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An Efficient Solution Method for 0-1 Random Fuzzy Programming Problems Considering the Relaxation Problems 考虑松弛问题的0-1随机模糊规划问题的有效求解方法
Pub Date : 2008-06-17 DOI: 10.2174/1874243200802010038
T. Hasuike, H. Ishii, H. Katagiri
This paper considers a general 0-1 random fuzzy programming problem including some previous 0-1 stochastic and fuzzy programming problems. The proposal problem is not a well-defined problem due to including random fuzzy variables. Therefore, by introducing chance constraint and fuzzy goal for objective function and considering the maximi- zation for the degrees of possibility that the objective function value satisfies the fuzzy goal, main problem is transformed into a deterministic equivalent problem. Furthermore, by using the assumption that each random variable is distributed ac- cording to a normal distribution, the problem is equivalently transformed into a basic 0-1 programming problem, and the efficient strict solution method to find an optimal solution is constructed.
本文考虑了一个一般的0-1随机模糊规划问题,它包含了一些以前的0-1随机和模糊规划问题。提案问题由于包含随机模糊变量而不是一个定义良好的问题。因此,通过对目标函数引入机会约束和模糊目标,并考虑目标函数值满足模糊目标的可能性最大,将主要问题转化为确定性等价问题。在此基础上,利用随机变量按正态分布的假设,将该问题等效转化为一个基本的0-1规划问题,构造了求最优解的高效严格解方法。
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引用次数: 4
Variational Inequalities for Modeling Auction Markets with Price Mappings 用价格映射建模拍卖市场的变分不等式
Pub Date : 2008-06-06 DOI: 10.2174/1874243200802010029
I. Konnov
We propose several new models for separate and spatially distributed auction based markets where partici- pants' reactions are described by general price mappings and show that they admit equivalent variational inequality for- mulations. This approach is utilized for the derivation of existence and uniqueness results and for construction of efficient solution methods.
我们提出了几个独立的和空间分布的基于拍卖市场的新模型,其中参与者的反应由一般价格映射描述,并表明它们承认等效变分不等式。利用该方法推导了存在唯一性结果,构造了有效的求解方法。
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引用次数: 4
On the Efficiency of Feasible Solutions of a Multicriteria Assignment Problem 一类多准则分配问题可行解的有效性
Pub Date : 2008-04-25 DOI: 10.2174/1874243200802010025
A. Bufardi
The particular structure of the assignment problem made of it a very popular subject of study and an important research tool in operations research and management science. In addition to the importance that the assignment problem represents in its own, it can appear as a relaxation of more complex combinatorial optimization problems. That is why the assignment problem has received great attention from the operations research community. The assignment problem may appear as an optimization problem with multiple objectives. In this paper, we address the problem of efficiency of feasible solutions of a multicriteria assignment problem. It is done in two steps. In the first step, we determine whether or not a given feasible solution of a multicriteria assignment problem is efficient. In a second step, if the feasible solution is not ef- ficient, we provide an efficient solution that dominates it. The proposed method consists of transforming the original prob- lem into an assignment problem with side constraints for which solution techniques already exist.
作业问题的特殊结构使其成为一门非常受欢迎的研究课题,也是运筹学和管理学中重要的研究工具。除了分配问题本身所代表的重要性之外,它还可以作为更复杂的组合优化问题的松弛。这就是为什么赋值问题受到运筹学界的极大关注。分配问题可以表现为具有多个目标的优化问题。本文研究了一类多准则分配问题的可行解的效率问题。它分两步完成。在第一步中,我们确定给定的多准则分配问题的可行解是否有效。在第二步,如果可行的解决方案不是有效的,我们提供一个有效的解决方案,主导它。该方法将原问题转化为具有边约束的赋值问题,且赋值问题已存在求解方法。
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引用次数: 9
Minimizing Makespan on Parallel Machines with Machine Eligibility Restrictions 具有机器资格限制的并行机器最大完工时间最小化
Pub Date : 2008-03-12 DOI: 10.2174/1874243200802010018
Chien-Hung Lin, C. Liao
In this paper, we consider a parallel machine problem where machines and jobs can be classified into two levels: high and low levels. A high-level machine can process all jobs while a low-level machine can process only low-level jobs. The objective of the problem is to minimize the makespan. This problem is a special case of the parallel machine problem with machine eligibility restrictions. The problem is NP-hard and a heuristic algorithm has recently been proposed. However, there are no algorithms in the literature that can solve the problem to optimality. In this paper, we develop such an exact algorithm by utilizing some useful properties inherent in the problem. Computational experiments show that the developed algorithm can find the optimal solution for various-sized problems in a short time.
