  One of the important problems for datacenter resource management is to place
virtual machines (VMs) to physical machines (PMs) such that certain cost,
profit or performance objective is optimized, subject to various constraints.
In this paper, we consider an interesting and difficult VM placement problem
with disk anti-colocation constraints: a VM's virtual disks should be spread
out across the physical disks of its assigned PM. For solutions, we use the
mixed integer programming (MIP) formulations and algorithms. However, a
challenge is the potentially long computation time of the MIP algorithms. In
this paper, we explore how reformulation of the problem can help to reduce the
computation time. We develop two reformulations, by redefining the variables,
for our VM placement problem and evaluate the computation time of all three
formulations. We show that they have vastly different computation time. All
three formulations can be useful, but for different problem instances. They all
should be kept in the toolbox for tackling the problem. Out of the three,
formulation COMB is especially flexible and versatile, and it can solve large
problem instances.
