Exact Method with Dominance Rules for Solving Scheduling on a Single Machine Problem with Multiobjective Function

Abstract

The present article proposes an exact algorithm for the single-machine scheduling problem to minimize the sum of total completion times, range of lateness and maximum tardiness on a single machine (1/ /(∑ C_(σ_j + R_L + T_max)), where machine idle time is prohibited. In this paper, one of the multiobjective function problem for single criteria on just one machine is being studied. To obtain the optimal solution for the suggested problem, we propose to use Branch and Bound method (BAB) depending upon some dominance rules. This exact method used new technique to obtain three upper bounds (UB) and single lower bound (LB). The proposed BAB method proved its sufficiency by the practical results for n ≤ 15 in a reasonable time. Lastly, we proved a theorem as special case for our problem.