Taylor Series Approach to Grey Multiobjective Integer linear Fractional Programming Problem and A case study for environmental economic energy dispatch

Document Type : Original Article

Authors

1 Department of Mathematics, Faculty of science, Helwan University, Cairo, Egypt.

2 Department of Mathematics and Theoretical Physics, Nuclear Research Centre, Egyptian Atomic Energy Authority, Cairo, Egypt.

Abstract

Abstract
This paper presents the use of a Taylor series for multiobjective 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 multi-objective 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 covert the fractional functions into polynomials. In the proposed approach, a value of each grey parameter is determined and Taylor series approach unified functions by using the weights. 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. 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 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.

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