Title: A modified generalised inverse method for solving geometric programming problems with extended degrees of difficulties (K ≥ 0)
Authors: Harrison O. Amuji; Fidelis I. Ugwuowo; Walford I.E. Chukwu; Peter. I. Uche
Addresses: Department of Statistics, Federal University of Technology, Owerri, Nigeria ' Department of Statistics, University of Nigeria, Nsukka, Nigeria ' Department of Statistics, University of Nigeria, Nsukka, Nigeria ' Department of Statistics, University of Nigeria, Nsukka, Nigeria
Abstract: We have developed a new method of solving geometric programming problems with as many positive degrees of difficulties as possible. Geometric programming has no direct solution whenever its degrees of difficulties are greater than zero; this has hindered the development of geometric programming and discouraged so many researchers into the area. The indirect solution, which has been in existence, involves the conversion of geometric programming problems to linear programming, separable programming, augmented programming etc. These conversions make the beauty of geometric programming to be lost and also terminate the existence of geometric programming. The newly developed method (modified generalised inverse method) consistently produces global optimal solutions; satisfies the orthogonality and normality conditions; optimal objective function; and produce optimal primal and dual decision variables which satisfy the optimal objective function. The method was applied on some positive degrees of difficulty geometric programming problems and the results compare to the results from existing methods. The method was validated by some proposition; corollary and lemma. With this breakthrough, geometric programming problems can be modeled and solved without restrictions.
Keywords: exponent matrix; degree of difficulty; generalised inverse; primal decision variables; dual decision variables; objective function.
International Journal of Operational Research, 2020 Vol.38 No.1, pp.19 - 30
Received: 08 Dec 2016
Accepted: 04 Mar 2017
Published online: 29 Mar 2020 *