If there is no customer waiting in the system, instead of shutting down, the system operates at a low production rate until a certain threshold of inventory is reached. If the inventory is empty and a new customer emerges, the system switches to a high production rate where the switching time is assumed to be exponentially distributed. Potential customers arrive according to the Poisson process. They are strategic in the sense that they make decisions on whether to stay for product or leave without purchase on the basis of on their utility value and the system information on whether the number of products is observable to customers or not. The strategic behavior is explored, and a Stackelberg game between production manager and customers is formulated where the former is the game leader. We find that the optimal inventory threshold minimizing the cost function can be obtained by a search algorithm. Numerical results demonstrate that the expected cost function in an observable case is not greater than that in an unobservable case. If a customer's delay sensitivity is relatively small, these two cases are entirely identical. With increasing of delay sensitivity, the optimal inventory threshold might be positive or zero, and hence, a demarcation line is depicted to determine when a make‐to‐stock policy is advantageous to the manager.     

3-连通3-正则图中的可序子集

图G的k元点集X={x1,x2,…,xk}被称为G的k-可序子集,如果X的任意排列都按序排在G的某个圈上.称G是k-可序图,如果G的每一个k元子集都是G的k-可序子集.称G为k-可序Hamilton图,如果X的任意排列都位于G的Hamilton圈上.研究了3-连通3-正则图的可序子集的存在性问题.     

An inventory model with partial backordering and unit backorder cost linearly increasing with the waiting time

As the implementation of JIT practice becomes increasingly popular, each echelon in a supply chain tends to carry fewer inventories, and thus the whole supply chain is made more vulnerable to lost sales and/or backorders. The purpose of this paper is to recast the inventory model to be more relevant to current situations, where the penalty cost for a shortage occurrence at a downstream stage in a supply chain is continually transmitted to the upstream stages. The supplier, in this case, at the upstream of the supply chain is responsible for all the downstream shortages due to the chain reaction of its backlog. The current paper proposes a model in which the backorder cost per unit time is a linearly increasing function of shortage time, and it claims that the optimal policy for the supplier is setting the optimal shortage time per inventory cycle to minimize its total relevant cost in a JIT environment.     

Optimal pricing and quantity of products with two offerings

This paper analyzes the decision of a firm offering two versions of a product, a deluxe and a regular. While both products satisfy the same market, the deluxe version is sold at a high price relative to its cost and is aimed at the high end of the demand curve. The regular version is sold at a low price relative to its cost and is targeted to customers at the low end of the demand curve. This two-offering strategy is especially popular with book publishers where a paperback book is introduced some time after the hardbound version is introduced. The time between the introduction of the two versions of the product is accompanied by a downward shift in the demand curve due to customers losing interest in the product or satisfying their demand from a secondary used market. We solve a profit maximization model for a firm using a two-offering strategy. The model is solved for linear and exponential deterioration in demand, which is assumed to be deterministic. Also, a model with linear deterioration in demand, which is assumed to be stochastic, is solved. The results indicate that substantial improvements in profit can be obtained by using the two-offering strategy. Numerical sensitivity analysis and examples are used to illustrate the results.