具有模糊三角要素的机会约束型DEA模型

确定性 DEA是一种数据敏感的评价方法 ,在某些不利情况下 ,数据的轻微变动将极大的影响评价结果 .针对这一不足 ,根据模糊机会约束规划的理论框架 ,基于 C2 R模型 ,建立了具有模糊三角要素的机会约束型 DEA模型 ( FCCPDEA) ,用机会约束来描述这一不确定性 .在 FCCPDEA模型中 ,从令决策者满意的角度出发 ,用决策者期望各决策单元能达到的最大效率 ,即效率基数 ,来代替理想效率 1,使评价更符合现实 .     

Two-storage inventory model with lot-size dependent fuzzy lead-time under possibility constraints via genetic algorithm

Multi-item inventory models with stock dependent demand and two storage facilities are developed in a fuzzy environment where processing time of each unit is fuzzy and the processing time of a lot is correlated with its size. These are order-quantity reorder-point models with back-ordering if required. Here possibility and crisp constraints on investment and capacity of the small storehouse respectively are considered. The models are formulated as fuzzy chance constrained programming problem and is solved via generalized reduced gradient (GRG) technique when crisp equivalent of the constraints are available. A genetic algorithm (GA) is developed based on fuzzy simulation and entropy where region of search space gradually decreases to a small neighborhood of the optima and it is used to solve the models whenever the equivalent crisp form of the constraint is not available. The models are illustrated with some numerical examples and some sensitivity analyses have been done. For some particular cases results observed via GRG and GA are compared.     

基于模糊机会约束规划的最优产量决策

研究了模糊环境下,双寡头市场中两企业的最优产量决策问题。在四种博弈结构下,结合Cournot模型、Stackelberg模型以及模糊可能性理论,建立了模糊机会约束规划模型来确定两企业的最优产量水平。最后通过一个算例说明,基于市场的最大收益,最优决策应为两企业均为追随者。     

A note on chance constrained programming with fuzzy coefficients

This paper deals with nonlinear chance constrained programming as well as multiobjective case and goal programming with fuzzy coefficients occurring in not only constraints but also objectives. We also present a fuzzy simulation technique for handling fuzzy objective constraints and fuzzy goal constraints. Finally, a fuzzy simulation based genetic algorithm is employed to solve a numerical example.     

Some Aspects of Stability in Stochastic Programming

Some developments in structure and stability of stochastic programs during the last decade together with interrelations to optimization theory and stochastics are reviewed. With weak convergence of probability measures as a backbone we discuss qualitative and quantitative stability of recourse models that possibly involve integer variables. We sketch stability in chance constrained stochastic programming and provide some applications in statistical estimation. Finally, an outlook is devoted to issues that were not discussed in detail and to some open problems.     

An algebraic geometry algorithm for scheduling in presence of setups and correlated demands

We study here a problem of schedulingn job types onm parallel machines, when setups are required and the demands for the products are correlated random variables. We model this problem as a chance constrained integer program.Methods of solution currently available—in integer programming and stochastic programming—are not sufficient to solve this model exactly. We develop and introduce here a new approach, based on a geometric interpretation of some recent results in Gröbner basis theory, to provide a solution method applicable to a general class of chance constrained integer programming problems.Out algorithm is conceptually simple and easy to implement. Starting from a (possibly) infeasible solution, we move from one lattice point to another in a monotone manner regularly querying a membership oracle for feasibility until the optimal solution is found. We illustrate this methodology by solving a problem based on a real system.Corresponding author.     

A new methodology for crisp equivalent of fuzzy chance constrained programming problem

This paper deals with a chance constrained programming model, where both fuzziness and randomness are present in the objective function and constraints. The concept of fuzzy random variable, mean and variance of fuzzy random variable, minimum of fuzzy numbers are used in the model. The methodology is verified through a numerical example.     

