Mousumi Kumar

A priority-based goal programming method for solving academic personnel planning problems with interval-valued resource goals in university management system

This paper describes a goal programming (GP) procedure for modelling and solving academic resource planning problems in university management system. In the academic resource planning context, certain objectives having the characteristics of fractional programming problems are considered as interval-valued goals to make a satisfactory decision regarding staff allocation for smooth functioning of the academic activities of the departments. In the proposed approach, the interval-valued goals are first converted into the standard goals by using interval arithmetic technique. Then, the fractional goals are transformed into linear goals by using linearisation approach to solve the problem by employing linear GP methodology. In the model formulation of the problem, both the aspects of GP, minsum and minimax approaches, are addressed to construct the goal achievement function for minimising the possible regret towards achieving the goal values within the target intervals specified by the decision maker (DM) in the decision making environment. A demonstrative case example of the University of Kalyani, West Bengal (W.B.), India is considered to expound the proposed model.

A linear approximation approach to chance constrained multiobjective decision making problems

This article presents a linear approximation approach to the fuzzy goal programming (FGP) formulation of solving multiobjective decision making (MODM) problems with chance constraints.

A linear fuzzy goal programming approach for solving patrol manpower deployment planning problems — A case study

This paper demonstrates a fuzzy goal programming (FGP) procedure for modeling and solving patrol manpower deployment problems of Metropolitan cities to deterring traffic violations and accidents and thereby reducing accident rate in a traffic control planning horizon.

A priority based interval-valued Goal Programming approach for land utilization planning in agricultural system: A case study

This paper demonstrates a Goal Programming (GP) Procedure for modeling and solving land utilization planning problems having interval-valued objective goals for optimal production of seasonal crops in agricultural system. In the proposed approach, utilization of total land for cultivation, aspiration levels of production of crops, expected profit from the farm as well as certain ratios of crops production and profit achievement are described interval-valued for goal achievement in the context of making proper cropping plan. In the model formulation of the problem, the defined interval-valued goals are converted into conventional goals by using interval arithmetic technique in interval programming (IP) and introducing under- and over-deviational variables to each of them. Again, certain ratio goals which are inherent to the problem are transformed into linear goals by employing the linear transformation approach to solve the problem by using the linear GP methodology. In the decision process, both the minsum GP and minmax GP approaches are addressed in the achievement function for minimizing the possible regret towards goal achievement from the optimistic point of view in the inexact decision making environment. The potential use of the approach demonstrated via a case example of the Nadia District, West Bengal (W.B), INDIA.

A fuzzy goal programming approach for solving multiobjective fuzzy stochastic programming problems

This article presents a fuzzy goal programming (FGP) procedure for solving a stochastic multiobjective decision making (MODM) problem having the finite probabilistic aspiration levels for achievement of the chance constrained goals.

A Hierarchical Optimization Method to Solve Environmental-Economic Power Generation and Dispatch Problem with Fuzzy Data Uncertainty

This paper presents how the hierarchical decision structure can be effectively used for modeling and solving an environmental-economic thermal power generation and dispatch problems in a fuzzy decision environment. In the proposed approach, minimization of the functions of fuel-cost, environmental-emission and transmission-loss are considered at the three hierarchical levels to solve the problem within a power plant operational system. In the model formulation, a priority based linear fuzzy goal programming (LFGP) method is employed to achieve the highest membership value (unity) of the defined fuzzy goals to the extent possible on the basis of priorities in the decision making horizon. To illustrate the effective use of the approach, the problem of standard IEEE 6-Generator 30-Bus System is considered.

A Linear Goal Programming Method for Solving Chance-Constrained Multiobjective Problems with Interval Data Uncertainty

This paper presents a goal programming (GP) method for modeling and solving multiobjective decision-making problems having interval parameter sets and a set of chance constraints in uncertain environments. In the proposed approach, planned interval goals defined for the objective goals are converted into standard linear goals in GP by using interval arithmetic technique and introducing under- and over-deviational variables to each of them. The chance constraints are also converted into deterministic equivalents and Taylor series approximation technique is used to transform the defined quadratic constraints into linear form to solve the problem effectively by employing linear GP method. Then, from the optimistic point of view of decision-maker, the framework of interval-valued GP is addressed to design goal achievement function for minimizing possible deviations concerned with achievement of goals within their target intervals specified in the decision situation. The approach is illustrated by a numerical example.

An Iterative Fuzzy Goal Programming Method to Solve Fuzzified Multiobjective Fractional Programming Problems

This paper presents a fuzzy goal programming (FGP) approach for modeling and solving multiobjective fractional programming problems (MOFPPs) with fuzzy numbers parameter sets. In the proposed approach, first the notion of α-cut in fuzzy sets (FSs) is used to transform a problem into conventional MOFPP by using the tolerance membership functions in FSs. In model formulation, membership functions are converted into fuzzy goals for measuring the degree of satisfaction of decision maker (DM) with the solution for achievement of fuzzily described objectives of the problem. In the solution process, an iterative parametric method is addressed within the framework of minsum FGP model to reach the highest membership value (unity) to the extent possible in the decision making environment. The efficiency of the proposed approach is illustrated by a numerical example. The model solution is also compared with the solution obtained by using other approaches studied previously.

A penalty function based fuzzy goal programming procedure for solving multiobjective decision making problems

This paper presents how fuzzy penalty functions can be grafted to the fuzzy goal programming formulation of a multiobjective decision making problem for making proper decisions in uncertain environment. In the proposed approach, the fuzzily described objectives are first characterized by the associated membership functions. The membership functions are then transformed into membership goals by assigning the highest degree (unity) as the aspiration level and introducing under- and over- deviational variables to each of them. In the model formulation, the penalty functions in terms of degree of achievement of membership values in different ranges are introduced to the framework of the model for minimizing deviations from the goal levels to the extent possible for arriving at most satisfactory solution in the decision making context. In the solution process, the minsum fuzzy goal programming method is employed to achieve the solution on the basis of relative weights of importance of achieving the aspired goal levels in the decision making horizon. A numerical example is provided to illustrate the efficient use of the approach.