Given a set of $N$ jobs and two machines A and B, each machine can process only one job at a time. Each job, if processed, must be processed by machine A before processed by machine B. The processing time of job $i$ at machine A and B is $t_{i}^{A}$ and $t_{i}^{B}$ respectively. The deadline and the profit of job $i$ are $d_i$ and $p_i$ respectively. All jobs are available at time 0.