差分—等级依赖效用模型研究

等级依赖效用模型在决策权重设置上存在理论缺陷;差分-等级依赖效用模型在有限理性假设下,考虑结果差分变化对决策权重的影响,提出基于差分的决策权重与概率权重的组合权重控制机制,可克服等级依赖效用模型的缺陷;针对差分-等级依赖效用模型的检验表明模型可很好解释拆分效应;差分-等级依赖效用模型保持了等级依赖效用模型的理论框架,可对人们的风险决策行为做出更好的解释和预测.     

情绪影响下选时博弈模型及其最优策略

依据Quiggin的秩依期望效用理论研究经典选时博弈问题。通过引入可以刻画局中人在博弈中情绪状态的非线性决策权重函数,将RDEU有限策略博弈扩展到连续博弈,构建了RDEU选时博弈模型。基于Riccati微分方程的解法,求出博弈模型中局中人的最优策略。最后,通过数值仿真,分析了不同情绪状态对局中人博弈决策行为的影响。研究发现,情绪对混合策略意义下的局中人最优策略有着显著的影响,在乐观情绪状态下,局中人对混合策略极易产生自信和较高的信任倾向,表现出"风险爱好者"行为;在悲观情绪状态下,局中人往往对混合策略缺乏自信和信任,表现出“风险厌恶者”行为。     

基于博弈论和相对熵的基坑支护方案优选

基坑支护方案优选是一项多属性决策,提出了一种基于博弈论组合赋权和相对熵的逼近理想解(TOPSIS)决策模型.首先采用信息熵确定客观权重,运用层次分析法确定主观权重,然后引入博弈论集结模型将主客观权重科学化组合,得到综合权重,最后采用一种基于相对熵的逼近理想解决策方法进行基坑支护方案优选,并结合工程实例进行验证.结果证明:基于相对熵的TOPSIS决策模型在案例中的评价结果与工程实际相吻合.     

基于连续直觉梯形模糊相似测度的多属性群决策方法

针对评价值以直觉梯形模糊数形式给出的多属性群决策问题,提出一种基于α-截集,β-截集及连续区间有序加权平均(COWA)算子的连续直觉梯形模糊平均算子,并定义一种新的连续直觉梯形模糊相似测度,基于该相似测度构建群决策专家权重和属性权重确定模型,进而提出了一种基于连续直觉梯形模糊相似测度的多属性群决策方法。最后分析了决策者态度参数λ对群决策专家权重、属性权重以及方案排序值的影响,并通过投资方案选择问题的分析对新方法的有效性和合理性进行了说明。     

基于SMAA和公共权重的决策单元效率评价与排序

在数据包络分析(DEA)中,公共权重模型是决策单元效率评价与排序的常用方法之一。与传统DEA模型相比,公共权重模型用一组公共的投入产出权重评价所有决策单元,评价结果往往更具有区分度且更为客观。本文考虑决策单元对排序位置的满意程度,提出了基于最大化最小满意度和最大化平均满意度两类新的公共权重模型。首先,基于随机多准则可接受度分析(SMAA)方法,计算出每个决策单元处于各个排名位置的可接受度;然后,通过逆权重空间分析,分别求得使最小满意度和平均满意度最大化的一组公共权重;最后,利用所求的公共权重,计算各决策单元的效率值及相应的排序。算例分析验证了本文提出的基于SMAA的公共权重模型用于决策单元效率评价与排序的可行性。     

电动汽车充换电站选址规划的可拓评价研究

为对未来电动汽车的充换电站的选址规划决策提供科学依据和理论支持,建立电动汽车充换电站选址决策的评价指标体系.运用可拓学理论和方法,构建了基于可拓方法的电动汽车充换电站选址合理性的可拓评价模型,基于熵权法确定评价指标权重.最后通过一个仿真算例验证所提模型的正确性和有效性.     

犹豫模糊动态灰靶决策方法

针对属性权重及阶段权重完全未知的犹豫模糊动态多属性决策问题,提出一种考虑决策信息无量纲化的动态决策方法.首先,基于变异系数提出一种新的决策群体分歧度.并基于这种分歧度建立属性权重确定模型;其次,根据数据的平均年龄及各阶段决策信息间相关关系,提出一种阶段权重确定方法.然后,将灰靶决策方法推广到犹豫模糊环境下,并基于模糊聚类算法思想对方案进行排序.最后,给出算例说明方法可行性.     

