多重因素约束下的网格搜索对策问题研究

首次基于搜索成本及搜索资源等限制因素,构造局中人面向多重约束条件的可行策略集合,建立相应的搜索空间;在给定搜索点权值的基础上,考虑搜索成本与搜索成功概率等因素,构造相应的支付函数,建立多重因素约束下的网格搜索对策模型.为简化模型求解,将对策论问题转化为约束最优化问题,求解约束问题获得最优值,转化为模型的对策值,并给出双方最优混合策略.最后,给出军事想定实例,说明上述模型的实用性及方法的有效性.     

基于遗传算法的多约束网格检查对策问题研究

综合考虑物品数量以及列容量约束,将隐藏成本与检查概率引入支付函数,建立一种新的多约束的网格检查对策模型.根据矩阵对策性质及Hlder不等式,将对策论问题转化为非线性整数规划问题.提出一个基于遗传算法的模型求解方法,将归一化处理得到的变量进行二进制编码,通过数据变换将问题转化为无约束问题,采用轮盘赌选择、多点交叉及单点变异操作求解模型.仿真结果表明了模型及所提算法的有效性.     

具有风险因素的多联盟部分合作对策

多联盟部分合作对策是指对策中的局中人通过引入合作函数,彼此合作或采取单独行动来对非合作对策规则进行更改,形成具有多联盟结构的扩展型部分合作对策.本文克服多联盟部分合作对策中不同局中人联盟单调递增约束,局中人加入联盟后可以退出加入到其他联盟中;同时考虑风险因素的影响,采用专家打分法和网络分析法(ANP)重新确定联盟局中人各自所占的权重,对多联盟部分合作对策中构造的合作子对策的联盟收益分配方式进行改进,从而建立具有风险因素的多联盟部分合作对策模型,并利用逆推归纳法得到对策解的算法.最后通过实例说明所建模型及结论的合理性,体现实际经济管理过程中结盟的变化和风险的影响.     

求解一个整数方程的新解法

ni=1aixi =p是一个由实验数据问题抽象而出的整数方程求非负整数解的数学模型 .为了使该问题实现计算机求解的可能 ,本文首先将原问题转化为讨论一类整数规划最优解问题 .从对应松弛规划问题的目标函数值为 0的最优解出发 ,根据舍入凑整法原则 ,再次将问题转化为另一简化后的整数方程 ,这样大大缩小了解的范围 ,及进一步迅速降低了方程右端的 p值 ,使其在计算机上求解的运算量大大降低而能得以实现     

多周期多产品采购量分配优化模型

为了解决随机需求与价格折扣并存条件下的多周期多产品采购量分配问题,建立了相应的多目标混合整数随机规划模型.该模型的特点是:①模型的约束条件中兼具确定性和随机性;②通过累计需求和累计采购量表示多周期的库存持有成本;③通过约束条件方程式准确地表现随机需求和价格折扣两大假设条件.针对该模型的特殊结构,提出了一种适用的求解策略:首先,通过把机会约束转化为确定性等价类,从而将多目标混合整数随机规划模型转化为确定型多目标混合整数规划模型;然后,采用目标规划法求得问题的满意解.此外,通过应用算例说明了模型的有效性和可行性.     

基于Selectope解集和局中人最大满意度的合作对策解的研究

针对决策者在获取Selectope解集后难以聚焦到最终分配方案上的问题,论文对合作对策的解集进行了研究。首先借助Harsanyi红利在局中人中进行分配的思想,得到Selectope解集作为研究问题的可行域。之后,在局中人完全理性的条件下,充分考虑局中人参与合作的初衷,运用超出值的概念,构建了描述局中人最大满意度的目标函数,进而得到基于Selectope解集与局中人最大满意度的非线性规划模型,用于合作对策收益分配问题的求解。最后,通过算例验证了该求解思路的可行性与求解结果的合理性。研究结果表明,论文提出的求解思路能够有效缩减Selectope解集的体量,为决策者提供一个精炼的抉择空间,在一定程度上拓展了Selectope解集的应用,同时,构建的局中人最大满意度的非线性函数对局中人满意度研究也有一定的参考价值。     