本文考虑了一个机器和作业可分为高、低两层的并行机问题。高级机器可以处理所有作业,而低级机器只能处理低级作业。这个问题的目标是最小化完工时间。该问题是具有机器合格性限制的并行机问题的一个特例。这个问题是np困难的,最近提出了一种启发式算法。然而,目前文献中还没有一种算法可以将问题求解到最优。在本文中,我们利用问题固有的一些有用的性质,开发了这样一个精确的算法。计算实验表明,该算法可以在短时间内找到各种规模问题的最优解。
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引用次数: 4
Long Memory and Structural Breaks in the Spanish Stock Market Index 西班牙股市指数的长记忆和结构性断裂
Pub Date : 2008-02-28 DOI: 10.2174/1874243200802010013
G. Caporale, L. Gil‐Alana
It is well known that the Spanish stock market index (IBEX 35) exhibits unit roots. However, the implications of possible structural breaks in this series have not been deeply investigated. In this paper, we show that, when including a break at the beginning of 1998, the order of integration of the series becomes slightly smaller, strengthening the evidence of mean-reverting behaviour. When the break date is supposed to be unknown, it is found to be January 1998, with both subsamples still being characterised by a high degree of persistence.
众所周知,西班牙股票市场指数(ibex35)具有单位根。然而,在这一系列中可能的结构断裂的含义尚未深入研究。在本文中,我们表明,当包含1998年初的中断时,该序列的积分顺序变得稍微小一些,加强了均值回归行为的证据。当中断日期被认为是未知时,它被发现是1998年1月,两个子样本仍然具有高度持久性的特征。
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引用次数: 4
Comparing Fundamentals of Additive and Multiplicative Aggregation in Ratio Scale Multi-Criteria Decision Making 比率尺度多准则决策中加性聚合与乘性聚合的基础比较
Pub Date : 2008-02-15 DOI: 10.2174/1874243200802010001
E. U. Choo, W. Wedley
Additive and multiplicative aggregations of ratio scale preferences are frequently used in multi-criteria decision making models. In this paper, we compare the advantages and limitations of these two aggregation rules by exploring only their fundamental properties after ratio scaled local priorities and criteria weights have been successfully generated from the decision maker. The comparisons of these properties are therefore independent of ancillary procedures such as interac- tive elicitations from decision makers, pairwise comparisons and calculations of local priorities and criteria weights. We compare six fundamental properties of the two aggregation rules. The criteria weights used in the multiplicative aggrega- tion have complicated meanings which are not well understood and often mixed up in the ambiguous notion of "criteria importance". As the scaling factors of the local preference values do not appear explicitly in the computations of the rela- tive ratios of the overall preferences in the multiplicative aggregation model, the relative ratios remain unchanged when the scaling factors are changed or an alternative is added or deleted. Furthermore, the relative ratios in the multiplicative aggregation do not depend on similar local preference values which cancel each other out mathematically. It is quite evi- dent that the additive aggregation model is superior and easier for decision makers to use and understand. We recommend the additive aggregation rule over the multiplicative aggregation rule. Fundamental basic elements of the MCDM framework are first depicted without any specific interpretations im- posed on these elements. It is assumed that no relevant crite- rion is missed and each criterion is autonomous. In section 3, the measures of criteria weight, local and overall preferences are assumed to be in ratio scale. Some necessary conditions and the role of normalization are discussed. We then give a brief literature review, with particular attention to the differ- ent ancillary procedures and contradicting opinions in model interpretations. Additive and multiplicative aggregation rules are formally introduced in Section 5. In Section 6, we elabo- rate and compare the fundamental properties of these aggre- gation rules. Finally, we summarize and give some conclu- sions. 