I am working with Integer Optimization optimization. I have a problem with t tasks and every task i needs w_i weeks to be completed and p_i_t workers on that specific week. There is a total time in weeks to complete all tasks. I need to optimize (min) the max value of workers needed in any week (variables to define: starting week for every particular task, or similar). Weeks needed per task and amount of worker in each week are given as data points.
There is also a constraint: once a task starts, it should be finished (can't be paused). All tasks could run in parallel if needed.
How can I model this optimization problem formally?
