I have the following problem:
Given $n$ workers and $n$ tasks I have to assign a worker to each task where each worker has a time to get to the task, and each task has a preparation time. for example, task 1 preparation time is 10 minutes, it will take worker A 2 minutes to get there, 5 minutes for worker B, and 7 minutes for worker C.
My objective is to assign workers such that the waiting time is minimised.
I modelled it to a Weighted Bipartite Graph
Where each edge has a weight and each blue node (task) has a negative weight and we need to assign a worker such that the total cost will be as close to zero
Which algorithms should I look into to solve this?