Bijay Baran Pal

A goal programming procedure for fuzzy multiobjective linear fractional programming problem

Abstract This paper presents a goal programming (GP) procedure for fuzzy multiobjective linear fractional programming (FMOLFP) problems. In the proposed approach, which is motivated by Mohamed (Fuzzy Sets and Systems 89 (1997) 215), GP model for achievement of the highest membership value of each of fuzzy goals defined for the fractional objectives is formulated. In the solution process, the method of variable change on the under- and over- deviational variables of the membership goals associated with the fuzzy goals of the model is introduced to solve the problem efficiently by using linear goal programming (LGP) methodology. The approach is illustrated by two numerical examples.

A goal programming procedure for solving problems with multiple fuzzy goals using dynamic programming

Abstract This paper describes how the preemptive priority based goal programming (GP) can be used to solve a class of fuzzy programming (FP) problems with the characteristics of dynamic programming (DP). In the proposed approach, the membership functions of the objective goals of a problem with fuzzy aspiration levels are defined first. Then, under the framework of preemptive priority based GP a multi-stage DP model of the problem for achievement of the highest degree (unity) of each of the membership functions is developed. In the decision process, the goal satisficing philosophy of GP is used recursively to arrive at the most satisfactory solution. Two numerical examples are provided to illustrate the approach.

A fuzzy goal programming procedure for solving quadratic bilevel programming problems

This article presents a fuzzy goal programming (FGP) procedure for solving quadratic bilevel programming problems (QBLPP). In the proposed approach, the membership functions for the defined fuzzy objective goals of the decision makers (DM) at both the levels are developed first. Then, a quadratic programming model is formulated by using the notion of distance function minimizing the degree of regret to satisfaction of both DMs. At the first phase of the solution process, the quadratic programming model is transformed into an equivalent nonlinear goal programming (NLGP) model to maximize the membership value of each of the fuzzy objective goals on the extent possible on the basis of their priorities in the decision context. Then, at the second phase, the concept of linear approximation technique in goal programming is introduced for measuring the degree of satisfaction of the DMs at both the levels by arriving at a compromised decision regarding the optimality of two different sets of decision variables controlled separately by each of them. A numerical example is provided to illustrate the proposed approach.

A Fuzzy Goal Programming Approach for Solving Bilevel Programming Problems

This paper presents a fuzzy goal programming procedure for solving linear bilevel programming problems. The concept of tolerance membership functions for measuring the degree of satisfactions of the objectives of the decision makers at both the levels and the degree of optimality of vector of decision variables controlled by upper-level decision maker are defined first in the model formulation of the problem. Then a linear programming model by using distance function to minimize the group regret of degree of satisfactions of both the decision makers is developed. In the decision process, the linear programming model is transformed into an equivalent fuzzy goal programming model to achieve the highest degree (unity) of each of the defined membership function goals to the extent possible by minimizing their deviational variables and thereby obtaining the most satisfactory solution for both the decision makers. To demonstrate the approach, a numerical example is solved and compared the solution with the solutions of other two fuzzy programming approaches [11,12 ] studied previously.

Using genetic algorithm for solving quadratic bilevel programming problems via fuzzy goal programming

This article presents how genetic algorithm (GA) can be efficiently used to fuzzy goal programming (FGP) formulation of quadratic bilevel programming problems (QBLPPs) in a hierarchical decision system. In the proposed approach, the concept of tolerance membership functions in fuzzy sets for measuring the achievement of highest membership value (unity) of the defined fuzzy goals of a problem to the extent possible by minimising the under-deviational variables of the defined membership goals on the basis of priorities of achieving the fuzzy goals is considered. In the decision making process, the sensitivity analysis with variations of priority structure of the goals is performed and then the notion of Euclidean distance function is used to identify the appropriate priority structure under which the most satisfactory decision can be reached in the fuzzy decision environment. The potential use of the approach is illustrated by a numerical example.

An application of genetic algorithm method for solving patrol manpower deployment problems through fuzzy goal programming in traffic management system: a case study

This article demonstrates a fuzzy goal programming (FGP) approach with the use of genetic algorithm (GA) for proper deployment of patrol manpower to various road-segment areas in urban environment in different shifts of a time period to deterring violation of traffic rules and thereby reducing the accident rates in a traffic control planning horizon. To expound the potential use of the approach, a case example of the city Kolkata, West Bengal, INDIA, is solved.