基于熵的多目标多维模糊决策模型

顾及多目标多维决策中存在的模糊性和随机性,基于Jaynes的信息熵最大原理,提出一种模糊环境下带有主观监督因子和信息熵的目标函数,导出了新的计算模糊决策识别矩阵与目标权重的模糊交叉计算公式.该模型将基于目标的客观决策与主观决策有机结合起来,为求解最优模糊决策识别矩阵和确定目标最优权重提供了一种有效途径,并把信息熵作为评价决策优劣的指标,进一步发展了多目标多维模糊决策理论模型.将本文提出的模糊决策方法应用于16家电炉炼钢企业的模糊综合评价,取得了较为满意的效果.     

考虑群体一致性的区间犹豫模糊TOPSIS决策方法

在区间犹豫模糊多属性决策问题中,针对区间犹豫模糊元中人为添加元素从而影响最终决策结果客观性的问题,文章提出一种基于群体一致性的区间犹豫模糊多属性决策方法.首先,根据区间犹豫模糊元中的元素个数以及元素间的差异定义区间犹豫度,并基于犹豫度定义了区间群体一致性;然后,基于群体一致性构建属性权重确定模型,并确定各属性的权重.最后,计算各备选方案到理想点的距离,运用TOPSIS方法对备选方案进行排序,并通过一个算例证明文章方法的可行性和有效性.     

基于VIKOR和关联系数的犹豫三角模糊语言多属性决策方法

针对属性评价值为犹豫三角模糊语言集的多属性决策问题,提出一种基于VIKOR方法的犹豫三角模糊语言多属性决策方法.首先定义了犹豫三角模糊语言集的相关概念.然后运用VIKOR和关联系数方法,在可接受优势和决策过程稳定的条件下对方案进行择优,在理论分析的基础上,提出了这种新方法的计算步骤.并构建了确定最优属性权重的非线性规划模型,研究了当专家权重和属性权重未知情况下的犹豫三角模糊语言多属性决策方法.最后通过实例说明了该方法的有效性和可行性.     

The effect of information on the quality of decisions

We study the effect of additional information on the quality of decisions. We define the extreme case of complete information about probabilities as our reference scenario. There, decision makers (DMs) can use expected utility theory to evaluate the best alternative. Starting from the worst case—where DMs have no information at all about probabilities—we find a method of constantly increasing the information by systematically limiting the ranges of the probabilities. In our simulation-based study, we measure the effects of the constant increase in information by using different forms of relative volumes. We define these as the relative volumes of the gradually narrowing areas which lead to the same (or a similar) decision as with the probability in the reference scenario. Thus, the relative volumes account for the quality of information. Combining the quantity and quality of information, we find decreasing returns to scale on information, or in other words, the costs of gathering additional information increase with the level of information. Moreover, we show that more available alternatives influence the decision process negatively. Finally, we analyze the quality of decisions in processes where more states of nature are considered. We find that this degree of complexity in the decision process also has a negative influence on the quality of decisions.     

A compromise weight for multi-criteria group decision making with individual preference

In a multi-criteria group decision making process, it is often hard to obtain a solution due to the possible conflict preferences from different participants and the undeterministic weights assigned to each criterion. This problem can be defined as to identify a set of weights for the given criteria to achieve a compromise of the conflict on different preferences. When such a compromise weight does not exist, we need to adjust (to reverse or to withdraw) some or all of the preferences from different participants. This paper describes a minimax principle based procedure of preference adjustments with a finite number of steps to find the compromise weight. At each iteration, we either find the weight or identify some ‘wrong’ preferences. We also define a consistency index for each participant to measure the distance between the individuals' preference and the final group decision. Corresponding theoretical work is referred to in support of the procedure, and numerical examples are provided for illustration. This study is further extended to the case of multiple assessments.     

