Several methods exist for solving the interval linear programming (ILP) problem. In most of these methods, we can only obtain the optimal value of the objective function of the ILP problem. In this paper we determine the optimal solution set of the ILP as the intersection of some regions, by the best and the worst case (BWC) methods, when the feasible solution components of the best problem are positive. First, we convert the ILP problem to the convex combination problem by coefficients 0 ≤ λj, μij, μi ≤ 1, for i = 1, 2, . . . , m and j = 1, 2, . . . , n. If for each i, j, μij = μi = λj = 0, then the best problem has been obtained (in case of minimization problem). We move from the best problem towards the worst problem by tiny variations of λj, μij and μi from 0 to 1. Then we solve each of the obtained problems. All of the optimal solutions form a region that we call the optimal solution set of the ILP. Our aim is to determine this optimal solution set by the best and the worst problem constraints. We show that some theorems to validity of this optimal solution set.
[1]
Milan Hladík,et al.
How to determine basis stability in interval linear programming
,
2012,
Optimization Letters.
[2]
Jiri Rohn,et al.
Sufficient Conditions for Regularity and Singularity of Interval Matrices
,
1999,
SIAM J. Matrix Anal. Appl..
[3]
Tong Shaocheng,et al.
Interval number and fuzzy number linear programmings
,
1994
.
[4]
N. F. Stewart.
Interval arithmetic for guaranteed bounds in linear programming
,
1973
.
[5]
John W. Chinneck,et al.
Linear programming with interval coefficients
,
2000,
J. Oper. Res. Soc..
[6]
Jana Koníckocá,et al.
Sufficient condition of basis stability of an interval linear programming problem
,
2001
.
[7]
Gordon H. Huang,et al.
Enhanced-interval linear programming
,
2009,
Eur. J. Oper. Res..
[8]
G. Alefeld,et al.
Introduction to Interval Computation
,
1983
.
[9]
M. Fiedler,et al.
Linear Optimization Problems with Inexact Data
,
2006
.