Chance constrained programming models for refinery short-term crude oil scheduling problem

The main objective of this work is to put forward chance constrained mixed-integer nonlinear stochastic and fuzzy programming models for refinery short-term crude oil scheduling problem under demands uncertainty of distillation units. The scheduling problem studied has characteristics of discrete events and continuous events coexistence, multistage, multiproduct, nonlinear, uncertainty and large scale. At first, the two models are transformed into their equivalent stochastic and fuzzy mixed-integer linear programming (MILP) models by using the method of Quesada and Grossmann [I. Quesada, I E. Grossmann, Global optimization of bilinear process networks with multicomponent flows, Comput. Chem. Eng. 19 (12) (1995) 1219–1242], respectively. After that, the stochastic equivalent model is converted into its deterministic MILP model through probabilistic theory. The fuzzy equivalent model is transformed into its crisp MILP model relies on the fuzzy theory presented by Liu and Iwamura [B.D. Liu, K. Iwamura, Chance constrained programming with fuzzy parameters, Fuzzy Sets Syst. 94 (2) (1998) 227–237] for the first time in this area. Finally, the two crisp MILP models are solved in LINGO 8.0 based on scheduling time discretization. A case study which has 267 continuous variables, 68 binary variables and 320 constraints is effectively solved with the solution approaches proposed.     

A hybrid intelligent algorithm for portfolio selection problem with fuzzy returns

Portfolio selection theory with fuzzy returns has been well developed and widely applied. Within the framework of credibility theory, several fuzzy portfolio selection models have been proposed such as mean–variance model, entropy optimization model, chance constrained programming model and so on. In order to solve these nonlinear optimization models, a hybrid intelligent algorithm is designed by integrating simulated annealing algorithm, neural network and fuzzy simulation techniques, where the neural network is used to approximate the expected value and variance for fuzzy returns and the fuzzy simulation is used to generate the training data for neural network. Since these models are used to be solved by genetic algorithm, some comparisons between the hybrid intelligent algorithm and genetic algorithm are given in terms of numerical examples, which imply that the hybrid intelligent algorithm is robust and more effective. In particular, it reduces the running time significantly for large size problems.     

区域废弃物网络系统的选址-运输优化模型

区域废弃物网络系统优化设计包括设施的选址和废弃物运输路线的确定。考虑了多类型设施、多种废弃物流和模糊数形式的废弃物产生量,建立了模糊机会约束规划模型来求得整个系统的优化配置。通过将模型中的机会约束清晰化,将模糊机会约束规划模型转化成等价的确定模型来求解。实例表明了模型的有效性。     

A Class of Chance Constrained Multi-objective Portfolio Selection Model Under Fuzzy Random Environment

This paper deals with a class of chance constrained portfolio selection problems in the fuzzy random decision making system. An integrated fuzzy random portfolio selection model with a chance constraint is proposed on the basis of the mean-variance model and the safety-first model. According to different definitions of chance, we consider two types of fuzzy random portfolio selection models: one is for the optimistic investors and the other is for the pessimistic investors. In order to deal with the fuzzy random models, we develop a few theorems on the variances of fuzzy random returns and the equivalent partitions of two types of chance constraints. We then transform the fuzzy random portfolio selection models into their equivalent crisp models. We further employ the ε-constraint method to obtain the efficient frontier. Finally, we apply the proposed models and approaches to the Chinese stock market as an illustration.     

一类系数为梯形模糊数的整数规划

介绍了模糊数学和整数规划的背景、现状、以及发展趋势,并以模糊结构元理论定义了梯形模糊加权序,进一步证明了模糊整数规划模型的最优解等价于整数规划模型的最优解,再利用整数规划模型的最优解的求解方法求解模糊整数规划模型的最优解,最后,通过算例验证方法的可行性.     

