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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.
Highlights
Linear programming (LP) is one of the most popular models used in decision making and optimization problems
T, (1997) Integer programming (IP) problems are optimization problems that min or max the objective function taking into consideration the limits of constraints and integer variables
In the presented paper a solution algorithm has been proposed to solve fully rough multiobjective integer linear programming problems by two methods and found rough value efficient solutions and decision rough integer variables, .In the first phase of the solution approach and to avoid the complexity of this problem we began by converting the rough nature of this problem into an equivalent crisp problem
Summary
Linear programming (LP) is one of the most popular models used in decision making and optimization problems. H. T, (1997) Integer programming (IP) problems are optimization problems that min or max the objective function taking into consideration the limits of constraints and integer variables. More widely application of integer programming can be used to appropriately describe the decision problems on the management and effective use of resources in engineering technology, business management and other numerous fields [15]. G. Mavrotas in (2009) Effective implementation of the ε-constraint method in Multi-Objective Mathematic programming problems see [20]. The focus of our study is improvement a method to solve fully rough multi objective integer linear programming. In our problem we assume that all parameters and decision variables in the both of constraints and the objective functions are rough intervals (RIs). Numerical examples for demonstrating the solution procedure of the proposed method and the conclusion are given
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