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.     

Optimization of Multilevel Investments Using Dynamic Programming Based on Fuzzy Cash Flows

Dynamic programming is applicable to any situation where items from several groups must be combined to form an entity, such as a composite investment or a transportation route connecting several districts. The most desirable entity is constructed in stages by forming sub-entities of progressively larger size. At each stage of the development, the sub-entities that are candidates for inclusion in the most desirable entity are retained, and all other sub-entities are discarded. In deterministic dynamic programming, a specification of the current state and current decision is enough to tell us with certainty the new state and costs during the current stage. In many practical problems, these factors may not be known with certainty, even if the current state and decision are known. In this paper, the dynamic programming is applied to the situation where each investment in the set has the following characteristics: the amount to be invested has several possible values, and the rate of return varies with the amount invested. Each sum that may be invested represents a distinct level of investment, and the investment therefore has multiple levels. A fuzzy present worth based dynamic programming approach is used. A numeric example for a multilevel investment with fuzzy geometric cash flows is given. A computer software named FUZDYN is developed for various problems such as alternatives having different lives, different uniform cash flows, and different ranking methods.     

IRREVERSIBLE INVESTMENT AND OPTIMAL FOREST EXPLOITATION

A forest harvest scheduling model which includes as activities the level of investment in harvest capacity and the accumulated harvest capacity in each period, is presented. The inclusion of these activities, in addition to the harvest activities, allows for the removal of harvest-flow constraints found in more typical Model II formulations of the harvest scheduling problem. The optimal harvest and investment policy can be determined by linear programming or quadratic programming methods, depending on whether prices are constant or supply-dependent. The new model better reflects economic reality than existing models, and provides a method for determining the optimal economic development of a forest industry, and the optimal draw-down of old growth forest. Numerical examples are given.     

Calculating risk neutral probabilities and optimal portfolio policies in a dynamic investment model with downside risk control

This paper presents a method for solving multiperiod investment models with downside risk control characterized by the portfolio’s worst outcome. The stochastic programming problem is decomposed into two subproblems: a nonlinear optimization model identifying the optimal terminal wealth distribution and a stochastic linear programming model replicating the identified optimal portfolio wealth. The replicating portfolio coincides with the optimal solution to the investor’s problem if the market is frictionless. The multiperiod stochastic linear programming model tests for the absence of arbitrage opportunities and its dual feasible solutions generate all risk neutral probability measures. When there are constraints such as liquidity or position requirements, the method yields approximate portfolio policies by minimizing the initial cost of the replication portfolio. A numerical example illustrates the difference between the replicating result and the optimal unconstrained portfolio.     

Modeling international investment decisions for financial holding companies

This research analyzes the internationalization process model developed by Johanson and Vahlne and derives two integer programming investment decision models that consider the risk attitudes of investment firms. Johanson and Vahlne’s model provides a starting point for building a model that suits the investment approach and decision making process of financial holding companies. In practice, when firms make an international investment decision, there is a need for a model that can generate outputs based on financial measures such as profit, investment returns, and tolerable levels of risk. Thus, in this paper, Johanson and Vahlne’s concepts are studied and financial managers are interviewed to derive models that match the investment decision procedures of the firms. The model helps firms manage the risks of their investments and derive accurate investment strategies based on investment objectives and constraints.     

新兴产业两阶段期权规划决策模型

新兴产业中处于横向竞争地位的初创企业,会呈现渐变和突变两种不同的演化状态。不同状态下的横向竞争企业,价值变化都具有高度的不确定性。为了降低投资决策的不确定性风险,获取稳定的投资收益,对处于渐变和突变状态下的初创企业,首先运用期权组合的方法,进行第一阶段的变量预估决策;然后依据期权投资的收益情况,再运用线性规划技术进行第二阶段的补偿优化决策。论文通过阿里巴巴、京东、苹果和诺基亚四家样本公司的数据,检验了两阶段期权规划决策模型的实际效果,结论显示该方法能降低新兴产业投资中的不确定性干扰,在获取稳定收益的同时,使风险处于可控状态。     

Duality in mathematics and linear and integer programming

Linear programming (LP) duality is examined in the context of other dualities in mathematics. The mathematical and economic properties of LP duality are discussed and its uses are considered. These mathematical and economic properties are then examined in relation to possible integer programming (IP) dualities. A number of possible IP duals are considered in this light and shown to capture some but not all desirable properties. It is shown that inherent in IP models are inequality and congruence constraints, both of which give on their own well-defined duals. However, taken together, no totally satisfactory dual emerges. The superadditive dual based on the Gomory and Chvátal functions is then described, and its properties are contrasted with LP duals and other IP duals. Finally, possible practical uses of IP duals are considered.The author is indebted to Professor H. B. Griffiths for many stimulating conversations on this topic.     

