On Solving Fully Rough Multi-Objective Integer Linear Programming Problems

Document Type : Research and Reference

Authors

Department of mathematics, Faculty of science. Tanta University

Abstract

In this paper a suggested algorithm to solve fully rough multi-objective
integer linear programming problem [FRMOILP] is described. In order
to solve this problem and find rough value efficient solutions and
decision rough integer variables by the slice-sum method with the
branch and bound technique, we will use two methods, the first one is
the method of weights and the second is ε- Constraint method. The basic
idea of the computational phase of the algorithm is based on
constructing two LP problems with interval coefficients, and then to four
crisp LPs. In addition to determining the weights and the values of ε-
constraint. Also, we reviewed some of the advantages and disadvantages
for them. We used integer programming because many linear
programming problems require that the decision variables are integers.
Also, rough intervals (RIs) are very important to tackle the uncertainty
and imprecise data in decision making problems. In addition, the
proposed algorithm enables us to search for the efficient solution in the
largest range of possible solutions range. Also, we obtain N suggested
solutions and which enables the decision maker to choose the best
decisions. Finally, two numerical examples are given to clarify the
obtained results in the paper.

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