二度价格歧视的进一步研究

系统地讨论了二度价格歧视条件下垄断厂商的收益最大化条件和利润最大化条件 .首先分别讨论了线性需求函数和非线性需求函数情形下的收益最大化问题 ,接着讨论了线性需求函数和非线性需求函数情形下的利润最大化问题 .针对上述问题 ,本文均给出了严谨的理论分析和有关的计算公式 .本文的研究成果具有较大的理论价值和应用价值     

基于Logistic函数的互补关系创新产品的扩散叠加模型研究

运用Logistic函数构建了创新产品扩散叠加模型及相互共生模型,以分析不完全竞争条件下互补关系创新产品的扩散问题;在此基础上,利用平衡点稳定性分析法,计算了在时间变量不断变化的情况下,创新产品扩散叠加的演化趋势和扩散叠加模型的平衡点,并对平衡点的稳定性进行了分析。     

一个非对称风险度量模型及组合证券投资分析

在分析Jia&Dyer的风险-价值理论基础上,给出了一个基于预先给定的目标收益的非对称风险函数。该风险函数是低于参考点的离差和高于参考点的离差的加权和,它利用一阶"上偏矩"来修正二阶下偏矩,进一步建立了在此非对称风险函数下的二次规划组合证券投资模型;并证明了该模型与三阶随机占优准则的一致性;最后通过上海证券市场的实际数据验证了该模型的有效性和实用性。     

基于产量柔性的经济生产批量模型研究

传统经济生产批量（ＥＰＬ）模型没有考虑制造系统的产量柔性，机器的生产率和单位生产成本都被假定为不变的。然而机器的生产率是容易改变的，且单位生产成本依赖于生产率。本文对传统的ＥＰＬ模型进行了扩展，生产率变为决策变量，单位生产成本变成生产率的函数。通过对模型的Ｋ－Ｔ条件的条件，我们提出了求解模型的简单算法。最后对产量柔性下的经济生产批量问题进行了分析。     

企业库存物资结构的优化方法

本文概述了企业物资供应的重要性及目前企业库存积压的原因，分析了过去在库存周转量计算方法中存在问题，引进了适合现代市场经济条件下的库存结构优化方法－进消差训存控制模型，并对此模型提出了的出发点，目标，依据，适用条件等都作了阐述，并对此模型作了实证性的应用，收到了明显经济效果，论证了此模型在实际应用中的可行性和有效性。     

改进区间可接受度的证券投资组合区间二次规划模型

本文首先基于Markowitz的经典均值方差模型，针对不确定环境下的投资组合问题，把证券的收益率、风险损失率和流动性用区间数描述，建立了一种新的含交易成本的证券投资组合区间二次规划模型。其次，为求解该模型，提出了改进的区间可接受度确定性转换方法，通过引入优化水平α与可接受水平η将不确定二次规划转化为确定型规划。最后，通过数值实验将提出的方法与传统方法进行比较，结果表明本文所提出的方法与模型具有相对较好的可行性与实用性。     

线性红利界限下的复合Poisson风险模型

本文在线性红利界限下讨论复合Poissson风险模型,得到在破产后发放红利和不发放红利两种情况下的风险模型的一些性质,并得到折扣罚金函数的积分微分方程及边界条件.     

企业人力资源规划模型的研究

本文针对企业人力资源的合理安排建立了规划模型,并讨论了效益函数建立的依据,研究了模型的求解方法,针对实例的计算,说明所应用的算法是有效的.为进一步研究人力资源规划问题,提供了一种定量的手段.     

基于遗传算法的CVaR模型

条件风险值模型在金融和管理科学中有着广泛的应用.已有的CVaR模型通常是一个线性规划模型,其中每个阶段的损失函数常用线性函数近似,然而,在一些实际问题中,这些函数通常是非线性函数,用非线性函数近似会更加符合实际规律.本文通过引入非线性损失函数值,将原有模型转化为一个非线性规划模型,并通过一种改进的遗传算法求出新的CVaR模型的近似最优解.结合实例说明该方法能够同时降低cvaR和VaR两个重要风险度量指标.     

