I have a generalized assignment problem, where each worker can have many tasks, and where there's a (non-integer) cost for starting a worker. I want to minimize costs. The starting cost can be pretty high, so it's preferable not to start a worker, if possible.
Is this solvable, or can it be at least approximated? I'm totally new to LP/MIP and am having trouble finding papers / lectures / textbooks.
e.g. if there're two workers A,B and two tasks 1,2 with costs
A1=1.4, B1=6, A2=3, B2=24
Then normally, the optimal configuration is
A2,B1 (Task 2 on A, Task 1 on B), the total cost being
But in my situation the initial cost of creating each worker is say,
90. So the optimal configuration becomes
Moreover, workers are bound by the total volume of the tasks (e.g. RAM pre-configured by each worker) they can be assigned.