A Linear Goal Programming Procedure for Academic Personel Management Problems in University System

This article describes a goal programming (GP) procedure for proper allocation of teaching personnel to the teaching departments for smooth functioning of the academic activities of a university. In the academic resource planning context, both the crisp and fuzzy goal objectives which are frequently involved with the problem are discussed. Again, certain ratios in the fractional forms which are inherently associated to the problem are also taken into consideration. In the model formulation, achievement of the highest membership value (unity) of the membership functions of the defined fuzzy goal as well as attainment of the prescribed goal levels of the crisp goals to the extent possible are considered. In the solution process, the fractional goals are transformed into the linear goals by using the linear transformation approach studied previously. A case study of University of Kalyani, West Bengal, India is considered to expound the potential use of the proposed model.

A Goal Programming approach for solving Interval valued Multiobjective Fractional Programming problems using Genetic Algorithm

In this article, the efficient use of a genetic algorithm (GA) to the goal programming (GP) formulation of interval valued multiobjective fractional programming problems (MOFPPs) is presented. In the proposed approach, first the interval arithmetic technique [1] is used to transform the fractional objectives with interval coefficients into the standard form of an interval programming problem with fractional criteria. Then, the redefined problem is converted into the conventional fractional goal objectives by using interval programming approach [2] and then introducing under-and over-deviational variables to each of the objectives. In the model formulation of the problem, both the aspects of GP methodologies, minsum GP and minimax GP [3] are taken into consideration to construct the interval function (achievement function) for accommodation within the ranges of the goal intervals specified in the decision situation where minimization of the regrets (deviations from the goal levels) to the extent possible within the decision environment is considered. In the solution process, instead of using conventional transformation approaches [4, 5, 6] to fractional programming, a GA approach is introduced directly into the GP framework of the proposed problem. In using the proposed GA, based on mechanism of natural selection and natural genetics, the conventional roulette wheel selection scheme and arithmetic crossover are used for achievement of the goal levels in the solution space specified in the decision environment. Here the chromosome representation of a candidate solution in the population of the GA method is encoded in binary form. Again, the interval function defined for the achievement of the fractional goal objectives is considered the fitness function in the reproduction process of the proposed GA. A numerical example is solved to illustrate the proposed approach and the model solution is compared with the solutions of the approaches [6, 7] studied previously.

A Goal Programming Procedure for Solving Interval Valued Multiobjective Fractional Programming Problems

This article presents a goal programming (GP) procedure for solving interval valued multiobjective fractional programming problems (MOFPPs) with interval objective functions in an inexact environment. In the proposed approach, the interval objective functions are first converted into the standard objective goals in the fractional GP formulation by using the interval arithmetic technique. Then, in the decision process, the fractional goals are transformed into the linear goals by linearization approach by B.B. Pal et al (2008) studied previously. In solution process, the executable GP model of the problem is formulated with the objective to minimize the regret with the view to achieve the goals in their specified ranges and thereby arriving at a most satisfactory solution in the decision making environment. Two numerical examples are solved to illustrate the proposed approach and the model solution of one problem is compared with the solution of a fuzzy programming approach by B.B. Pal et al. (2008) studied previously.

A linear Goal Programming approach to multiobjective fractional programming with interval parameter sets

This paper presents a Goal Programming (GP) approach to solving multiobjective fractional programming problems (MOFPPs) involving interval coefficients and target intervals. In the proposed approach, interval-valued fractional objectives are converted into the standard fractional objective goals in GP formulation. The fractional goals are then transformed into linear goals within the framework of GP by using the linear transformation approach. In the GP model formulation, the goal achievement function for minimising the lower bounds of the necessary regret intervals of the goal objectives for the defined interval parameter sets from the optimistic point of view is taken into consideration. In the solution process, the mixed 0-1 method is used to overcome the computational complexity arises for non-convex in nature of the formulated model of the problem. Two numerical examples are provided to illustrate the solution approach.