2. BASIC ELEMENTS OF MCDM MODEL The basic elements of a typical MCDM model include a set A={A1,A2,…,An} of n alternatives A1,A2,…,An and a set C={C1,C2,…,Cm} of m criteria C1,C2,…,Cm. The effect of the criteria C1,C2,…,Cm in C is represented by positive num- bers w1,w2,…,wm respectively. The vector w=(w1,w2,…,wm) is called the criteria weight vector of the criteria C1,C2,…,Cm in C. The criteria weight vector w is derived from question- ing the DM. The alternatives A1,A2,…,An can be evaluated under each individual criterion Cp, p=1,2,…,m. For each criterion Cp (p=1,2,…,m), the local preference of the alterna- tives A1,A2,…,An in A with respect to Cp is represented b
比率尺度偏好的加性和乘性聚合在多准则决策模型中经常被使用。在本文中,我们通过对两种聚合规则的基本性质的研究,比较了这两种聚合规则的优点和局限性,并成功地从决策者那里生成了比例缩放的局部优先级和标准权重。因此,这些属性的比较是独立于辅助程序的,如决策者的交互引出,两两比较以及局部优先级和标准权重的计算。我们比较了这两种聚合规则的六个基本性质。在乘法聚合中使用的标准权重具有复杂的含义,这些含义不被很好地理解,并且经常混淆在“标准重要性”的模糊概念中。在乘法聚合模型中,由于局部偏好值的比例因子没有明确地出现在总体偏好相对比率的计算中,因此,当比例因子发生变化或增加或删除一个备选方案时,相对比率保持不变。此外,乘法聚合中的相对比率不依赖于相似的局部偏好值,这些偏好值在数学上相互抵消。结果表明,加性聚合模型具有较好的优越性,便于决策者使用和理解。我们建议使用加法聚合规则,而不是乘法聚合规则。首先描述了MCDM框架的基本元素,而没有对这些元素进行任何具体的解释。假设没有遗漏任何相关的准则,并且每个准则都是自治的。在第3节中,假定标准权重、局部偏好和总体偏好的度量为比例尺度。讨论了规范化的必要条件和作用。然后,我们给出了一个简短的文献综述,特别注意不同的辅助程序和矛盾的意见,在模型解释。第5节正式介绍了加法和乘法聚合规则。在第6节中,我们阐述并比较了这些聚合规则的基本性质。最后,对全文进行了总结,并给出了一些结论。2. 典型MCDM模型的基本元素包括n个备选项A1,A2,…,An的集合a ={A1,A2,…,An}和m个准则C1,C2,…,Cm的集合C={C1,C2,…,Cm}。标准C1,C2,…,Cm在C中的作用分别用正数w1,w2,…,wm表示。向量w=(w1,w2,…,wm)被称为c中标准C1,C2,…,Cm的标准权重向量。标准权重向量w来源于对DM的质疑。选择A1,A2,…,An可以在每个单独的标准Cp, p=1,2,…,m下进行评估。对于每个准则Cp (p=1,2,…,m), A中的备选方案A1,A2,…,An相对于Cp的局部偏好分别用正数x1p,x2p,…,xnp表示。向量xp=(x1p,x2p,…,xnp)称为A中A1,A2,…,An相对于Cp的局部偏好向量。局部偏好向量x1,x2,…,xm是通过对DM的质疑得到的。
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引用次数: 34
An Approximation Algorithm for the Capacitated Arc Routing Problem 电容电弧布线问题的一种近似算法
Pub Date : 2008-02-14 DOI: 10.2174/1874243200802010008
Sanne Wøhlk
In this paper we consider approximation of the Capacitated Arc Routing Problem, which is the problem of serv- icing a set of edges in a graph using a fleet of capacity constrained vehicles. We present a 7  3  2 W approximation algorithm for the problem and prove that this algorithm outperforms the only existing approximation algorithm for the problem. Fur- thermore, we give computational results showing that the new algorithm performs very well in practice. When solving an optimization problem to suboptimality, two goals are followed. The first goal is to obtain a solution that is as close to the optimal as possible, which leads to the construction of problem specific heuristics and meta heuris- tics, where the latter often outperforms the former. The sec- ond goal is to obtain a solution, which is guaranteed to be within a certain factor of the optimal. This goal leads to the construction of approximation algorithms. In this paper we will present an algorithm for the Capaci- tated Arc Routing Problem (CARP) with the triangle ine- quality preserved by the cost matrix, which is an approxima- tion algorithm with at most the same approximation factor as the only existing approximation algorithm for the problem, and which performs very well in practice, in that it is highly competitive to the existing problem-specific heuristics for the problem on the set of 143 benchmark instances. We refer to the algorithm as A-ALG.
