An improved three-step method for solving the interval linear programming problems

An improved ThSM for solving the ILP problems

Abstract

Feasibility condition, which ensures that the solution space does not violate any constraints, and optimality condition, which guarantees that all points of the solution space are optimal, are very significant conditions for the solution space of interval linear programming (ILP) problems. Among existing methods for ILP problems, the best-worst cases (BWC) method and two-step method (TSM) do not ensure feasibility condition, while the modified ILP (MILP), robust TSM (RTSM), improved TSM (ITSM) and three-step method (ThSM) guarantee feasibility condition, their solution spaces may not be completely optimal. Based on analyses of the above-mentioned methods on the point of view of feasibility and optimality conditions, we propose the improved ThSM (IThSM), which ensures both feasibility and optimality conditions, for ILP problems via introducing an extra step to optimality.