ON FUZZY GOAL PROGRAMMING*

This paper illustrates how the goal programming problem with fuzzy goals having linear membership functions may be formulated as a single goal programming problem. Also, a previously defined method for dealing with fuzzy weights for each of the goals is re-examined.     

Application of fuzzy goal programming technique to land use planning in agricultural system

This paper presents how fuzzy goal programming can be efficiently used for modelling and solving land-use planning problems in agricultural systems for optimal production of several seasonal crops in a planning year. In the model formulation of the problem, utilization of total cultivable land, supply of productive resources, aspiration levels of various production of crops as well as the total expected profit from the farm are fuzzily described. In the decision-making situation, minimization of the under-deviational variables of the membership goals with highest membership value (unity) as their achievement levels defined for the membership functions of the fuzzy goals of the problem on the basis of the priorities of importance of achieving the aspired levels of the fuzzy goals to the extent possible is considered. As a study region, the District Nadia, West Bengal, India is taken into account. To expound the potential use of the approach, the model solution is compared with the existing cropping plan of the District as well as a solution of the problem obtained by using the additive fuzzy goal programming model studied by Tiwari et al. (Fuzzy sets and systems 24(1987)27.) previously.     

ON THE (RE)DISCOVERY OF FUZZY GOAL PROGRAMMING

An earlier paper and subsequent commentaries in Decision Sciences described purportedly new methods for formulating and solving goal programming problems with fuzzy goals. This note suggests that much of what these articles propose is but a rediscovery of well-known results.     

A goal programming model for paper recycling system

The conflict between economic optimization and environmental protection has received wide attention in recent research programs for waste management system planning. This has also resulted in a set of new waste management goals in reverse logistics system planning. The purpose of this analysis is to formulate a mixed integer goal programming (MIGP) model to assist in proper management of the paper recycling logistics system. The model studies the inter-relationship between multiple objectives (with changing priorities) of a recycled paper distribution network. The objectives considered are reduction in reverse logistics cost; product quality improvement through increased segregation at the source; and environmental benefits through increased wastepaper recovery. The proposed model also assists in determining the facility location, route and flow of different varieties of recyclable wastepaper in the multi-item, multi-echelon and multi-facility decision making framework. The use of the model has been illustrated through a problem of paper recycling in India.     

Financial planning using goal programming

Financial planners within industrial organizations are often given the impossible task of formulating a multi-year financial plan which is severely over-constrained. As the planner attempts to meet one objective another variable (or ratio of variables) becomes unacceptable and he is faced with the familiar ‘balloon squeezing’ effect. The problem is one of multiple conflicting objectives (goals) hence lends itself very well to a goal programming method of solution. This approach provides a powerful ‘what-if’ device for the financial planner and allows him to arrive at a satisfactory solution by examining the various trade-offs among the conflicting goals. To be an effective and usable tool, the individual goals are not assigned a priority coefficient as is typical of most goal programming applications. Rather, the planner can reflect his priorities in the manner in which he performs the subsequent what-if analyses. Also, a more flexible penalty function is introduced allowing the planner to assign a more realistic set of penalities which vary in severity over a specified range. Methods of implementing this concept are discussed which overcome the problems created by the immense storage requirements and the necessity of assigning the various penalties.     

A survey of goal programming

In this paper the applications of goal programming to industrial and economic planning are reviewed, and it is shown how the linear programming framework can be extended to include a series of goals (or objectives). A planning method is suggested in which the decision maker is presented with a list of all the possible attainable goals from which he picks the most appropriate set.     

WARRANTY COST ESTIMATION: A GOAL PROGRAMMING APPROACH

This paper proposes a goal programming approach to the warranty cost estimation problem. Past research on this topic has mostly dealt with a single objective—the minimization of the warranty reserve cost or the maximization of profit. A more realistic approach to warranty cost problems could, however, involve several goals, some of which might be conflicting to others. In this paper, three goals are prioritized. The goals considered are minimization of warranty reserve cost per unit, offering a minimum level of warranty time based on an allowable proportion of failures within the warranty period, and capturing a minimum specified market share of the product. An example is illustrated using the proposed formulation, and goal achievements are discussed.     

多专家判断的模糊偏好信息集结规划方法

本文给出了一种群决策中通过专家判断矩阵集结专家判断信息的方法。在考虑各专家具有不同强度的偏好效用和容许部分专家给出不完整信息的情况下,将专家判断信息集结转化为一类模糊规划问题,通过最大化群组满意度获得最终的群决策结果。最后,本文通过一个算例说明该方法的可行性及有效性。     

Governmental planning and budgeting with multiple objective models

This paper presents a goal programming model development and application for a state level public health care agency. Only limited applications of macro planning processes related to health care have been presented in the literature. In that regard, this paper describes briefly the goal programming model, the background of the agency involved and the specific models developed. Three formulations of the model are presented involving (1) the resources required to achieve all goals, (2) the goal attainment status utilizing a likely budget and (3) a proposal for resolving the goal desire-resource limitation dilemma.     

OPTIMIZING ORGANIZATIONAL GOALS IN ASSIGNING FACULTY TEACHING SCHEDULES

The administration of higher education, as with other administrative environments, has become increasingly complex. This paper presents a mathematical model which addresses one of the administrative tasks concerning administrators in all institutions, the establishment of faculty teaching schedules. The assignment technique utilized by the model is linear programming with two special characteristics: goal programming and mixed-integer programming. The goal programming characteristic refers to the provision of explicit stack variables to take on values representing deviations from assignment criteria that may result in resolving conflicts which arise from interactive administrative priorities. The mixed-integer programming characteristic refers to a requirement of the model that certain variables take on only integer values if they appear in the final solution. The model is demonstrated using two different sets of preference orderings for goal achievement.     

