We have a warehouse at which a number of trucks arrive. We have the time of arrival and departure of each truck and the amount of worker-hour(s) it takes to load/unload each truck. So for e.g, a truck can arrive at 10 AM and leave at 1 AM and requires a total of 6 worker-hours to load/unload. So we would need 2 workers working for the three hours, or 3 workers working two hours within that window or any suitable combination to load/unload.
Now if we have shifts defined for workers, let's say 9AM-5PM and 5PM-12AM and when we hire a worker we hire them for the whole shift and have to pay even if they sit idly during that. So for the given inputs above, how do we minimize the cost(worker-hours) while ensuring that all the trucks are loaded/unloaded within the time it is available at the warehouse.
Now, I know that this is not an easy optimization problem with a clear, closed form solution. But I am unable to even approach this problem. So if anyone could guide on how to approach this problem and what class of optimization problems this belongs to, it'd be great.
Assumptions:
- Truck times are arbitrary. There can be overlap between the time trucks are at the warehouse and there could also be times when no truck is there.
- Any reasonable assumption that I might've missed.