On Solving Fully Rough Multi-Objective Integer Linear Programming Problems

Abstract

In this paper a suggested algorithm to solve fully rough multi-objectiveinteger linear programming problem [FRMOILP] is described. In orderto solve this problem and find rough value efficient solutions anddecision rough integer variables by the slice-sum method with thebranch and bound technique, we will use two methods, the first one isthe method of weights and the second is e- Constraint method. The basicidea of the computational phase of the algorithm is based onconstructing two LP problems with interval coefficients, and then to fourcrisp LPs. In addition to determining the weights and the values of e-constraint. Also, we reviewed some of the advantages and disadvantagesfor them. We used integer programming because many linearprogramming problems require that the decision variables are integers.Also, rough intervals (RIs) are very important to tackle the uncertaintyand imprecise data in decision making problems. In addition, theproposed algorithm enables us to search for the efficient solution in thelargest range of possible solutions range. Also, we obtain N suggestedsolutions and which enables the decision maker to choose the bestdecisions. Finally, two numerical examples are given to clarify theobtained results in the paper.