A fuzzy goal programming approach to portfolio selection

Portfolio selection is a usual multiobjective problem. This paper will try to deal with the optimum portfolio for a private investor, taking into account three criteria: return, risk and liquidity. These objectives, in general, are not crisp from the point of view of the investor, so we will deal with them in fuzzy terms. The problem formulation is a goal programming (G.P.) one, where the goals and the constraints are fuzzy. We will apply a fuzzy G.P. approach to the above problem to obtain a solution. Then, we will offer the investor help in handling the results.     

Interactive fuzzy goal programming approach for bilevel programming problem

This paper presents an interactive fuzzy goal programming (FGP) approach for bilevel programming problems with the characteristics of dynamic programming (DP).     

Priority based fuzzy goal programming technique to fractional fuzzy goals using dynamic programming

This paper describes the use of preemptive priority based fuzzy goal programming method to fuzzy multiobjective fractional decision making problems under the framework of multistage dynamic programming. In the proposed approach, the membership functions for the defined objective goals with fuzzy aspiration levels are determined first without linearizing the fractional objectives which may have linear or nonlinear forms. Then the problem is solved recursively for achievement of the highest membership value (unity) by using priority based goal programming methodology at each decision stages and thereby identifying the optimal decision in the present decision making arena. A numerical example is solved to represent potentiality of the proposed approach.     

Fuzzy linear programming models for new product design using QFD with FMEA

Quality function deployment (QFD) is a customer-driven approach in processing new product developments in order to maximize customer satisfaction. Determining the fulfillment levels of design requirements (DRs) and parts characteristics (PCs) is an important decision problem during QFD activity processes for new product development. Unlike the existing literature, which mainly focuses on the determination of DRs, this paper proposes fuzzy linear programming models to determine the fulfillment levels of PCs under the requirement to achieve the determined contribution levels of DRs for customer satisfaction. In addition, considering the design risk, this paper incorporates failure modes and effect analysis (FMEA) into QFD processes, which is treated as the constraint in the models. To cope with the vague nature of product development processes, fuzzy approaches are used for both FMEA and QFD. The illustration of the proposed models is performed with a numerical example to demonstrate the applicability in practice.     

Three fuzzy goal programming models for index portfolios

Studies show that most actively managed mutual funds struggle to beat the market, driving an increase in the popularity of index investing. Index investing instruments, including index funds and Exchange-traded Funds, aim to track market performance. This study pursues both tracking error minimization and excess return maximization, two conflicting objectives, to construct an index portfolio. In the real-world financial environment, the desires and expectations of decision makers are generally imprecise. This study applies fuzzy theory to deal with imprecise objectives. This study represents minimizing tracking error and maximizing excess return as ‘fuzzy goals’ to improve traditional goal programming, which is suitable for handling multiple conflicting objectives, but subject to establishing crisp goals. Three fuzzy goal programming (FGP) models that track indexes are compared and discussed, and the results show that through certain membership functions and tracking models, an index tracking portfolio with a tracking error lower than the 0050 index fund, and a similar excess return to 0050 index fund can be constructed using additive type FGP. max-min type FGP underperforms the additive type FGP in index fund construction.     

An interactive fuzzy goal programming approach for multi-period multi-product production planning problem

This study addresses an interactive multiple fuzzy goal programming (FGP) approach to the multi-period multi-product (MPMP) production planning problem in an imprecise environment. The proposed model attempts to simultaneously minimize total production costs, rates of changes in labor levels, and maximizing machine utilization, while considering individual production routes of parts, inventory levels, labor levels, machine capacity, warehouse space, and the time value of money. Piecewise linear membership functions are utilized to represent decision maker’s (DM’s) overall satisfaction levels. A numerical example demonstrates the feasibility of applying the proposed model to the MPMP problem. Furthermore, the proposed interactive approach facilitates the DM with a systematic framework of decision making process which enables DM to modify the search direction to reach the most satisfactory results during solving process.     

Solving multi-level multi-objective linear programming problems through fuzzy goal programming approach

In this paper, two new algorithms are presented to solve multi-level multi-objective linear programming (ML-MOLP) problems through the fuzzy goal programming (FGP) approach. The membership functions for the defined fuzzy goals of all objective functions at all levels are developed in the model formulation of the problem; so also are the membership functions for vectors of fuzzy goals of the decision variables, controlled by decision makers at the top levels. Then the fuzzy goal programming approach is used to achieve the highest degree of each of the membership goals by minimizing their deviational variables and thereby obtain the most satisfactory solution for all decision makers.     

