So this is quite effective and we may use the same ideas for a linear programming approach.
Let's make a temporary assumption that the job order is fixed on each loom. Then the max weighted tardiness problem with this assumption is solved by the following model. This is the quantity of job j on loom m. This simple relationship links the speed of loom m for job j with the time spent on loom m by the same quantity. Once the job order is fixed, then the completion for each job is the following. For job 1 this is the time spent for the first job so this is the completion time of job 1 which has to be less than the deadline plus some extra time computed from the weighted tardiness. Then for the second job this sum is the completion time of the second job and so on. And this for job n. So that what we want now is given that we want for each job this fixed quantity to be processed. Then we simply have to minimise this value of the tardiness. However, this is true for a fixed order of this job.