Branch and Bound and Heuristic Methods for Solving Multi-Objective Function for Machine Scheduling Problems

In this paper, we suggest a multi-objective Machine Scheduling Problem (MSP). The discussed problem is the sum of total completion time, total tardiness, total earliness time, total late work and total number of late jobs. This work includes the theoretical analysis, discussion and proofs for many special cases for our problem. In addition, we discuss the effect of dominance rules in decreasing the completion in solving the discussed problem. Also we proposed the branch and bound (BAB) method to obtain optimal solution for this problem with good upper and lower bound and suggest heuristic methods to give a near optimal solution for the problem.