Multi-objective stochastic programming for portfolio selection

Generally, in the portfolio selection problem the Decision Maker (DM) considers simultaneously conflicting objectives such as rate of return, liquidity and risk. Multi-objective programming techniques such as goal programming (GP) and compromise programming (CP) are used to choose the portfolio best satisfying the DM’s aspirations and preferences. In this article, we assume that the parameters associated with the objectives are random and normally distributed. We propose a chance constrained compromise programming model (CCCP) as a deterministic transformation to multi-objective stochastic programming portfolio model. CCCP is based on CP and chance constrained programming (CCP) models. The proposed program is illustrated by means of a portfolio selection problem from the Tunisian stock exchange market.     

不同风险态度下的三层供应链集成优化

研究了在决策者不同风险态度下的由供应商、分销商和零售商组成三层供应链集成优化问题。考虑供应链中价格、质量、交货、需求和供应的不确定风险因素为模糊变量,应用可信性理论建立了模糊机会约束规划模型,可信性测度的置信水平代表了决策者的风险偏好程度。使用模糊变量的乐观值和悲观值将机会约束转化为清晰的等价形式。最后,通过数值算例分析了决策者的风险态度的变化对集成供应链的影响。     

模糊环境下动态供应商选择的混合整数非线性规划模型

基于供应商选择问题的动态性和模糊性,考虑在每个周期内生产商的需求能力及供应商的供应能力为模糊变量,本文将一个多阶段多商品多渠道的供应商选择问题视为一个0-1混合整数模糊动态非线性规划问题,目标函数为总成本最小化。然后建立了0-1混合整数模糊动态非线性规划模型。为了求解该模型,通过可信性理论把模型中模糊机会约束清晰化,将该模型转化为一个确定型的0-1混合整数动态非线性规划模型。最后给出了一个数值算例验证了模型的可行性。     

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.     

Stochastic chance constrained mixed-integer nonlinear programming models and the solution approaches for refinery short-term crude oil scheduling problem

Stochastic chance constrained mixed-integer nonlinear programming (SCC-MINLP) models are developed in this paper to solve the refinery short-term crude oil scheduling problem which concerns crude oil unloading, mixing, transferring and multilevel inventory control under demands uncertainty of distillation units. The objective of these models is the minimum expected value of total operation cost. It is the first time that the uncertain demands of Crude oil Distillation Units (CDUs) in these problems are set as random variables which have discrete and continuous joint probability distributions. This situation is close to the real world industry use. To reduce the computation complexity, these SCC-MINLP models are transformed into their equivalent stochastic chance constrained mixed-integer linear programming models (SCC-MILP). Stochastic simulation and stochastic sampling technologies are introduced in detail to solve these complex SCC-MILP models. Finally, case studies are effectively solved with the proposed approaches.     

A note on second-order stochastic dominance constraints induced by mixed-integer linear recourse

We introduce stochastic integer programs with second-order dominance constraints induced by mixed-integer linear recourse. Closedness of the constraint set mapping with respect to perturbations of the underlying probability measure is derived. For discrete probability measures, large-scale, block-structured, mixed- integer linear programming equivalents to the dominance constrained stochastic programs are identified. For these models, a decomposition algorithm is proposed and tested with instances from power optimization.     

A hybrid differential evolution algorithm to vehicle routing problem with fuzzy demands

In this paper, the vehicle routing problem with fuzzy demands (VRPFD) is considered, and a fuzzy chance constrained program model is designed, based on fuzzy credibility theory. Then stochastic simulation and differential evolution algorithm are integrated to design a hybrid intelligent algorithm to solve the fuzzy chance constrained program model. Moreover, the influence of the dispatcher preference index on the final objective of the problem is discussed using stochastic simulation, and the best value of the dispatcher preference index is obtained.     

约束全局整数规划问题的填充函数法

本文给出了一类新的求解箱约束全局整数规划问题的填充函数，并讨论了其填充性质．基于提出的填充函数，设计了一个求解带等式约束、不等式约束、及箱约束的全局整数规划问题的算法．初步的数值试验结果表明提出的算法是可行的。