基于决策者满意度的区间DEA的求解

定义了一种反映决策者满意度的区间数序关系,基于此将区间DEA中的区间不等式约束转化为确定型约束。研究了区间DEA模型向确定型DEA模型转化过程中的数据一致性问题。在保持数据一致性的前提下,根据决策者给出的满意度水平,将区间DEA转化为确定型DEA并进行求解。最后给出算例,并总结和分析了决策单元的DEA效率值随满意度水平变化的规律。     

模糊合作对策的区间Shapley值

本文主要研究合作对策中支付函数是区间模糊数的情形,利用区间数运算的性质,拓广了shapley值在经典意义下的三条公理,并给出了唯一满足此三条公理的shapley函数形式,最后将此区间shapley分配方法应用到利益分配的实例中.由证明可知,支付函数是区间数的合作对策的分配的结果也是一个区间数,并且由各个联盟所对应的区间支付范围内的不同实数值所组成的对策是经典合作对策,并且其shapley值一定包含在区间shapley值中.由于本文研究的是支付函数模糊化的一种特殊形式一区间数,从而为求解具有其他模糊化形式的支付的合作对策奠定了一定的基础.     

结合关键指标的第三方物流供应商区间分析

通过结合众多学者对供应商评价指标的研究和当前第三方物流供应商选择的现实情况，构建出评价指标体系，并对各指标进行区间数处理，再运用层次分析法确定各指标的区间权重，在此基础上用线性规划法从全面评价和关键指标评价两方面对各供应商分别进行排序，排序和最小的为最优供应商。实例分析表明，该方法切实可行，更贴近实际。     

联合订货区间值EOQ模型及变权Shapley值成本分摊方法

研究多个销售商企业组成联盟向一个供应商订购同种商品的联合订货问题。考虑到实际问题中很难预测到精确的需求，本文用区间表示单位时间需求量，研究允许缺货的销售商企业联合订货区间值EOQ模型，其中缺货完全回补。以联合订货平均成本最小为目标，结合连续有序加权集结算子求解出联合订货的周期、区间值订货量和区间值平均成本。定义变权Shapley值，给出区间值合作博弈的区间值变权Shapley值的求解方法，得出区间值变权Shapley值的表达式可直接利用相关联盟值的左、右端点计算得到。考虑联盟和局中人的相对重要性，结合需求率确定合成权重，提出基于区间值变权Shapley值的联合订货成本分摊方法。利用数值算例验证模型和方法的有效性。本文可为解决联合订货成本分摊问题提供决策参考。     

超效率DEA模型的区间扩展

将一种改进的DEA模型-超效率DEA(SE-DEA)模型[1]拓展到区间投入产出情形,得到区间SE-DEA模型。定义了一种反映决策者满意度的区间数序关系。当决策者给定一满意度水平,将区间SE-DEA中的区间不等式约束转化为确定型约束。研究了该满意度水平的另一层含义,即决策者对除被评价决策单元外的其它决策单元的偏好程度,据此将区间SE-DEA中的区间等式约束和区间目标函数转化为确定型。最终将区间SE-DEA转化为某一满意度水平下的确定型SE-DEA,并进行求解。最后将文中方法应用于天津市某4家科研所的效率预测问题之中。     

信息不完全确定的区域产品模糊区间聚类方法

区域产品分类与选择是区域经济发展中最重要和最基础的工作.在产品选择与分类时,需要确定指标权系数和分类阈值等参数,这在实际应用中是比较困难的.针对这种情况,提出了一种信息不完全确定的区域产品模糊区间聚类方法.该方法构建了指标权系数信息不完全确定的最优模糊区间聚类模型,利用遗传算法和改进的FCM算法联合求解所得优化模型,得到指标权系数、最优聚类中心和最优划分,进而确定各产品所属类别.最后将该方法应用于某区域的产品分类和主导产品的确定中,实例计算说明该方法的可行性和有效性.     

