A goal programming approach for fuzzy multiobjective fractional programming problems

Fuzzy multiple objective fractional programming (FMOFP) is an important technique for solving many real-world problems involving the nature of vagueness, imprecision and/or random. Following the idea of binary behaviour of fuzzy programming (Chang 2007 Chang, C-T. 2007. Binary Behavior of Fuzzy Programming with Piecewise Membership Functions. IEEE Transactions on Fuzzy Systems, 15: 342–349.  [Google Scholar]), there may exist a situation where a decision-maker would like to make a decision on FMOFP involving the achievement of fuzzy goals, in which some of them may meet the behaviour of fuzzy programming (i.e. level achieved) or the behaviour of binary programming (i.e. completely not achieved). This is turned into a fuzzy multiple objective mixed binary fractional programming (FMOMBFP) problem. However, to the best of our knowledge, this problem is not well formulated by mathematical programming. Therefore, this article proposes a linearisation strategy to formulate the FMOMBFP problem in which extra binary variable is not required. In addition, achieving the highest membership value of each fuzzy goal defined for the fractional objective function, the proposed method can alleviate the computational difficulties when solving the FMOMBFP problem. To demonstrate the usefulness of the proposed method, a real-world case is also included.     

A hybrid fuzzy goal programming approach with different goal priorities to aggregate production planning

In this study a hybrid (including qualitative and quantitative objectives) fuzzy multi objective nonlinear programming (H-FMONLP) model with different goal priorities will be developed for aggregate production planning (APP) problem in a fuzzy environment. Using an interactive decision making process the proposed model tries to minimize total production costs, carrying and back ordering costs and costs of changes in workforce level (quantitative objectives) and maximize total customer satisfaction (qualitative objective) with regarding the inventory level, demand, labor level, machines capacity and warehouse space. A real-world industrial case study demonstrates applicability of proposed model to practical APP decision problems. GENOCOP III (Genetic Algorithm for Numerical Optimization of Constrained Problems) has been used to solve final crisp nonlinear programming problem.     

Multiple-criteria decision-making in two-sided assembly line balancing: A goal programming and a fuzzy goal programming models

Two-sided assembly lines are especially used at the assembly of large-sized products, such as trucks and buses. In this type of a production line, both sides of the line are used in parallel. In practice, it may be necessary to optimize more than one conflicting objectives simultaneously to obtain effective and realistic solutions. This paper presents a mathematical model, a pre-emptive goal programming model for precise goals and a fuzzy goal programming model for imprecise goals for two-sided assembly line balancing. The mathematical model minimizes the number of mated-stations as the primary objective and it minimizes the number of stations as a secondary objective for a given cycle time. The zoning constraints are also considered in this model, and a set of test problems taken from literature is solved. The proposed goal programming models are the first multiple-criteria decision-making approaches for two-sided assembly line balancing problem with multiple objectives. The number of mated-stations, cycle time and the number of tasks assigned per station are considered as goals. An example problem is solved and a computational study is conducted to illustrate the flexibility and the efficiency of the proposed goal programming models. Based on the decision maker's preferences, the proposed models are capable of improving the value of goals.     

An intuitionistic fuzzy goal programming approach for finding pareto-optimal solutions to multi-objective programming problems

Multi-objective optimization in the intuitionistic fuzzy environment is the process of finding a Pareto-optimal solution that simultaneously maximizes the degree of satisfaction and minimizes the degree of dissatisfaction of an intuitionistic fuzzy decision. In this paper, a new method for solving multi-objective programming problems is developed that unlike other methods in the literature, provides compromise solutions satisfying both the conditions of intuitionistic fuzzy efficiency and Pareto-optimality. This method combines the advantages of the intuitionistic fuzzy sets concept, goal programming, and interactive procedures, and supports the decision maker in the process of solving programming problems with crisp, fuzzy, or intuitionistic fuzzy objectives and constraints. A characteristic of the proposed method is that it provides a well-structured approach for determining satisfaction and the dissatisfaction degrees that efficiently uses the concepts of violation for both objective functions and constraints. Another feature of the proposed method comes from its continuous interaction with the decision maker. In this situation, through adjusting the problem's parameters, the decision maker would have the ability of revisiting the membership and non-membership functions. Therefore, despite the lack of information at the beginning of the solving process, a compromise solution that satisfies the decision maker's preferences can be obtained. A further feature of the proposed method is the introduction of a new two-step goal programming approach for determining the compromise solutions to multi-objective problems. This approach ensures that the compromise solution obtained during each iterative step satisfies both the conditions of intuitionistic fuzzy efficiency and Pareto-optimality. The application of the proposed model is also discussed in this paper.     

Application of fuzzy goal programming approach to multi-objective linear fractional inventory model

In this paper, we propose a model and solution approach for a multi-item inventory problem without shortages. The proposed model is formulated as a fractional multi-objective optimisation problem along with three constraints: budget constraint, space constraint and budgetary constraint on ordering cost of each item. The proposed inventory model becomes a multiple criteria decision-making (MCDM) problem in fuzzy environment. This model is solved by multi-objective fuzzy goal programming (MOFGP) approach. A numerical example is given to illustrate the proposed model.     