线性二层决策问题的期望收益模型及算法

下层反应不唯一时 ,如何确定二层线性决策问题最优策略为一非确定型决策问题 .对此类问题 ,本文通过引入领导者对追随者合作程度的期望系数 ,提出期望收益模型 .利用双罚函数把该问题转换为一单层次优化问题 ,并提出一种求解问题的全局优化算法 .应用此模型分析二层线性问题可知 :对存在不确定性反应的二层决策问题 ,下层追随者与上层领导者的合作态度是领导者确定其最优策略的关键 ;对下层追随者而言 ,某些情况下 ,采取与领导者部分合作的态度对其自身收益的提高是合理的     

A Semidefinite Programming Approach to the Quadratic Knapsack Problem

In order to gain insight into the quality of semidefinite relaxations of constrained quadratic 0/1 programming problems we study the quadratic knapsack problem. We investigate several basic semidefinite relaxations of this problem and compare their strength in theory and in practice. Various possibilities to improve these basic relaxations by cutting planes are discussed. The cutting planes either arise from quadratic representations of linear inequalities or from linear inequalities in the quadratic model. In particular, a large family of combinatorial cuts is introduced for the linear formulation of the knapsack problem in quadratic space. Computational results on a small class of practical problems illustrate the quality of these relaxations and cutting planes.     

摩擦市场上允许买空卖空的投资组合问题

证券交易市场上存在着诸如交易费用、税收等摩擦.投资者在交易过程中,不可避免地要受到市场摩擦的影响.本文以投资者所获取的最大投资效用为目标函数,建立了摩擦市场上最优投资组合问题的数学模型;同时对于之前解决此类问题的很多文章中“证券市场不允许买空卖空风险资产和借贷无风险资产”的假设条件做了扩展,得到一个摩擦市场上适用于“允许买空卖空或借贷”的证券投资组合的二次规划模型.     

Tracking and outperforming large stock-market indices

Enhanced index-tracking funds aim to achieve a small target excess return over a given financial benchmark index with minimum additional risk relative to this index, i.e., a minimum tracking error. These funds are attractive to investors, especially when the index is large and thus well diversified. We consider the problem of determining a portfolio for an enhanced index-tracking fund that is benchmarked against a large stock-market index subject to real-life constraints that may be imposed by investors, stock exchanges, or investment guidelines. In the literature, various solution approaches have been proposed to enhanced index tracking that are based on different linear and quadratic tracking-error functions. However, it remains an open question which tracking-error function should be minimized to determine good enhanced index-tracking portfolios. Moreover, the existing approaches may neglect real-life constraints such as the minimum trading values imposed by stock exchanges or may not devise good feasible portfolios within a reasonable computational time when the index is large. To overcome these shortcomings, we propose novel mixed-integer linear and quadratic programming formulations and novel matheuristics. To address the open question, we minimize different tracking-error functions by applying the proposed matheuristics and exact solution approaches based on the proposed mixed-integer programming formulations in a computational experiment using a set of problem instances based on large stock-market indices with up to more than 9,000 constituents. The results of our study suggest that minimizing the so-called tracking error variance, which is a quadratic function, is preferable to minimizing other tracking-error functions.     

公交系统随机平衡网络设计模型及求解算法

本文根据公交网络的具体特点,对公交网络进行了系统的描述,提出一个双层规划模型来描述随机平衡公交网络设计问题。在双层规划模型中,上层模型为一个标准的公交网络设计模型,下层模型是一个公交网络随机平衡配流模型。针对所提出的模型,设计了基于灵敏度分析的求解算法。最后,给出一个简单算例加以证明。     

基于协同效应的知识创新团队伙伴选择方法

在知识创新团队的伙伴选择问题中着重考虑了伙伴间的协同效应信息。首先,分析了伙伴之间的协同关系与协同效应,描述了考虑多个协同效应评价指标的知识创新团队伙伴选择问题;然后,建立了团队伙伴选择的数学模型,该模型是一个0-1二次整数规划问题,为了求解该问题,开发了一种GRASP启发式算法;最后,通过一个实例分析说明了所提出方法的可行性和实际应用价值。     