本文考虑了有容弧线路问题的逼近问题,该问题是利用容量受限的车辆车队对图中的一组边进行服务的问题。我们提出了一个732w的近似算法,并证明该算法优于现有的唯一近似算法。计算结果表明,该算法在实际应用中具有良好的性能。当将优化问题求解到次优性时,要遵循两个目标。第一个目标是获得尽可能接近最优的解决方案,这导致构建特定于问题的启发式和元启发式,后者通常优于前者。第二个目标是得到一个解,该解保证在最优解的一定因子范围内。这个目标导致了近似算法的构建。本文提出了一种用代价矩阵保存三角形线质量的电容弧路由问题(CARP)的近似算法,它是一种近似因子最多与该问题现有的唯一近似算法相同的近似算法,在143个基准实例集上,它与现有的针对该问题的问题特定启发式算法具有很强的竞争力,在实践中表现得非常好。我们把这个算法称为A-ALG。
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引用次数: 26
Optimal Population Size and Urban-Rural Composition of a Distant, Large, Arid Island: A Model and Some Numerical Simulations 偏远干旱大岛屿最优人口规模与城乡构成:一个模型与数值模拟
Pub Date : 2007-08-28 DOI: 10.2174/1874243200701010009
Amnon Levy, R. Zamani
Low population density and large distance from civilization centers generate high costs of isolation. Immigra- tion reduces these costs for veteran residents but reduces social and cultural cohesion, increases the demand for scarce re- sources and affects the rate of urban unemployment. An expected net benefit maximization model for determining the op- timal population size and the equilibrium urban-rural composition of an island similar to Australia is constructed. The model is simulated for various agricultural water prices. The simulation results illustrate the central role of the effect of immigration on urban unemployment rate in the determination of the island's optimal population size. INTRODUCTION This paper deals with the optimal population size and rural-urban composition of a distant, large, arid island. The island's current population is small and has a low fertility rate. Distance and dispersion hinder communication and provision of commodities and services and the island's in- habitants bear mental and material costs of isolation. Immi- gration is the main way for increasing the island's population density, strengthening the island's international integration and, thereby, moderating the costs of isolation borne by the island's inhabitants. However, immigration reduces the is- land's levels of cultural and social cohesion. It also affects the island's rural and urban land and water use and natural
人口密度低,远离文明中心,与世隔绝的代价很高。移民减少了老居民的这些成本,但减少了社会和文化凝聚力,增加了对稀缺资源的需求,并影响了城市失业率。本文构建了一个期望净效益最大化模型,用于确定一个类似澳大利亚的岛屿的最优人口规模和均衡城乡构成。该模型对不同的农业水价进行了模拟。模拟结果说明了移民对城市失业率的影响在确定岛屿最优人口规模中的核心作用。本文研究了一个遥远的干旱大岛屿的最优人口规模和城乡构成。该岛目前的人口很少,生育率也很低。距离和分散妨碍了交流和提供商品和服务,岛上的居民承受着与世隔绝的精神和物质代价。移民是增加该岛人口密度、加强该岛融入国际社会、从而减轻该岛居民因孤立而付出代价的主要途径。然而,移民降低了本土的文化和社会凝聚力。它还影响到岛上农村和城市的土地和水的使用和自然
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引用次数: 1
The Impacts of Asian Currency Crisis on International Portfolio Diversification 亚洲货币危机对国际投资组合多元化的影响
Pub Date : 2007-08-28 DOI: 10.2174/1874243200701010001
Takkee Hui, R. Kurniawan, Hsuan-Yi Cheng
This paper is to investigate the benefits of including bonds and stocks markets in the optimal portfolio using the classical model. Three types of investments: stocks alone, bonds alone, and a mix of stocks and bonds are considered. Ef- ficient frontier is constructed for each type of investment. This study is also to include international diversification choices before and after the recent Asian currency crisis. It has been shown that the risk of investment can be reduced by diversifi- cation across countries. For both before and after Asian currency crisis, our results show that investing in the bond mar- kets alone will provide substantial return and optimal risk reduction for investors who are risk averse. However, the com- bination of stocks and bonds will provide a better mix giving a highest return per unit risk. After the Asian currency crisis, the bond markets selected are shifted from North America markets to Oceania markets and France market. This analysis provides a comprehensive study for Singaporean investors but the research can be repeated from a different perspective such as Japan and US point of view.
本文利用经典模型研究了将债券和股票市场纳入最优投资组合的收益。考虑了三种类型的投资:单独的股票,单独的债券,以及股票和债券的组合。对每一种投资类型都构造了有效边界。本研究亦包括亚洲货币危机前后的国际多元化选择。事实证明,投资风险可以通过跨国多元化来降低。在亚洲货币危机前后,我们的研究结果表明,对于风险厌恶的投资者而言,单独投资债券市场将提供可观的回报和最佳的风险降低。然而,股票和债券的组合将提供一个更好的组合,提供最高的单位风险回报。亚洲货币危机后,债券市场的选择从北美市场转向大洋洲市场和法国市场。这一分析为新加坡投资者提供了一个全面的研究,但研究可以从不同的角度,如日本和美国的角度进行重复。
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引用次数: 0
The Sensitivity Analysis of the International Investment Decision Model 国际投资决策模型的敏感性分析
Pub Date : 2006-12-01 DOI: 10.2174/1874243200802010060
Tsui-Yii Shih, C. Trappey
Johanson and Vahlne's research provides a starting point for building a model that suits general international investments and decision making processes. This research derives an integer programming investment decision model that also considers investment costs and the risk attitudes of firms. The sensitivity analysis of the revised model demonstrates how risk attitudes and investment costs influence the optimal investment decision. Compared to the cost factors, the influ- ence of attitudes toward risk are the key to the overall decision making process.
Johanson和Vahlne的研究为建立一个适合一般国际投资和决策过程的模型提供了一个起点。本文建立了考虑投资成本和企业风险态度的整数规划投资决策模型。修正模型的敏感性分析显示了风险态度和投资成本对最优投资决策的影响。与成本因素相比,风险态度的影响是整个决策过程的关键。
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引用次数: 1
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The Open Operational Research Journal
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