# The max-min resource assignment problem

I am wondering if there are any results for the following max-min assignment problem:

Given $$n$$ machines $$C = \{C_1, C_2, \dots, n\}$$ with the $$k$$-th machine has power $$C_k$$. There are $$m$$ tasks $$T = \{T_1, T_2, \dots, T_m\}$$. Each machine can cover a subset of the tasks in $$T$$. Now we assign each task to a machine that can cover it. The set of tasks assigned to the $$k$$-th machine is $$\mathit{CT}(k)$$. If the $$j$$-th task is assigned to the $$k$$-th machine, its received power is $$C_k/|\mathit{CT}(k)|$$. The question is: how to assign each task to a machine that can cover it, such that the minimum received power of all tasks are maximized?