Using Branch and Bound and Local Search Methods to Solve Multi-objective Machine Scheduling Problem

In this research, we suggested the problem scheduling of n jobs on a single machine to decrease schedule multi-objective function; the sum cost of total completion time, the total number of late jobs, total tardiness and the maximum tardiness $(\Sigma C_{i}+ \Sigma U_{i}+\Sigma T_{i}+T_{max})$, which is NP-hard problem. In this research, we proposed the branch and bound algorithm (BAB) to obtain the optimal solution. We used some local search methods (descent method (DM) and genetic algorithm (GA)) to obtain an optimal solution or a near-optimal solution. Also, we developed a simple algorithm (SPT-MA) to find a solution near the optimum solution. The (SPT-MA) algorithm proofs its good performance in solving the problem in a reasonable time.