Optimal and Near Optimal Solutions for Multi Objective Function on a Single Machine

This In this paper, we studied one of the multi objective function problem on a single machine which is represented by the sum of total completion times, range of lateness and maximum tardiness on a single machine. As an exact solving method, we proposed the branch and bound (BAB) method to find the optimal solution for our problem, by using two techniques which are including new Upper bounds and Lower bounds. In addition, we introduce the idea of Dominance Rules to be used in BAB method to reduce the time by reducing the number of branching nodes in the search tree. Lastly, we suggested two heuristic methods to find near optimal solutions for our problem. The practical results proved the efficiency of BAB method in obtaining optimal solutions and the good performance of the proposed heuristic methods.