To efficiently solve the three criteria (objectives) sequencing problem on a single machine, we propose the modified branch and bound (MBAB) algorithm in this article. The criteria (objectives) are total completion time ($\sum C_j$), total lateness ($\sum L_j$), and maximum tardiness ($T_{\max}$). On a single machine, a collection of $n$ independent tasks (jobs) must be sequenced. Tasks (jobs) $j$ ($j=1,2,3,\dots,n$) require processing time $p_j$ and due date $d_j$. Conclusions for the modified branch and bound (MBAB) algorithm are formulated based on the outcomes of computing tests.