一类多目标模糊系数线性规划问题

讨了一类所系数均为模糊数的多目标线性规划问题，通过对模糊数的比较，将模糊多目标线性规划模型转化为清晰的多目标模型，并应用一种基于线性隶属函数的模糊规划算法求其协调解，最后给出了一个数值例子。     

具有模糊系数约束的多目标线性规划

研究了一类具有模糊系数约束的多目标线性规划问题．根据各目标函数的梯度方向来量化目标之间的冲突程度．以此提出了一种确定目标权重的新方法，然后基于惩罚函数运用梯度上升算法求问题的有效解．最后给出了一个数值例子。     

一类变量为梯形模糊数的线性规划

针对变量为梯形模糊数的模糊线性规划问题,利用结构元方法定义了一种模糊数的排序准则,讨论了如何将变量是梯形模糊数的线性规划去模糊化,即将含有变量为梯形模糊数的模糊线性规划转化为经典模糊线性规划.同时,证明了该模型的最优解等价于经典的线性规划的最优解,再利用单纯形法求出最优解.并设计了求解该类模型的算法.通过算例验证了该方法的可行性和算法的有效性,从而为变量模糊的广义模糊线性规划问题的研究提供了新的方法.     

多产品供应商选择的模糊多目标整数规划模型

以成本、质量、交货为目标,考虑供应商供应能力、采购数量、供应数量的柔性、评价等级等约束,建立了多产品供应商选择的模糊多目标规划模型.采用降半梯形分布的隶属度函数将模糊多目标规划模型转化为单目标线性规划并求解,应用算例证明了模型的有效性和可行性.     

一种变量是梯形模糊数的两层多随从线性规划模型及其算法

针对具有递阶特征的多层管理系统,本文建立了一种变量为梯形模糊数的两层多随处线性规划模型.利用模糊结构元理论,通过模糊数的结构元加权序,将梯形模糊数的排序转化为单调有界函数的排序,从而证明了该模型的最优解等价于两层多随处线性规划模型的最优解;进而提出了求解该模型的有效算法.最后,通过两个数值算例验证了该方法的可行性.     

基于模糊理论的机械多目标优化设计

多目标优化设计各分目标间的矛盾性和不可公度性增加了解决问题的难度,常规求解多目标优化设计方法一般只能求出问题的有效解,而得不到设计的最优结果。该文以蜗杆传动多目标优化设计为例,采用改进的遗传算法求得若干有效解后,根据模糊理论中的相似优先比法从中确定出最有效解,即最优解,并可排出它们的优劣顺序。     

带有积压定单的最优模糊存储模型

本文提出一个新的具有积压定单的关于模糊总需求的模糊存储模型。在模糊函数原理下，给出了模糊总存储成本。为了寻找最优解，使用积分均值法白化模糊总存储成本，利用Lingo8．0求解不等式约束问题，我们发现最优解都是确定的实数。此外，当模糊总需求是确定的实数时，我们提出模型的最优解与经典的具有积压定单存储模型具有相同的结果。     

导管架海洋平台结构模糊优化设计

考虑约束条件边界的模糊性,建立了导管架海洋平台结构模糊优化设计模型。对模糊优化模型中的设计变量、目标函数和约束条件进行了模糊处理。针对导管架海洋平台的特点,用模糊优选法确定约束条件边界容差系数,由界限搜索法求解模糊约束集和模糊目标集之交集的最优水平截集*l,进而求得模糊优化问题的最优解。以胜利油田埕北11#井采油平台为例进行了模糊优化设计,并与确定性优化设计相比较,分析了两种优化设计中设计变量的走向及原因,算例结果还显示目标函数值比确定性优化设计值有较大幅度下降,说明考虑模糊因素进行优化设计的可行性和科学性。     

求解模糊线性规划问题的一种解法

本文首先建立一类模糊线性规划问题的对偶问题,利用求解对偶问题,得到原规划问题的最优解。由于将模糊向量转移到目标函数中去,因而初始可行基只计算一次,从而可压缩计算量,文中给出了一般计算步骤和数值例子,并对两种算法进行了比较,结果表明新算法计算量小。 文中还证明了原规划与对偶规划的最优判决相等。     

