A Branch-and-Bound Algorithm for non-Integer Linear Programs with Fuzzy Right-Hand Side Coefficients

One algorithm design paradigm that makes it possible to use the spatial features of problems to prone the state space is Branch and Bound (B&B), especially with the treatment of ambiguous numbers in linear programming models. In order to solve optimization problems, B&B algorithms arrange the collection of potential solutions into a structure a tree like that is known as the tree of search and systematically list all of its nodes. The strategy of the search, the strategy of branching, and the rules of pruning are the three algorithmic elements that control how a B&B algorithm behaves. The branch-and-bound (B&B) algorithm is a common way to treat the ILP problem through the improvement process of which the method. We study and identify useful sophisticated branch-and-bound algorithms and improvement systems to control the process of converting the optimal solution coefficients into integer numbers. In addition, the linear programming model, especially of the restrictions right-hand side, contains fuzzy numbers, which enables us to convert them into an integer number and improve the model for elimination and control in order to obtain a linear programming model with integer numbers. When using the graphical method to find the optimal solution, it was found that the solution does not fulfill the condition of integers (non-integer), where in this case the method of branch and bound was used in addressing the case, which continuously divided the issue into sub-issues. The optimal solution was reached, and although it fulfilled the condition that the values of the two variables are integers, the objective function value has decreased from its value in the solution that is optimal to the actual problem.