Title: A modified two-step method for solving interval linear programming problems
Authors: Mehdi Allahdadi
Addresses: Mathematics Faculty, University of Sistan and Baluchestan, Zahedan, Iran
Abstract: In this paper, we propose a new method for solving interval linear programming (ILP) problems. For solving the ILP problems, two important items should be considered: feasibility (i.e., solutions satisfy all constraints) and optimality (i.e., solutions are optimal for at least a characteristic model). In some methods, a part of the solution space is infeasible (i.e., it violates any constraints) such as the best and worst cases method (BWC) proposed by Tong in 1994 and two-step method (TSM) proposed by Huang et al. in 1995. In some methods, the solution space is completely feasible, but is not completely optimal (i.e., some points of the solution space are not optimal) such as modified ILP method (MILP) proposed by Zhou et al. in 2009 and improved TSM (ITSM) proposed by Wang and Huang in 2014. Firstly, basis stability for the ILP problems is reviewed. Secondly, the solving methods are analysed from the point of view of the feasibility and optimality conditions. Later, a new method which modifies the TSM by using the basis stability approach is presented. This method gives a solution space that is not only completely feasible, but also completely optimal.
Keywords: basis stability; feasibility; interval linear programming; ILP; optimality; two-step method; TSM.
DOI: 10.1504/IJMOR.2019.101620
International Journal of Mathematics in Operational Research, 2019 Vol.15 No.2, pp.181 - 196
Received: 29 Dec 2016
Accepted: 30 Mar 2018
Published online: 16 Aug 2019 *