含模糊服务水平的可控提前期供应链库存优化

在文献"含服务水平约束的可控提前期供应链Stackelberg模型与协调机制研究"(管理学报,2008)的基础上,进一步将服务水平约束看作一个模糊数,进而探讨具有模糊服务水平约束的可控提前期供应链库存优化问题,并采用模糊非线性规划的方法进行求解。采用数值实验方法,对所建的库存优化模型进行了分析,结果表明:最优订货批量、提前期、供应链各方库存成本和获得该成本的隶属度水平均随对模糊服务水平弹性区间的不同主观估计变化而变化。但当模糊服务水平弹性区间增大到一定程度时,会出现服务水平约束无效的情形,则最优订货决策,库存总成本,及获得该成本的隶属度均不会再发生变化。     

A fully fuzzified,intelligent theory-of-constraints product-mix decision

The present research work outlines a fuzzified approach using fuzzy linear programming (FLP) using a suitably designed smooth logistic membership function (MF) for finding fuzziness patterns at disparate levels of satisfaction for theory of constraints-based (TOC) product-mix decision problems. The objective of the present work is to find fuzziness patterns of product-mix decisions with disparate levels of satisfaction of the decision-maker (DM). Another objective is to provide a robust, quantified monitor of the level of satisfaction among DMs and to calibrate these levels of satisfaction against DM expectations. Product-mix decision should take into account considerations such as the DM's level of satisfaction (sometimes called ‘emotions’) in order to make the decision a robust one. Sensitivity of the decision has been focused on a bottleneck-free, optimal product-mix solution of a TOC problem. The inefficiency of traditional linear programming (LP) in handling multiple-bottleneck problems using TOC is discussed using an illustrative example. Relationships among the degree of fuzziness, level of satisfaction and the throughput of modified TOC guide decision-makers (DM) under tripartite fuzzy environment in obtaining their product-mix choice trading-off with a pre-determined allowable fuzziness.     

A rolling horizon approach for material requirement planning under fuzzy lead times

This paper proposes a fuzzy multi-objective integer linear programming (FMOILP) approach to model a material requirement planning (MRP) problem with fuzzy lead times. The objective functions minimise the total costs, back-order quantities and idle times of productive resources. Capacity constraints are included by considering overtime resources. Into the crisp MRP multi-objective model, we incorporate the possibility of occurrence of each uncertain lead time using fuzzy numbers. Then FMOILP is transformed into an auxiliary crisp mixed-integer linear programming model by a fuzzy goal programming approach for each fuzzy lead time combination. In order to defuzzify the set of solutions associated with each fuzzy lead time combination, a solution method based on the centre of gravity concept is addressed. Model validation with a numerical example is carried out by a novel rolling horizon procedure where uncertain lead times are updated during each planning period according to the centre of gravity obtained. For illustration purposes, the proposed solution approach is satisfactorily compared to a rolling horizon approach in which lead times are allocated when the possibility of occurrence is established at one.     

Multi-objective mixed integer programming and an application in a pharmaceutical supply chain

Multi-objective integer linear and/or mixed integer linear programming (MOILP/MOMILP) are very useful for many areas of application as any model that incorporates discrete phenomena requires the consideration of integer variables. However, the research on the methods for the general multi-objective integer/mixed integer model has been scant when compared to multi-objective linear programming with continuous variables. In this paper, an MOMILP is proposed, which integrates various conflicting objectives. We give importance to the imprecise nature of some of the critical factors used in the modelling that can influence the effectiveness of the model. The uncertainty and the hesitation arising from estimating such imprecise parameters are represented by intuitionistic fuzzy numbers. The MOMILP model with intuitionistic fuzzy parameters is first converted into a crisp MOMILP model, using appropriate defuzzification strategies. Thereafter, the MOMILP is transformed into a single objective problem to yield a compromise solution with an acceptable degree of satisfaction, using suitable scalarisation techniques such as the gamma-connective technique and the minimum bounded sum operator technique. The proposed solution method is applied to several test problems and a multi-objective pharmaceutical supply chain management model with self generated random data.     