Reliability analysis of non‐repairable systems modeled by dynamic fault trees with priority AND gates

Many real‐life systems are typically involved in sequence‐dependent failure behaviors. Such systems can be modeled by dynamic fault trees (DFTs) with priority AND gates, in which the occurrence of the top events depends on not only combinations of basic events but also their failure sequences. To the author's knowledge, the existing methods for reliability assessment of DFTs with priority AND gates are mainly Markov‐state‐space‐based, inclusion–exclusion‐based, Monte Carlo simulation‐based, or sequential binary decision diagram‐based approaches. Unfortunately, all these methods have their shortcomings. They either suffer the problem of state space explosion or are restricted to exponential components time‐to‐failure distributions or need a long computation time to obtain a solution with a high accuracy. In this article, a novel method based on dynamic binary decision tree (DBDT) is first proposed. To build the DBDT model of a given DFT, we present an adapted format of the traditional Shannon's decomposition theorem. Considering that the chosen variable index has a great effect on the final scale of disjoint calculable cut sequences generated from a built DBDT, which to some extent determines the computational efficiency of the proposed method, some heuristic branching rules are presented. To validate our proposed method, a case study is analyzed. The results indicate that the proposed method is reasonable and efficient. Copyright © 2015 John Wiley & Sons, Ltd.     

Training in Managerial Economics

Managerial economics, sometimes called decision theory analysis (DTA), is a way of quantitatively analysing and structuring the making of a business decision. The basic mathematical concepts of DTA are presented through a simplified example’ due to Howard Raiffa. Special note is made of two characteristic features: arabic The assignment of numerical ('utility') values to the various possible final outcomes of a decision problem.

arabic The assignment of a priori ('Bayesian') probabilities to occurrences other than the decision maker's own choices.

Possible advantages and disadvantages of the use of DTA in a business enterprise are then discussed, and several recent examples of such use are given.

     

Industrial petrochemical production planning and expansion: A multi-objective linear programming approach

This paper considers a strategic model planning for the petrochemical industry. It concerns with the expansion in a firm producing multiple products in several regions of a country. The expansion of the existing facilities and the new ones are considered. It also exists a large amount of interdependencies among the firm’s products, because the output of one particular plant can be used as an input to the production of another plant in the same or different regions and to satisfy the final demand. The decision makers involved in the planning process should identify several objectives. Then, multiple objective programming is used for making trade-offs among the economic and operational factors considered. To define the interval criteria weights into the model we utilized the Analytic Hierarchy Process to bring them closer to the decision makers preferences. This work was sponsored by the Institut National Polytechnique de Toulouse, France, when the author was Associate Professor at the Département Génie des Systèmes Industriels.     

Continuous time shock markov decision processes with discounted criterion

This paper presents a new concept of Markov decision processes: continuous time shock Markov decision processes, which model Markovian controlled systems sequentially shocked by its environment. Between two adjacent shocks, the system can be modeled by continuous time Markov decision processes. But according to each shock, the system's parameters are changed and an instantaneous state transition occurs. After presenting the model, we prove that the optimality equation, which consists of countable equations, has a unique solution in some function space Ω     

机场蓄车池出租车司机的选择决策研究 ——以首都机场为例

随着中国全面小康的逐步实现,乘客下飞机后乘坐出租车回市区已经成为大多数人的选择.着眼出租车送客至机场后的情景,以出租车司机的盈利最大化为目标,讨论出租车司机的两种决策选择——决策A是留在机场蓄车池等待回城区的乘客,决策B是空载回城找生意.控制时间相同的条件下,用机场接客的订单金额来估计决策A的收益,用司机单位时间内平均收益乘以经营时长来衡量决策B的收益.以北京市首都国际机场为例,从数学模型的角度为出租车司机提供决策条件,有效实现司机利润最大化.     

A Note on the Suboptimality of Path-Dependent Pay-Offs in Lévy Markets

Abstract

Cox and Leland used techniques from the field of stochastic control theory to show that, in the particular case of a Brownian motion for the asset log-returns, risk-averse decision makers with a fixed investment horizon prefer path-independent pay-offs over path-dependent pay-offs. In this note we provide a novel and simple proof for the Cox and Leland result and we will extend it to general Lévy markets where pricing is based on the Esscher transform (exponential tilting). It is also shown that, in these markets, optimal path-independent pay-offs are increasing with the underlying final asset value. We provide examples that allow explicit verification of our theoretical findings and also show that the inefficiency cost of path-dependent pay-offs can be significant. Our results indicate that path-dependent investment pay-offs, the use of which is widespread in financial markets, do not offer good value from the investor's point of view.