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. | Yugoslav Journal of Operations Research 28 (2018), Number 4, 435-451 DOI: AN IMPROVED THREE-STEP METHOD FOR SOLVING THE INTERVAL LINEAR PROGRAMMING PROBLEMS Mehdi ALLAHDADI Mathematics Faculty, University of Sistan and Baluchestan, Zahedan, Iran m allahdadi@ Chongyang DENG School of Science, Hangzhou Dianzi University, Hangzhou, PR China dcy@ Received: January 2018 / Accepted: July 2018 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 the 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, whose solution spaces may not be completely optimal. We propose an improved ThSM (IThSM) for ILP problems, which ensures both feasibility and optimality conditions, ., we introduce an extra step to optimality. Keywords: Feasibility, Interval Linear Programming, Optimality, Robust two-step Method, Three-step Method. MSC: 65G40, 80M50, 90C05. 1. INTRODUCTION Interval linear programming (ILP) is used to deal with uncertainties of many real-world problems, where parameters may be specified as lying between lower and upper bounds. There are several methods for solving ILP models, which are divided into two sub-models to obtain the solution set [2, 3, 4, 10, 12, 14, 24, 26, 27, 28]. 436 M. Allahdadi and C. Deng / An improved ThSM for solving the ILP problems Also, there are some methods for ILP models. Tong [26] proposed the best and worst cases (BWC) method by converting the ILP model into two sub-models, the best and worst sub-models which have the .
