  We study online multidimensional variants of the generalized assignment
problem which are used to model prominent real-world applications, such as the
assignment of virtual machines with multiple resource requirements to physical
infrastructure in cloud computing. These problems can be seen as an extension
of the well known secretary problem and thus the standard online worst-case
model cannot provide any performance guarantee. The prevailing model in this
case is the random-order model, which provides a useful realistic and robust
alternative. Using this model, we study the $d$-dimensional generalized
assignment problem, where we introduce a novel technique that achieves an
$O(d)$-competitive algorithms and prove a matching lower bound of $\Omega(d)$.
Furthermore, our algorithm improves upon the best-known competitive-ratio for
the online (one-dimensional) generalized assignment problem and the online
knapsack problem.