Fuzzy extensions to Integer Programming models of cell-formation problems in machine scheduling

Cell formation has received much attention from academicians and practitioners because of its strategic importance to modern manufacturing practices. Existing research on cell formation problems using integer programming (IP) has achieved the target of solving problems that simultaneously optimise: (a) cell formation, (b) machine-cell allocation, and (c) part-machine allocation. This paper will present extensions of the IP model where part-machine assignment and cell formation are addressed simultaneously, and also a significant number of constraints together with an enhanced objective function are considered. The main study examines the integration of inter-cell movements of parts and machine set-up costs within the objective function, and also the combination of machine set-up costs associated with parts revisiting a cell when part machine operation sequence is taken into account. The latter feature incorporates a key set of constraints which identify the number of times a part travels back to a cell for a later machine operation. Due to two main drawbacks of IP modelling for cell formation, i.e. (a) only one objective function can be involved and (b) the decision maker is required to specify precisely goals and constraints, fuzzy elements like fuzzy constraints and fuzzy goals will be considered in the proposed model. Overall the paper will not only include an extended and enhanced integer programming model for assessing the performance of cell formation, but also perform a rigorous study of fuzzy integer programming and demonstrate the feasibility of achieving better and faster clustering results using fuzzy theory.     

Dynamic portfolio optimization with risk control for absolute deviation model

In this paper, we present a new multiperiod portfolio selection with maximum absolute deviation model. The investor is assumed to seek an investment strategy to maximize his/her terminal wealth and minimize the risk. One typical feature is that the absolute deviation is employed as risk measure instead of classical mean variance method. Furthermore, risk control is considered in every period for the new model. An analytical optimal strategy is obtained in a closed form via dynamic programming method. Algorithm with some examples is also presented to illustrate the application of this model.     

多约束的多阶段积极投资组合模型及实证研究

构建投资组合时需要衡量其风险, 除了考虑组合本身的风险暴露, 还需考虑其相对基准组合的风险暴露. 再者, 确定组合权重时需要根据市场的规则加入合适的约束. 基于此, 为了较为完整地考虑现实投资组合面临的风险及交易约束, 将绝对风险(CVaR)和相对风险(跟踪误差)作为风险约束, 将交易成本、卖空限制和多元权值作为交易限制约束, 构建一个新的多阶段投资组合模型, 并利用动态规划和非线性优化方法进行求解. 最后, 利用上证50成分股中41只股票构建投资组合进行实证研究. 实证结果表明构建的多阶段投资组合模型能持续战胜基准组合且优于单阶段投资组合, 同时也表明模型考虑多元权值约束具有现实意义.     

Binary fuzzy goal programming

Goal programming is an important technique for solving many decision/management problems. Fuzzy goal programming involves applying the fuzzy set theory to goal programming, thus allowing the model to take into account the vague aspirations of a decision-maker. Using preference-based membership functions, we can define the fuzzy problem through natural language terms or vague phenomena. In fact, decision-making involves the achievement of fuzzy goals, some of them are met and some not because these goals are subject to the function of environment/resource constraints. Thus, binary fuzzy goal programming is employed where the problem cannot be solved by conventional goal programming approaches. This paper proposes a new idea of how to program the binary fuzzy goal programming model. The binary fuzzy goal programming model can then be solved using the integer programming method. Finally, an illustrative example is included to demonstrate the correctness and usefulness of the proposed model.     

带交易费用的证券组合投资选择的优化模型

本文利用在约束条件中加入证券多样化选择约束的办法来抵减非系统风险 ,就证券组合投资的选择问题 ,建立了带交易费用的综合考虑收益和风险的多目标规划模型 ,然后通过变换将不可微的多目标规划问题转化为一个多目标线性规划问题 ,最后给出了问题的一个算法和算例     

A hybrid model of integer programming and variable neighbourhood search for highly-constrained nurse rostering problems

This paper presents a hybrid multi-objective model that combines integer programming (IP) and variable neighbourhood search (VNS) to deal with highly-constrained nurse rostering problems in modern hospital environments. An IP is first used to solve the subproblem which includes the full set of hard constraints and a subset of soft constrains. A basic VNS then follows as a postprocessing procedure to further improve the IP’s resulting solutions. The satisfaction of the excluded constraints from the preceding IP model is the major focus of the VNS. Very promising results are reported compared with a commercial genetic algorithm and a hybrid VNS approach on real instances arising in a Dutch hospital. The comparison results demonstrate that our hybrid approach combines the advantages of both the IP and the VNS to beat other approaches in solving this type of problems. We also believe that the proposed methodology can be applied to other resource allocation problems with a large number of constraints.     

A mixed integer programming model for multistage mean–variance post-tax optimization

In this paper, we introduce a mixed integer stochastic programming approach to mean–variance post-tax portfolio management. This approach takes into account of risk in a multistage setting and allows general withdrawals from original capital. The uncertainty on asset returns is specified as a scenario tree. The risk across scenarios is addressed using the probabilistic approach of classical stochastic programming. The tax rules are used with stochastic linear and mixed integer quadratic programming models to compute an overall tax and return-risk efficient multistage portfolio. The incorporation of the risk term in the model provides robustness and leads to diversification over wrappers and assets within each wrapper. General withdrawals and risk aversion have an impact on the distribution of assets among wrappers. Computational results are presented using a study with different scenario trees in order to show the performance of these models.     