基于区间直觉模糊数相关系数的多准则决策模型

针对权重信息完全未知,评价信息为区间直觉模糊数的多准则决策问题,提出新的基于区间直觉模糊数相关系数的决策方法,弥补了基于距离测度决策方法造成信息混淆的不足,同时考虑了犹豫度的影响,进而降低了评价信息损失.通过构建并求解基于参照方案相关系数总偏差最小的非线性规划模型获得准则权重,从新的视角给出准则权重的确定方法.利用各备选方案与理想方案、临界方案的加权相关系数得到与理想方案的相对贴近度,以此对方案进行排序.最后通过实例对比分析说明了该方法的有效性.     

区间数计划网络的关键路问题研究

论文针对区间数计划网络的特点,提出了基于限制期约束的区间关键路(deadline based interval critical path, DBICP)的概念,通过相关定理的证明给出了求解DBICP的算法,该算法拓展了Stefan Chanas和Pawel Zielinski关于区间关键路问题的研究成果.     

基于改进自适应最优分割法的风险预警区间模型研究——针对重大突发公共卫生事件

重大突发公共卫生事件，譬如新型冠状病毒疫情，严重危害着世界各国人民的生命安全，风险预警是构建重大突发公共卫生事件风险预警管控体系的关键所在，而其风险预警区间的精准确定是关乎预警等级的关键问题。基于自适应最优分割模型，引入熵值法计算各指标权重，采用多种函数拟合识别函数特征，构建了改进的自适应最优分割模型，定量科学划分了重大突发公共卫生事件风险预警区间。通过结合实际案例，应用Matlab软件进行仿真，验证了预警区间的吻合度，为构建重大突发公共卫生事件风险预警防控提供了理论参考。     

基于满秩灰损益值矩阵的灰矩阵博弈的矩阵法求解研究

以经典数学理论和思想发展起来的博弈理论对经济学、社会学等众多领域和学科产生了深远的影响,然而当博弈环境面临有限理性、有限知识和小样本、贫信息等不确定性条件,博弈的损益值只能用灰数进行描述时,经典博弈理论将一筹莫展.灰矩阵博弈的高效率的求解问题是该领域理论研究和实用中的必须解决的关键问题.在文献7的研究基础之上,本文深人地研究了基于满秩灰损益值矩阵的灰矩阵博弈的矩阵法求解问题.在基于灰混合策略的灰矩阵博弈模型的求解过程中,灰矩阵法是一种较为简便而有效的求解方法.本文定义了灰矩阵博弈的局中人1和局中人2灰满秩损益值扩充方阵的概念,并且证明了若这些灰满秩扩充方阵的逆阵的最后一行和最右边一列满足非负性的条件,那么,这些灰逆阵的最后一行和最右边一列的灰元素值就分别对应着局中人1和2的最优灰博弈策略及其最优灰博弈值.在此基础上,我们进一步地研究了基于局中人1和2的共同灰满秩扩充方阵的问题,并且证明了若该共同灰满秩扩充方阵的逆阵的最后一行和最右边一列(不包括最右下角的灰元素)满足非负性的条件,那么,该灰逆阵的最后一行和最右边一列的灰元素值就分别对应着局中人1和2的最优灰博弈策略及其最优灰博弈值.     

Rationalizing Policy Functions by Dynamic Optimization

We derive necessary and sufficient conditions for a pair of functions to be the optimal policy function and the optimal value function of a dynamic maximization problem with convex constraints and concave objective functional. It is shown that every Lipschitz continuous function can be the solution of such a problem. If the maintained assumptions include free disposal and monotonicity, then we obtain a complete characterization of all optimal policy and optimal value functions. This is the case, e.g., in the standard aggregative optimal growth model.     

基于区间灰色区间数的多准则决策方法

将灰色模糊数扩展,定义了区间灰色区间数及其距离.针对准则值为区间灰色区间数的信息不完全的多准则决策问题,提出了一种基于目标规划法的灰色模糊多准则决策方法,求得最优权重向量,从而得到各方案的排序.最后给出一个算例说明方法的可行性和有效性.     

