At first blush, this might be Job Shop Scheduling {1}. But I don't know {2}. If so, it is NP-Hard which means verifying an optimal solution is also in NP.
An LLM might be able to solve a toy scale problem with only four operations and lots of "machines." But I am skeptical it can solve problems of "interesting size" more effectively than numerical techniques because verification is also in NP. {3} Good luck.
{1} https://en.wikipedia.org/wiki/Job_shop_scheduling
{2} "All shifts covered" seems like a requirement for optimality.
{3} Assuming the problem is Job Shop Scheduling.
Note deepseek FAILED to figure it out
This is not what HN is used for. Don't create submissions just to report an AI response.