Cross-border logistics with fleet management: A goal programming approach

In this paper, we introduce the cross-border logistics problem with fleet management. A major phenomenon of implementation of open-door policy in China is the move of Hong Kong-based manufacturers’ production lines to China, crossing the border to take advantages of lower production costs, lower wages and lower rental costs. The finished products are then transshipped to Hong Kong, an efficient logistics hub well-equipped with reliable transportation facility, for exporting. We present a preemptive goal programming model for multi-objective cross-border logistics problem, in which three objectives are optimized hierarchically. We also describe a framework for incorporating decision-makers’ opinions for determination of goal priorities and target values. A set of Hong Kong data have been used to test the effectiveness and efficiency of the proposed model. Results demonstrate the decision-makers can find the flexibility and robustness of the proposed model by adjusting the goal priorities with respect to the importance of each objective.     

Revised multi-segment goal programming: Percentage goal programming

The multi-segment goal programming (MSGP) model is an extension model of GP wherein the core thinking is inherited from the multi-choice goal programming (MCGP) model. In this paper, we recommend certain points of the MSGP model and offer a Revised MSGP Model as an aid to burdened decision makers who cannot expect an either-or selection of coefficients in practice. The proposed model takes into account a scenario in which the selection of all possible coefficients pertaining to each decision variable in the MSGP model can be an in-between selection instead of an exclusive-or selection. We hope this study can fill in a possible gap that might exist when applying the MSGP model, and can offer an extension model for practitioners when they use this model to solve related decision problems.     

Genetic algorithm-based fuzzy goal programming for class of chance-constrained programming problems

This paper presents a procedure for solving a multiobjective chance-constrained programming problem. Random variables appearing on both sides of the chance constraint are considered as discrete random variables with a known probability distribution. The literature does not contain any deterministic equivalent for solving this type of problem. Therefore, classical multiobjective programming techniques are not directly applicable. In this paper, we use a stochastic simulation technique to handle randomness in chance constraints. A fuzzy goal programming formulation is developed by using a stochastic simulation-based genetic algorithm. The most satisfactory solution is obtained from the highest membership value of each of the membership goals. Two numerical examples demonstrate the feasibility of the proposed approach.     

Generating consensus priority point vectors: a logarithmic goal programming approach

The analytic hierarchy process (Saaty, The Analytic Hierarchy Process: Planning, Priority Setting, Resource Allocation, NewYork: McGraw-Hill 1980) is a popular technique for addressing multiple-criteria decision-making problems (MCDMs). Various techniques have been proposed for using the AHP in group situations. Fundamental to the AHP is the generation of priority point vectors from matrices of pairwise comparison data. In this paper, we present a logarithmic goal programming model for generating the ‘consensus’ priority point vector from the set of individual priority point vectors.Scope and purposeWithin modern organizations, multiple-criteria decision-making problems (MCDMs) often occur within a group context, and individual priorities for decision alternatives must be synthesized into a single set of priorities which represents the consensus opinion for the group. This requires a process for aggregating individual priorities into a set of group priorities. In this paper, we examine the use of the analytic hierarchy process (AHP) MCDM technique for the group situation, and present an approach for aggregating individual priorities into a set of group ‘consensus’ priorities.     

Revised multi-segment goal programming: Percentage goal programming

The multi-segment goal programming (MSGP) model is an extension model of GP wherein the core thinking is inherited from the multi-choice goal programming (MCGP) model. In this paper, we recommend certain points of the MSGP model and offer a Revised MSGP Model as an aid to burdened decision makers who cannot expect an either-or selection of coefficients in practice. The proposed model takes into account a scenario in which the selection of all possible coefficients pertaining to each decision variable in the MSGP model can be an in-between selection instead of an exclusive-or selection. We hope this study can fill in a possible gap that might exist when applying the MSGP model, and can offer an extension model for practitioners when they use this model to solve related decision problems.     

A goal programming approach to job evaluation

Job evaluatio refers to a systematic determination of the relative values of jobs in an organization. Often, jobs are evaluated based upon subjective judgement. By considering each job to consist of certain levels of different job factors, this paper develops a goal programming model to evaluate various levels of job factors. The main constraints in such a formation are obtained by using some existing benchmark jobs. The model development and application in evaluating new jobs are illustrated by solving an example problem consisting of four factors and six levels of each factor.     

Genetic based fuzzy goal programming for multiobjective chance constrained programming problems with continuous random variables

Solution procedure consisting of fuzzy goal programming and stochastic simulation-based genetic algorithm is presented, in this article, to solve multiobjective chance constrained programming problems with continuous random variables in the objective functions and in chance constraints. The fuzzy goal programming formulation of the problem is developed first using the stochastic simulation-based genetic algorithm. Without deriving the deterministic equivalent, chance constraints are used within the genetic process and their feasibilities are checked by the stochastic simulation technique. The problem is then reduced to an ordinary chance constrained programming problem. Again using the stochastic simulation-based genetic algorithm, the highest membership value of each of the membership goal is achieved and thereby the most satisfactory solution is obtained. The proposed procedure is illustrated by a numerical example.     

