Energy Efficient Scheduling via Partial Shutdown

We define a collection of new problems referred to as ``machine activation'' problems. The central framework we introduce considers a collection of M machines (unrelated or related), with machine $i$ having an activation cost of $a_i$. There is also a collection of N jobs that need to be performed, and $p_{ij}$ is the processing time of job $j$ on machine $i$. Standard scheduling models assume that the set of machines is fixed and all machines are available. We assume that there is an activation cost budget of $A$ -- we would like to select a subset S of the machines to activate with total cost $a(S)le A$ and find a schedule for the jobs on the machines in $S$ minimizing the makespan. In this work we develop bi-criteria approximation algorithms for this problem based on both LP rounding and a greedy approach.