混合整数半无限规划问题

本文主要讨论混合整数半无限规划(mixed integer semi-infinite programming, MISIP)问题的求解方法.首先分离内层约束中的连续变量和整数变量并将原问题转化为混合整数互补约束规划(mixed integer mathematical programming with complementarity constraints, MIMPCC)问题.其次在假设内层问题满足Slater约束规范的条件下得到了转化前后问题的等价性.继而分别将MIMPCC问题转化为可用常规优化软件求解的混合整数规划问题和非线性规划问题.由于在转化过程中会生成大量的变量和约束,为求解内层问题中变量较多的MISIP问题,本文提出一种行约束生成法,并证明该算法可在最多O(|Z|)次迭代之后得到最优解.最后通过一些数值实例验证算法的有效性.     

一般化两人零和模糊对策的模糊规划法

本文在充分考虑局中人的策略集是模糊子集的基础上,给出更一般化的具有模糊支付与模糊赢得的两人零和模糊对策的模糊规划模型。利用模糊数的序方法,得到了此对策求解问题可以转化为带有模糊参数的两个经典规划的求解问题。文末给出算例予以说明。     

多目标线性生产规划的模糊联盟对策

研究多目标生产规划的模糊联盟对策的求解问题,提出了求解多目标模糊联盟对策的Shapley值方法.通过建立多目标线性生产规划的模糊联盟对策模型,提出了多目标对策转化为多个单目标对策的权重分析法.结合多目标线性生产规划问题的实例,给出不同权重系数下局中人合作的利益分配策略.     

一类多步矩阵对策上的计策问题

以有序树为工具,研究了可以描述连环计,诱敌深入等多步矩阵对策上的一类计策模型.在不考虑信息环境的封闭对策系统中,及局中人对每一步矩阵对策的赢得矩阵,两个局中人的策略集合以及局中人的理性等的了解都是局中人的共同知识的假定下,提出了局中人的最优计策链及将计就计等概念,研究了局中人中计和识破计策的固有概率,讨论了局中人在什么情况下最好主动用计,在什么情况下最好从动用计以及求解最优计策等问题.     

消费者预防在线销售掺假行为的博弈模型及最优策略

建立了描述消费者与带掺假行为的在线零售商之间相互博弈的双层规划模型,其中消费者为领导者,在线零售商为随从者.消费者预防在线销售掺假行为的两种策略是进行商品品质检查和采用延期付款,在线零售商则依据消费者的预防策略决定是否销售掺假商品.根据消费者和在线零售商的可能采用的策略,对模型分四种情形展开分析与讨论,并分别在不同情形下得到了消费者与在线零售商的最优决策.结果表明,消费者延期付款的最优时间和进行商品品质检查能有效遏制在线零售商掺假行为.     

Risk and quality control in a supply chain: competitive and collaborative approaches

This paper provides a quantitative and comparative economic and risk approach to strategic quality control in a supply chain, consisting of one supplier and one producer, using a random payoff game. Such a game is first solved in a risk-neutral framework by assuming that both parties are competing with each other. We show in this case that there may be an interior solution to the inspection game. A similar analysis under a collaborative framework is shown to be trivial and not practical, with a solution to the inspection game being an ‘all or nothing’ solution to one or both the parties involved. For these reasons, the sampling random payoff game is transformed into a Neyman–Pearson risk constraints game, where the parties minimize the expected costs subject to a set of Neyman–Pearson risk (type I and type II) constraints. In this case, the number of potential equilibria can be large. A number of such solutions are developed and a practical (convex) approach is suggested by providing an interior (partial sampling) solution for the collaborative case. Numerical examples are developed to demonstrate the procedure used. Thus, unlike theoretical approaches to the solution of strategic quality control random payoff games, the approach we construct is both practical and consistent with the statistical risk Neyman–Pearson approach.     

基于极大熵理论的评价指标组合赋权模型

针对目前指标组合赋权方法中存在的赋权过于"僵硬"的通病,基于Jaynes E T提出的最大信息熵原理,构建了一种新的指标赋权模型.在模型中,以客观因素为目标规划主体,将主观因素转化为目标规划的约束条件,实现了主客观条件的融合.实例分析表明方法准确、有效,具有较高的应用价值.     