Allocating production batches to subcontractors by fuzzy goal programming

Allocating production batches to subcontractors arises frequently in industry. When subcontractors operate different equipment, batch assignment is a complex decision that must take into account both throughput and quality of finished goods. In this paper, a Mixed Integer Linear Goal Programming Model, where productivity uncertainty is taken into account through Fuzzy Set Theory, is developed. Our study was motivated by a real-world application arising in an Italian textile company. Computational results show that this method outperforms the hand-made solutions put to use by the management so far.     

Duality and transformations in multiphase and sequential linear goal programming

We consider herein a specific type of goal programming model, namely the lexicogrpahic linear goal programming model. Although the two most common methods of solution, the sequential process and the multiphase process, produce the same solutions, the interiors of the final tableaus will differ. We present algorithms which allow one to transform the sequential tableau into the multiphase tableau and vice versa and, in doing so, demonstrate the respective mathematical duals and their relationships. These results are particularly important when performing sensitivity analysis.     

Hedging an option portfolio with minimum transaction lots: A fuzzy goal programming problem

Options are designed to hedge against risks to their underlying assets such as stocks. One method of forming option-hedging portfolios is using stochastic programming models. Stochastic programming models depend heavily on scenario generation, a challenging task. Another method is neutralizing the Greek risks derived from the Black–Scholes formula for pricing options. The formula expresses the option price as a function of the stock price, strike price, volatility, risk-free interest rate, and time to maturity. Greek risks are the derivatives of the option price with respect to these variables. Hedging Greek risks requires no human intervention for generating scenarios. Linear programming models have been proposed for constructing option portfolios with neutralized risks and maximized investment profit. However, problems with these models exist. First, feasible solutions that can perfectly neutralize the Greek risks might not exist. Second, models that involve multiple assets and their derivatives were incorrectly formulated. Finally, these models lack practicability because they consider no minimum transaction lots. Considering minimum transaction lots can exacerbate the infeasibility problem. These problems must be resolved before option hedging models can be applied further. This study presents a revised linear programming model for option portfolios with multiple underlying assets, and extends the model by incorporating it with a fuzzy goal programming method for considering minimum transaction lots. Numerical examples show that current models failed to obtain feasible solutions when minimum transaction lots were considered. By contrast, while the proposed model solved the problems efficiently.     

An evaluation approach to logistics service using fuzzy theory,quality function development and goal programming

Logistics customer service is an important factor in the success of supply chain management. The aim of this study is to propose a novel approach for customer service management. For the improvement of logistics service operations, the proposed method integrates quality function development (QFD), fuzzy extended analytic hierarchy process (FEAHP), and multi-segment goal programming (MSGP). The advantage of the method includes the consideration of various logistics goals and the flexibility of setting multi-aspiration levels of evaluation criteria.     

A two-stage linear goal programming approach to eliciting interval weights from additive interval fuzzy preference relations

This article presents a linear goal programming framework to obtain normalized interval weights from interval fuzzy preference relations (IFPRs). A parameterized transformation equation is put forward to convert a normalized interval weight vector into IFPRs with additive consistency. Based on a linearization approximate relation of the transformation equation, a two-stage linear goal programming approach is developed to elicit interval weights and determine an appropriate parameter value from an additive IFPR. The first stage devises a linear goal programming model to generate optimal interval weight vectors by minimizing the absolute deviation between sides of the parameterized linearization approximate relation. The second stage aims to find a benchmark among the optimal solutions derived from the previous stage by minimizing the absolute deviation between the parameter and 1. The obtained benchmark is the closest to the original IFPR and can sufficiently reflect uncertainty of original judgments. A procedure is further proposed for solving group decision making problems with IFPRs. Two numerical examples including a comparative study with existing approaches are provided to illustrate validity and practicality of the proposed model.     

A fuzzy mixed integer goal programming approach for cooking and heating energy planning in rural India

In this study, a fuzzy mixed integer goal programming model (FMIGP) has been developed for rural cooking and heating energy planning in the Chikhli taluka of Buldhana district, Maharashtra, Central India. The model considers various scenarios such as economical, environmental, social acceptance and local resources to trade off between socio-economical and environmental issues related to cooking and heating energy in two villages namely Malshemba and Muradpur. Due to uncertainty involved in real world energy planning problems, exact input data is impossible to acquire. Hence FMIGP model is used to consider four fuzzy objectives. The solutions provide energy resource allocations at micro level with minimized cost, minimized emission, maximized social acceptance and maximized use of local resources. The proposed approach can handle fuzzy environmental realistic situation and can provide better solution to decision maker for rural energy planning.