Portfolio Selection Using Stochastic Dominance Criteria

The direct application of stochastic dominance criteria to portfolio selection problems has been thought impractical because an extremely large number of combinations of returns must be considered. This paper proposes and evaluates a rigorous statistical procedure for sampling the combinations of returns on candidate risky assets so that stochastic dominance criteria may be used directly in an efficient linear programming model for portfolio selection. The sampling scheme exploits the association of the return on each candidate stock with the return on a market index in a manner analogous to the Sharpe single-index model, thereby eliminating the large number of combinations with probabilities close to or equalling zero. Portfolios computed by the proposed linear programming stochastic dominance model are compared with those computed by the single-index quadratic programming model, using 180 months of recent data on a sample of NYSE common stocks.     

A multi-stage stochastic supply network design problem with financial decisions and risk management

In this paper, a multi-period supply chain network design problem is addressed. Several aspects of practical relevance are considered such as those related with the financial decisions that must be accounted for by a company managing a supply chain. The decisions to be made comprise the location of the facilities, the flow of commodities and the investments to make in alternative activities to those directly related with the supply chain design. Uncertainty is assumed for demand and interest rates, which is described by a set of scenarios. Therefore, for the entire planning horizon, a tree of scenarios is built. A target is set for the return on investment and the risk of falling below it is measured and accounted for. The service level is also measured and included in the objective function. The problem is formulated as a multi-stage stochastic mixed-integer linear programming problem. The goal is to maximize the total financial benefit. An alternative formulation which is based upon the paths in the scenario tree is also proposed. A methodology for measuring the value of the stochastic solution in this problem is discussed. Computational tests using randomly generated data are presented showing that the stochastic approach is worth considering in these types of problems.     

Strengthening a linear reformulation of the 0-1 cubic knapsack problem via variable reordering

The 0-1 cubic knapsack problem (CKP), a generalization of the classical 0-1 quadratic knapsack problem, is an extremely challenging NP-hard combinatorial optimization problem. An effective exact solution strategy for the CKP is to reformulate the nonlinear problem into an equivalent linear form that can then be solved using a standard mixed-integer programming solver. We consider a classical linearization method and propose a variant of a more recent technique for linearizing 0-1 cubic programs applied to the CKP. Using a variable reordering strategy, we show how to improve the strength of the linear programming relaxation of our proposed reformulation, which ultimately leads to reduced overall solution times. In addition, we develop a simple heuristic method for obtaining good-quality CKP solutions that can be used to provide a warm start to the solver. Computational tests demonstrate the effectiveness of both our variable reordering strategy and heuristic method.

     

Exact methods in optimum disassembly sequence search for problems subject to sequence dependent costs

Disassembling complex products is formally approached via network representation and subsequent mathematical modeling, aimed at selecting a good or optimum sequence of disassembly operations. This is done via heuristics, metaheuristics or mathematical programming. In contrast with heuristics and metaheuristics, which select a near-optimum solution, mathematical programming guarantees the selection of the global optimum. This problem is relatively simple if the disassembly costs can be assumed sequence independent. In practice, however, sequence dependent disassembly costs are frequently encountered, which causes NP-completeness of the problem. Although methods, e.g., based on the two-commodity network flow approach, are available to solve this constrained asymmetric Traveling Salesperson problem rigorously, this requires the introduction of integer variables. In this paper, a modification of the two-commodity network flow approach is proposed, which reduces the number of integer variables. This is applied to product structures that can be represented by a disassembly precedence graph. It is demonstrated that use of integer variables is completely avoided by iteratively solving a binary integer linear programming problem. This appears to be more efficient than solving the corresponding integer linear programming problem. It is demonstrated, on the basis of some cases, that this method might provide the exact solution of problems with increased complexity compared to those discussed so far in the literature. This appears particularly useful for evaluating heuristic and metaheuristic approaches.