A fuzzy goal programming approach to multi-objective optimization problem with priorities

In goal programming problem, the general equilibrium and optimization are often two conflicting factors. This paper proposes a generalized varying-domain optimization method for fuzzy goal programming (FGP) incorporating multiple priorities. According to the three possible styles of the objective function, the varying-domain optimization method and its generalization are proposed. This method can generate the results consistent with the decision-maker (DM)’s expectation, that the goal with higher priority may have higher level of satisfaction. Using this new method, it is a simple process to balance between the equilibrium and optimization, and the result is the consequence of a synthetic decision between them. In contrast to the previous method, the proposed method can make that the higher priority achieving the higher satisfactory degree. To get the global solution of the nonlinear nonconvex programming problem resulting from the original problem and the varying-domain optimization method, the co-evolutionary genetic algorithms (GAs), called GENOCOPIII, is used instead of the SQP method. In this way the DM can get the optimum of the optimization problem. We demonstrate the power of this proposed method by illustrative examples.     

A fuzzy goal programming approach for mid-term assortment planning in supermarkets

We develop a fuzzy mixed integer non-linear goal programming model for the mid-term assortment planning of supermarkets in which three conflicting objectives namely profitability, customer service, and space utilization are incorporated. The items and brands in a supermarket compete to obtain more space and better shelf level. This model offers different service levels to loyal and disloyal customers, applies joint replenishment policy, and accounts for the holding time limitation of perishable items. We propose a fuzzy approach due to the imprecise nature of the goals’ target levels and priorities as well as critical data. A heuristic method inspiring by the problem-specific rules is developed to solve this complex model approximately within a reasonable time. Finally, the proposed approach is validated through several numerical examples and results are reported.     

Fuzzy goal programming approach to multilevel programming problems

The purpose of this paper is to propose a procedure for solving multilevel programming problems in a large hierarchical decentralized organization through linear fuzzy goal programming approach. Here, the tolerance membership functions for the fuzzily described objectives of all levels as well as the control vectors of the higher level decision makers are defined by determining individual optimal solution of each of the level decision makers. Since the objectives are potentially conflicting in nature, a possible relaxation of the higher level decision is considered for avoiding decision deadlock. Then fuzzy goal programming approach is used for achieving highest degree of each of the membership goals by minimizing negative deviational variables. Sensitivity analysis with variation of tolerance values on decision vectors is performed to present how the solution is sensitive to the change of tolerance values. The efficiency of our concept is ascertained by comparing results with other fuzzy programming approaches.     

Product design and selection using fuzzy QFD and fuzzy MCDM approaches

Quality function deployment (QFD) is a useful analyzing tool in product design and development. To solve the uncertainty or imprecision in QFD, numerous researchers have applied the fuzzy set theory to QFD and developed various fuzzy QFD models. Three issues are investigated by examining their models. First, the extant studies focused on identifying important engineering characteristics and seldom explored the subsequent prototype product selection issue. Secondly, the previous studies usually use fuzzy number algebraic operations to calculate the fuzzy sets in QFD. This approach may cause a great deviation in the result from the correct value. Thirdly, few studies have paid attention to the competitive analysis in QFD. However, it can provide product developers with a large amount of valuable information. Aimed at these three issues, this study integrates fuzzy QFD and the prototype product selection model to develop a product design and selection (PDS) approach. In fuzzy QFD, the α-cut operation is adopted to calculate the fuzzy set of each component. Competitive analysis and the correlations among engineering characteristics are also considered. In prototype product selection, engineering characteristics and the factors involved in product development are considered. A fuzzy multi-criteria decision making (MCDM) approach is proposed to select the best prototype product. A case study is given to illustrate the research steps for the proposed PDS method. The proposed method provides product developers with more useful information and precise analysis results. Thus, the PDS method can serve as a helpful decision-aid tool in product design.     

Binary fuzzy goal programming approach to single model straight and U-shaped assembly line balancing

Assembly line balancing generally requires a set of acceptable solutions to the several conflicting objectives. In this study, a binary fuzzy goal programming approach is applied to assembly line balancing. Models for balancing straight and U-shaped assembly lines with fuzzy goals (the number of workstations and cycle time goals) are proposed. The binary fuzzy goal programming models are solved using the methodology introduced by Chang [Chang, C.T., 2007. Binary fuzzy goal programming. European Journal of Operational Research 180 (1), 29–37]. An illustrative example is presented to demonstrate the validity of the proposed models and to compare the performance of straight and U-shaped line configurations.     

A tolerance approach to the fuzzy goal programming problems with unbalanced triangular membership function

This paper investigates the application of tolerance concepts to goal programming in a fuzzy environment. Firstly, the paper presents how the fuzzy goal programming (FGP) problems with unequal weights can be formulated as a single linear programming problem with the concept of tolerances. Next, it illustrates a numerical example to demonstrate how convenient the present model is to solve a FGP problem with unequal weights and unbalanced linear membership functions     

A goal programming approach to energy forecasting

Goal programming besides, being a broadly used decision tool, is shown in this paper to be a powerful forecasting device too. It is used as the main component of an energy demand forecasting system, performing a function of an integrator of information on the future growth of energy demand. This information comes from a variety of sources. The most important is a set of econometric models, based on different approaches, which explain past behaviour of the energy demand system. Other sources of information used are statements on government energy policy, feasibility or technical reports and, finally, the forecaster's guess. Thus GP is intended to relax many of the assumptions of conventional econometric forecasting, which render it inadequate under the prevailing conditions of quickly changing energy structures.An implementation of the system on the Greek economy is also described in this paper. Four scenarios of energy demand growth up to 1990 are studied. The levels of energy requirements in these scenarios vary as a consequence of the patterns of economic development and rates of increase in the price of oil.     