Parametrization of a generalized linear and piece-wise linear programme

In this paper we consider a generalized linear and piece-wise linear programming problem for parametrization of its objective function. The interest is to determine the influence of the parameters on the stability of the optimal solution and on the optimal value of the objective function, and also to suggest a method for a step by step determination of optimal solutions. S. S. Chadha: Department of Mathematics, Hans Raj College, Delhi-7, India.     

Fuzzy Regression Analysis by Quadratic Programming Reflecting Central Tendency

In this paper, we propose fuzzy regression analysis based on a quadratic programming approach. In fuzzy regression analysis, a quadratic programming approach gives more diverse spread coefficients than a linear programming approach. Moreover, a quadratic programming approach can integrate the central tendency of least squares and the possibilistic properties of fuzzy regression. Due to the characteristic of the quadratic programming problem, the proposed approach can obtain the optimal regression model representing possibilistic properties with the central tendency. In this approach, we classify the given data into two groups, i.e., the center-located group and the remaining group. Then, the upper and the lower approximation models can be obtained based on the classification result. By changing the weight coefficients of the objective function in the quadratic programming problem, we can analyze the given data in various angles.

     

A fuzzy linear programming approach for municipal solid-waste management under uncertainty

In this study, a fuzzy linear programming (FLP) method is developed for dealing with uncertainties expressed as fuzzy sets that exist in the constraints’ left-hand and right-hand sides and the objective function. A direct transforming algorithm is advanced for solving the FLP model that improves upon the existing method through provision of a quantitative expression for uncertain relationships among a large number of fuzzy sets. The proposed solution method can greatly reduce computational requirements, which is particularly meaningful for the application of FLP to large-scale practical problems with many fuzzy sets. The developed FLP method is applied to a case of long-term waste-management planning. The results indicate that reasonable solutions have been obtained. They can be used for generating decision alternatives and to help managers identify desired policies for waste management under uncertainty. Compared with the conventional interval-parameter linear programming approach, FLP can provide more information for solutions, containing not only the lower and upper bounds but also the most possible value for decision variables and objective function.     

多阶段系统多目标优化的模糊优选动态规划方法及应用

在模糊权距离和隶属度概念的基础上,根据多阶段系统前后阶段联系特点,将模糊优选理论与动态规划原理有机地结合起来,提出能够有效地寻求多阶段多目标优化问题的最优均衡策略的模糊优选动态规划技术。为求解多目标多阶段系统的优化决策问题提供了新路。最后例举一个多级反应器系统最优控制的应用算例。     

Multi-objective optimization of fuzzy structural systems

It is recognized that there exists a vast amount of fuzzy information in both the objective and constraint functions of the optimum design of structures. Since most practical structural design problems involve several, often conflicting, objectives to be considered, a multi-objective fuzzy programming method is outlined in this work. The fuzzy constraints define a fuzzy feasible domain in the design space and each of the fuzzy objective functions defines the optimum solution by a fuzzy set of points. A method of solving a fuzzy multi-objective structural optimization problem using ordinary single-objective programming techniques is presented. The computational approach is illustrated with two numerical examples.     

Development of an optimal core steel slitting and inventory policy

The objective of this investigation is to develop an optimal slitting and inventory policy for a deterministic demand of steel over a finite planning horizon. The cost function includes the inventory carrying cost and the cost of scrap steel generated besides the usual fixed costs. The minimum of this cost function is obtained by using a combination of dynamic programming and integer linear programming which provides a practical and sound procedure. Actual data is used to determine the optimal solution for a planning horizon of ten weeks.     

A generalized interval fuzzy mixed integer programming model for a multimodal transportation problem under uncertainty

A generalized interval fuzzy mixed integer programming model is proposed for the multimodal freight transportation problem under uncertainty, in which the optimal mode of transport and the optimal amount of each type of freight transported through each path need to be decided. For practical purposes, three mathematical methods, i.e. the interval ranking method, fuzzy linear programming method and linear weighted summation method, are applied to obtain equivalents of constraints and parameters, and then a fuzzy expected value model is presented. A heuristic algorithm based on a greedy criterion and the linear relaxation algorithm are designed to solve the model.