具有不确定信息的风险型多目标决策理论及应用

具有不确定信息的多目标决策问题是一类常见的决策问题。给出该决策问题指标的分类方法和指标值的规格化公式,建立方案的距优距劣综合加权距离为最小的目标函数,从而得到一类求解这一问题的数学模型,并给出了一种目标权重的确定方法,很适用于实际问题,为解决不确定性系统的多目标决策问题提供了一种思路和方法。最后将其应用到水资源系统风险决策的一个实例中,表明了方法的可行性。     

The optimal value range problem for the Interval (immune) Transportation Problem

We address the problem of finding the range of the optimal cost of a transportation problem when supply and demand vary over an interval. We consider the specific version of a transportation problem with supply inequality constraints and demand equality constraints under the assumption that the transportation costs are immune against the transportation paradox. We investigate some theoretical properties of the problem which constitute the basis of a novel solution algorithm. Our results show that the proposed algorithm hugely outperforms the best existing solution approaches.     

Optimal ordering time interval taking account of time value

In this paper, the optimal inventory policies for an infinite lime span taking account of time value is discussed. First, bounds for the optimal ordering time interval are derived. Second, with these bounds, a simple algorithm to compute die optimal ordering time interval is developed. Numerical examples are given to illustrate the algorithm.     

Linear time-dependent constraints programming with MSVL

This paper investigates specifying and solving linear time-dependent constraints with an interval temporal logic programming language MSVL. To this end, linear constraint statements involving linear equality and non-strict inequality are first defined. Further, the time-dependent relations in the constraints are specified by temporal operators, such as . Thus, linear time-dependent constraints can be smoothly incorporated into MSVL. Moreover, to solve the linear constraints within MSVL by means of reduction, the operational semantics for linear constraints is given. In particular, semantic equivalence rules and transition rules within a state are presented, which enable us to reduce linear equations, inequalities and optimization problems in a convenient way. Besides, the operational semantics is proved to be sound. Finally, a production scheduling application is provided to illustrate how our approach works in practice.     

Best-worst multi-criteria decision-making method: Some properties and a linear model

The Best Worst Method (BWM) is a multi-criteria decision-making method that uses two vectors of pairwise comparisons to determine the weights of criteria. First, the best (e.g. most desirable, most important), and the worst (e.g. least desirable, least important) criteria are identified by the decision-maker, after which the best criterion is compared to the other criteria, and the other criteria to the worst criterion. A non-linear minmax model is then used to identify the weights such that the maximum absolute difference between the weight ratios and their corresponding comparisons is minimized. The minmax model may result in multiple optimal solutions. Although, in some cases, decision-makers prefer to have multiple optimal solutions, in other cases they prefer to have a unique solution. The aim of this paper is twofold: firstly, we propose using interval analysis for the case of multiple optimal solutions, in which we show how the criteria can be weighed and ranked. Secondly, we propose a linear model for BWM, which is based on the same philosophy, but yields a unique solution.     

分布式供应链中基于准时制的原油采购计划方法

本文研究了分布式供应链多供应商/多炼油厂的原油采购计划问题,建立了在有限资源约束下的准时制多目标采购优化数学模型,以实现总采购费用和供应链循环时间最小。然后,本文将非线性规划模型转化为线性规划模型,并利用层次分析法(Analytic Hierarchy Process,AHP)与多目标规划相结合的方法求解模型得到采购计划方案。数值仿真结果表明本文所提出的原油采购方法的有效性和实用性。     

RUTA: A framework for assessing and selecting additive value functions on the basis of rank related requirements

In this paper, we present a new preference disaggregation method, called RUTA, which infers a set of additive value functions from the preference information referring to the desired ranks of some reference alternatives. Real-life experience indicates that people willingly refer to the range of allowed ranks that a particular alternative should attain, or to constraints on the final scores of the alternatives. We develop a mathematical model for incorporating such preference information via mixed-integer linear programming (MILP). Then, we discuss how decision making could be supported with the use of the already proposed extreme ranking analysis (ERA), which indicates the best and worst ranks gained by each alternative over the set of compatible preference model instances. We also introduce a new interactive UTA-like technique, which aims at selecting a single value function representing the outcomes of ERA. In the interactive process, the decision maker (DM) is assigning priorities to different pre-defined targets, which are built on results of ERA, and refer to the comparison of the best and/or worst ranks for pairs of alternatives. In particular, the DM may choose to emphasize or neglect the advantage of some alternatives over the others, in terms of results of ERA. In this way, one obtains a synthetic representation of extreme ranking analysis at a higher level of abstraction.