A modified two-step method for solving interval linear programming problems (Q2205081)

Summary: 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 \textit{S. Tong} [``Interval number and fuzzy number linear programmings'', Fuzzy Set. Syst. 66, No. 3, 301--306 (1994; \url{doi:10.1016/0165-0114(94)90097-3})] and two-step method (TSM) proposed by \textit{G. H. Huang} et al. [Eur. J. Oper. Res. 83, No. 3, 594--620 (1995; Zbl 0899.90131)]. 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 \textit{X. Wang} and \textit{G. Huang} [Inf. Sci. 281, 85--96 (2014; Zbl 1355.90046)]. 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.