The set of all group relaxations of an integer program contains certain special members called Gomory relaxations. A family of integer programs with a fixed coefficient matrix and cost vector but varying right hand sides is a Gomory family if every program in the family can be solved by one of its Gomory relaxations. In this paper, we characterize Gomory families. Every TDI system gives a Gomor...

In this paper we investigate Multi-Objective Integer Linear Programming (MOILP) problems with unbounded feasible region and introduce recession direction for MOILP problems. Then we present necessary and sufficient conditions to have unbounded feasible region and infinite optimal values for objective functions of MOILP problems. Finally we present some examples with unbounded feasible region and fi...

In this paper fully fuzzy linear programming (FFLP) problem with both equality and inequality constraints is considered where all the parameters and decision variables are represented by non-negative trapezoidal fuzzy numbers. According to the current approach, the FFLP problem with equality constraints first is converted into a multi–objective linear programming (MOLP) problem with crisp const...

This paper proposes a compromise model, based on a new method, to solve the multi-objective large-scale linear programming (MOLSLP) problems with block angular structure involving fuzzy parameters. The problem involves fuzzy parameters in the objective functions and constraints. In this compromise programming method, two concepts are considered simultaneously. First of them is that the optimal ...

Linear programming is one of the most important usages of operation research methods in real life, that includes of one objective function and one or several constraints which can be in the form of equality and inequality. Most of the problems in the real world are include of inconsistent and astute uncertainty, because of this reason we can’t obtain the optimal solution easily. In this paper, ...