基于个人超出值的模糊联盟合作博弈最小二乘预核仁

本文给出了基于个人超出值的无限模糊联盟合作博弈最小二乘预核仁的求解模型,得到该模型的显式解析解,并研究该解的若干重要性质。证明了:本文给出的无限模糊联盟合作博弈的最小二乘预核仁与基于个人超出值的相等解(The equalizer solution),基于个人超出值的字典序解三者相等。进一步证明了:基于Owen线性多维扩展的无限模糊联盟合作博弈的最小二乘预核仁与基于个人超出值的经典合作博弈最小二乘预核仁相等。最后,通过数值实例说明本文提出的无限模糊联盟合作博弈求解模型的实用性与有效性。     

A dual-uncertainty-based chance-constrained model for municipal solid waste management

A double-sided dual-uncertainty-based chance-constrained programming (DDCCP) model was developed for supporting municipal solid waste management under uncertainty. The model was capable of tackling left-hand- and right-hand-side variables in constraints where those variables were affected by dual uncertainties (i.e. e.g. both fuzziness and randomness); and they were expressed as fuzzy random variables (FRVs). In this study, DDCCP model were formulated and solved based on stochastic and fuzzy chance-constrained programming techniques, leading to optimal solutions under different levels of constraints violation and satisfaction reliabilities. A long-term solid waste management problem was used to demonstrate the feasibility and applicability of DDCCP model. The obtained results indicated that DDCCP was effective in handling constraints with FRVs through satisfying them at a series of allowable levels, generating various solutions that facilitated evaluation of trade-offs between system economy and reliability. The proposed model could help decision makers establish cost-effective waste-flow allocation patterns under complex uncertainties, and gain in-depth insights into the municipal solid waste management system.     

On the theory of three-person differential games

A differential game of three players with dynamics described by linear differential equations under geometric constraints on the control parameters is considered. Sufficient conditions are obtained for the existence of the first player’s strategy guaranteeing that the trajectory of the game reaches a given target set for any admissible control of the second player and avoids the terminal set of the third player. An algorithm of constructing the first player’s strategy guaranteeing the game’s termination in finite time is suggested. A solution of a model example is given.     

Integrated analytical hierarch process and mathematical programming to supplier selection problem with quantity discount

In this article an integration of analytical hierarchy process and non-linear integer and multi-objective programming under some constraints such as quantity discounts, capacity, and budget is applied to determine the best suppliers and to place the optimal order quantities among them. This integration-based multi-criteria decision making methodology takes into account both qualitative and quantitative factors in supplier selection. While the analytical hierarchy process matches item characteristics with supplier characteristics, non-linear integer programming model analytically determines the best suppliers and the optimal order quantities among the determined suppliers. The objectives of the mathematical models constructed are maximizing the total value of purchase (TVP), minimizing the total cost of purchase (TCP) or maximizing TVP and minimizing TCP simultaneously. In addition, several “what if” scenarios are facilitated and the quality of the resulting models is evaluated on real-life data.     

动态模糊规划模型的构建及应用

常规规划模型通常存在如下两种缺陷:首先,它的目标系数及约束条件都是在硬性限制下的确定值,因而在建模方面弹性小、硬度大;其次,它的目标系数与时间无关,因此不能有效地刻划时时刻刻变化着的目标系数,而动态模糊规划模型可以有效地解决上述缺陷.首先应用模糊动态AHP确定目标系数;然后根据L-R模糊数的强序关系准则,将动态模糊规划模型分解为最优与最劣两个模糊规划模型;再根据以α水平截集为基础的求解方法,将上述两个模型进行相应的转换,建立具有风险分析功能的动态模糊规划模型;最后将其应用到一个实际算例中,收到较好的结果.     

Devising a Cooperation Policy for Emergency Networks

A mathematical programming model is proposed to select an optimal cooperation policy between autonomous service networks for dispatching purposes. In addition to traditional characteristics such as network topology and station location, this model takes into account 'political' constraints on minimum response-time in certain subzones. Such constraints are translated into performance requirements, which are imposed on the cooperation policy. Testing the model under different assumptions can be useful for analysing various cooperation policies. The paper formulates a mathematical programming model, derives example policies for various circumstances, and tests the sensitivity of the resultant policies to some parameters, such as the penalty for not providing service, and distances between adjacent networks. The paper suggests also a less constrained approach, which entails a linear programming model. A comparison between the two approaches is presented.