A Stochastic Programming Model for Currency Option Hedging

In this paper we use a stochastic programming approach to develop currency option hedging models which can address problems with multiple random factors in an imperfect market. The portfolios considered in our model are rebalanced at the end of each time period, and reinvestments are allowed during the hedging process. These sequential decisions (reinvestments) are based on the evolution of random parameters such as exchange rates, interest rates, etc. We also allow the inclusion of a variety of instruments in the hedging portfolio, including short term derivative securities, short term options, and futures. These instruments help generate strategies that provide good liquidity and low trade intensity. One of the important features of the model is that it incorporates constraints on sensitivity measures such as Delta and Gamma. By ensuring that these hedge parameters track a desired trajectory (e.g., the parameters of a target option), the new model provides investment strategies that are robust with respect to the perturbations measured by Delta and Gamma. In order to manage the explosion of scenarios due to multiple random factors, we incorporate sampling within a scenario aggregation algorithm. We illustrate that when compared with other myopic hedging methods in imperfect markets, the new stochastic programming model can provide better performance. Our examples also illustrate stochastic programming as a practical computational tool for realistic hedging problems.     

标准化风险度量与投资决策的双目标优化

标准化风险度量(SRM)作为投资中的一种新的风险度量，其较传统风险度量的优点及在投资项目比较中特有的优良性质已被证明，本文导出SRM在概率意义下的一种重要的等价形式，并以此为基础建立以标准化风险(SR)为目标或约束的投资决策优化方法，该方法的核心是将以SRM为风险度量的优化问题转化为线性规划问题的优化技术，此技术结合利用统计抽样数据，可优化含有大量金融工具的投资组合，本文在考虑交易成本的情形下建立了最小化投资的标准化风险的同时最大化其期望有效回报(EER)的双目标优化模型，最后，具体考虑了上证30指数股票组合的优化以说明所建议的方法及模型的应用并实证它们的可行、合理及优良性，其中统计抽样基于近期历史数据。     

Stochastic dual dynamic programming applied to nonconvex hydrothermal models

In this paper we apply stochastic dual dynamic programming decomposition to a nonconvex multistage stochastic hydrothermal model where the nonlinear water head effects on production and the nonlinear dependence between the reservoir head and the reservoir volume are modeled. The nonconvex constraints that represent the production function of a hydro plant are approximated by McCormick envelopes. These constraints are split into smaller regions and the McCormick envelopes are used for each region. We use binary variables for this disjunctive programming approach and solve the problem with a decomposition method. We resort to a variant of the L-shaped method for solving the MIP subproblem with binary variables at any stage inside the stochastic dual dynamic programming algorithm. A realistic large-scale case study is presented.     

Decision making under uncertainty: A semi-infinite programming approach

The subject of this paper is the formulation and discussion of a semi-infinite linear vector optimization problem which extends multiple objective linear programming problems to those with an infinite number of objective functions and constraints. Furthermore it generalizes in some way semi-infinite programming. Besides the statement of some immediately derived results which are related to known results in semi-infinite linear programming and vector optimization, the problem mentioned above is interpreted as a decision model, under risk or uncertainty containing continuous random variables. Thus we treat the case of an infinite number of occuring states of nature. These types of problems frequently occur within aspects of decision theory in management science.     

Portfolio construction on the Athens Stock Exchange: a multiobjective optimization approach

In this research article, our purpose is to propose a single-period multiobjective mixed-integer programming model for equity portfolio construction, in order to generate the Pareto optimal portfolios, using a variant of the well-known ε-constraint method. The decision maker's investment policy, i.e. constraints regarding the portfolio structure, is strongly taken into account. An illustrative application in the Athens Stock Exchange market is also presented.     

An approach to the valuation and decision of ERP investment projects based on real options

The risks and uncertainties inherent in most enterprise resources planning (ERP) investment projects are vast. Decision making in multistage ERP projects investment is also complex, due mainly to the uncertainties involved and the various managerial and/or physical constraints to be enforced. This paper tackles the problem using a real-option analysis framework, and applies multistage stochastic integer programming in formulating an analytical model whose solution will yield optimum or near-optimum investment decisions for ERP projects. Traditionally, such decision problems were tackled using lattice simulation or finite difference methods to compute the value of simple real options. However, these approaches are incapable of dealing with the more complex compound real options, and their use is thus limited to simple real-option analysis. Multistage stochastic integer programming is particularly suitable for sequential decision making under uncertainty, and is used in this paper and to find near-optimal strategies for complex decision problems. Compared with the traditional approaches, multistage stochastic integer programming is a much more powerful tool in evaluating such compound real options. This paper describes the proposed real-option analysis model and uses an example case study to demonstrate the effectiveness of the proposed approach.