Interactive fuzzy goal programming for multi-objective transportation problems

This paper presents an interactive fuzzy goal programming approach to determine the preferred compromise solution for the multi-objective transportation problem. The proposed approach considers the imprecise nature of the input data by implementing the minimum operator and also assumes that each objective function has a fuzzy goal. The approach focuses on minimizing the worst upper bound to obtain an efficient solution which is close to the best lower bound of each objective function. The solution procedure controls the search direction via updating both the membership values and the aspiration levels. An important characteristic of the approach is that the decision maker's role is concentrated only in evaluating the efficient solution to limit the influences of his/her incomplete knowledge about the problem domain. In addition, the proposed approach can be applied to solve other multi-objective decision making problems. The performance of this solution approach is evaluated by comparing its results with that of the two existing methods in the literature.     

Matrix games with fuzzy goals and fuzzy payoffs

A two person zero sum matrix game with fuzzy goals and fuzzy payoffs is considered and its solution is conceptualized using a suitable defuzzification function. Also, it is proved that such a game is equivalent to a primal–dual pair of certain fuzzy linear programming problems in which both goals as well as parameters are fuzzy.     

基于模糊规划法的企业价值链优化应用研究

本文通过阐述企业价值链的结构和优化目标,分析了模糊规划方法对于价值链优化研究的必要性,建立了企业价值链优化的模糊线性规划模型,并以轿车企业价值链为例给出了数值算例和结果分析,从企业在价值链优化方法的应用研究方面证明了方法的实用性。     

基于三角直觉模糊数Choquet积分算子的多属性决策方法

定义了三角直觉模糊数的Hamming距离,给出了属性独立情形下的三角直觉模糊数算术集成算子,并运用模糊测度和Choquet积分,定义了三角直觉模糊Choquet积分算子,并分析其有关性质。针对方案评价信息为三角直觉模糊数的关联多属性决策问题,利用三角直觉模糊Choquet积分算子集成得到方案的综合属性值,建立多目标优化模型并转化为线性目标规划求解,客观地确定了属性集的模糊测度,进而提出了相应的决策方法。实例分析表明了方法的有效性和合理性。     

INTEGER GOAL PROGRAMMING IN ADVERTISING MEDIA SELECTION

The media selection decision allocates advertising dollars among competing media so as to optimize promotional and corporate objectives. Linear programming attempts to model this process have been complicated by multiple and often conflicting management goals, the need for integer solutions, and nonlinearities. This study offers a technique that is sufficiently robust to simultaneously handle these problems. An alternative media selection framework is presented and the results of an illustrative application of integer goal programming are discussed. The proposed model improves on linear programming by success fully providing for optimal, integer solutions in settings that more realistically reflect the complexity of the media decision environment.     

An approachto the machine layout problem in a cellular manufacturing environment

The model of the machine layout problem MLP in a cellular manufacturing environment attains additional dimensions as it should satisfy the qualitative interconnections between the machines and the location restrictions of an existing factory environment. A new MLP model based on merging pre-emptive goal programming and simulated annealing has been developed for machine layout in cells. This model seeks to find feasible solutions by addressing practical issues of implementation as well as reducing the total travel distances for parts between machines. The new model can also be applied to facility layout problems FLP . The computational work is demonstrated by applying the model to problems of both quantitative and qualitative types, and has produced encouraging results. This model is particularly attractive for layout problems with realistic goals and constraints. To show the performance of the model in handling real-world problems, a practical example has been introduced and solved using the proposed model.     

基于模糊熵的人力资源结构优化配置

本文提出基于模糊熵的人力资源结构优化配置方法,并对现有人力资源结构合理性和协调性程度进行了科学评价。     

一种新的梯形模糊数互补判断矩阵的排序方法

研究了决策信息以梯形模糊数互补判断矩阵形式给出的有限方案决策问题。首先利用COWA算子,引入期望值函数概念对梯形模糊数来排序,排序结果可以根据决策者的乐观程度进行调节,更加合理。然后基于期望值函数,把梯形模糊数互补判断矩阵转化期望值互补判断矩阵进行排序,并利用决策者的乐观程度对排序结果进行敏感性分析。最后通过算例说明了该方法的可行性和有效性。     

多品种集约生产计划问题的模糊方法

提出具有模糊需求量和模糊能力约束以及资本水平约束的多品种类集约生产计划问题 的模糊优化模型及模糊解方法. 通过对模糊需求量和模糊等式的描述,提出了模糊需求环境下 生产- 库存平衡方程的两种等价的描述方法, 并给出了模糊等式的实用解释. 建立了具有模 糊需求量和模糊能力约束集约生产计划问题的优化模型FMAPP ,并给出了求解模型的参数规 划方法.     

Applying consistent fuzzy preference relations to partnership selection

Partnership selection has been important to the formation of a virtual enterprise. Based on the fuzzy preference programming (FPP) method proposed by Mikhailov [Fuzzy analytical approach to partnership selection in formation of virtual enterprises. Omega 2002;30:393–401], this investigation presents a consistent fuzzy preference relations method to select partners. Human thoughts are full of uncertainty, so the decision-makers cannot make exact pairwise comparisons. The FPP method solves this problem using an interval value instead of Saaty's 1–9 scale. In this study, the FPP method is reviewed, and then the consistent fuzzy preference relations method is elucidated. Finally, the presented method is applied to the example addressed by Mikhailov [Fuzzy analytical approach to partnership selection in formation of virtual enterprises. Omega 2002;30:393–401]. This study reveals that the proposed method yields consistent decision rankings from only n-1$n-1$ pairwise comparisons—the same number as in Mikhailov's research. Briefly, the presented consistent fuzzy preference relations method is an easy and practical way to provide rankings of partnership in making decision.