I have a set of workers $P$ and a set of jobs $I$. I'm evaluating the queue priority at every time interval $T$ and the worker will take the job with the highest priority. The priority is calculated based on arrival time, predetermined constants and etc and noted as $Q_i$ at time $t$.
How can I model this so that worker $p_1$ will take the job with the highest $Q_i$ and $p_2$ will take the second highest, and so on?
I know I have to create a binary variable that is $1$ if worker $p$ selects job $i$, $0$ otherwise.
If $x_{wjt}$ is a binary variable taking value 1 if worker $w$ takes job $j$ at time $t$ and zero otherwise, then $\pi_{wt}=\sum_j Q_j x_{wjt}$ gives you the priority of the job worker $w$ snags at time $t$ (0 if the worker does not take any job). So you want $\pi_{1t} \ge \pi_{2t}$ if both worker 1 and worker 2 pick up jobs at time $t$. What is unclear from your description is whether every worker picks up a job at every time epoch.