A method for solving fuzzy goal programming problems based on MINMAX approach

Narasimhan incorporated fuzzy set theory within goal programming formulation in 1980. Since then numerous research has been carried out in this field. One of the well-known models for solving fuzzy goal programming problems was proposed by Hannan in 1981. In this paper the conventional MINMAX approach in goal programming is applied to solve fuzzy goal programming problems. It is proved that the proposed model is an extension to Hannan model that deals with unbalanced triangular linear membership functions. In addition, it is shown that the new model is equivalent to a model proposed in 1991 by Yang et al. Moreover, a weighted model of the new approach is introduced and is compared with Kim and Whang’s model presented in 1998. A numerical example is given to demonstrate the validity and strengths of the new models.     

A fuzzy goal programming approach to integrated loading and scheduling of a batch processing machine

This paper concerns a real-life problem of loading and scheduling a batch-processing machine. The integrated loading and scheduling problem is stated as a multicriteria optimization problem where different types of objectives are included: (1) short-term objectives of relevance to the shop floor, such as throughput maximization and work-in-process inventory minimization, and (2) long-term objectives such as balancing of end product inventory levels and meeting financial targets imposed by the higher production planning level. Two types of uncertainty are considered: (1) uncertainty inherent in loading and scheduling objective targets (goals) such as the allocated budget and end product demand, and (2) uncertainty in importance relations among the objectives. These two types of uncertainty are modelled using fuzzy sets and fuzzy relations, respectively. A fuzzy goal programming model and the corresponding method are developed which handle both fuzzy and crisp goals and fuzzy importance relations among the goals. Numerical examples are given to illustrate the effectiveness of the developed model.     

A new approach to fuzzy programming

A fuzzy program is defined in the usual way as a sequence of statements (instruction) which are considered as functions (possibly fuzzy functions) and fuzzy predicates defined on the given input domain. The essential difference in the approach presented in this paper is the new interpretation of the execution of fuzzy programs, and a new method of evaluating fuzzy predicates. The result of the fuzzy program execution is an appropriate fuzzy subset in the output domain.     

Solving generalized goal programming problems using a visual interactive approach

In this paper we describe how generalized goal programming problems can be solved using our Visual Interactive Approach (Korhonen and Laakso, 1986). The method enables the decision maker to evaluate attainable solutions corresponding to his aspiration levels using computer graphics. Goals are divided into flexible and inflexible goals. This classification can be altered during the interactive process. If the problem is entirely linear, the approach can be implemented using any standard linear optimization package with a parametric optimization routine. In addition, a graphical display device is required.     

Solving a multi-objective multi-skilled manpower scheduling model by a fuzzy goal programming approach

Manpower scheduling is an intricate problem in production and service environments with the purpose of generating fair schedules that consider employers’ objectives and employees’ preferences as much as possible. However, sometimes, vagueness of information related to employers’ objectives and employees’ preferences leads to the fuzzy nature of the problem. This paper presents a multi-objective manpower scheduling model regarding the lack of clarity on the target values of employers’ objectives and employees’ preferences. Hence, a fuzzy goal programming model is developed for the presented model. Afterwards, two fuzzy solution approaches are used to convert the fuzzy goal programming model to two single-objective models. Finally, the results obtained by both single-objective models are compared with each other to select the solution that has the greatest degree of the satisfaction level of employers’ objectives and employees’ preferences.     

Lexicographical dynamic goal programming approach to a robust design optimization within the pharmaceutical environment

The primary objective of this paper is to develop a new robust design (RD) optimization procedure based on a lexicographical dynamic goal programming (LDGP) approach for implementing time-series based multi-responses, while the conventional experimental design formats and frameworks may implement static responses. First, a parameter estimation method for time-dependent pharmaceutical responses (i.e., drug release and gelation kinetics) is proposed using the dual response estimation concept that separately estimates the response functions of the mean and variance, as a part of response surface method. Second, a multi-objective RD optimization model using the estimated response functions of both the process mean and variance is proposed by incorporating a time-series components within a dynamic modeling environment. Finally, a pharmaceutical case study associated with a generic drug development process is conducted for verification purposes. Based on the case study results, we conclude that the proposed LDGP approach effectively provides the optimal drug formulations with significantly small biases and MSE values, compared to other models.