Taylor series approach to grey multi objective integer linear fractional programming problem and a case study for environmental economic energy dispatch

Abstract EN

This paper presents the use of a Taylor series for multi objective integer linear fractional programming problem having grey parameters in the right-side of the constraints (GMOILFP).

to deal with the grey parameters in the right-side of the constraints the positioned programming should be used.

an equivalent grey multiobjective linear fractional programming problem (GMOLFP) is formulated using Gomory's cutting plane method.

the Taylor series, which is a series expansion that a representation of a function, is applied to convert the fractional functions into polynomials.

in the proposed approach a white value of each grey parameter is determined, Taylor series is applied and the functions are unified by using the nonnegative weighted sum method.

thus, the problem is reduced to a single linear objective with grey parameter in the right side of the constrains.

an algorithm for solving GMOILGP problem with grey interval coefficients using positioned programming and Taylor series polynomials is proposed.

a numerical example is provided to demonstrate the efficiency and feasibility of the proposed approach.

a special case study for handling the environmental economic energy dispatch problem also is included in this paper, the main goal of this problem is how to schedule committed generators to meet the load required to minimize the pollution emissions and fuel cost.

the model formulation for a special case study problem is presented, the mathematical model will be considered as (GMOLFP) and the problem is solved according to the proposed solution algorithm.