Branch and bound method to minimized three criteria

الملخص EN

This paper addresses the problem of minimizing the sum of total completion times, maximum earliness and maximum tardiness on a single machine with unequal release date.

A branch and bound algorithm with forward approach, in order to find the exact (optimal) solution for itwith two lower bounds (LB_1,LB_2) and four upper bounds〖(UB_1,UB_2,UB_3,UB_4) that introduced in this paper.

Ten special cases are suggested and proved that yield optimal solution.

In general, this problem is strongly NP-hard, and solved it with up to 30 jobs.