On Solving Fully Rough Multi-Objective Integer Linear Programming Problems | ||
| Delta Journal of Science | ||
| Article 1, Volume 41, Issue 1, June 2019, Pages 1-11 PDF (1.81 M) | ||
| Document Type: Research and Reference | ||
| DOI: 10.21608/djs.2020.139224 | ||
| Authors | ||
| El-Saeed Ammar; Abdusalam Emsimir | ||
| 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. | ||
| Keywords | ||
| Integer linear programming; weightings; ε- Constraint; Upper approximation; Lower approximation; Multi Objective; Crisp coefficients | ||
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