Literature for Generalized Load Balancing i am looking for literature on this kind of problem.
$$
\begin{align}
\min_x \max_k &amp;\quad \sum_{i,j} x_{ij}c_{ijk}\\
\text{subject to}&amp;\\
&amp;\sum_j x_{ij}=1,&amp;&amp; \forall i\in\mathcal J\\
&amp;x_{ij}\in\{0,1\},&amp;&amp; \forall i\in\mathcal J, j\in\mathcal M
\end{align}
$$


$\mathcal J$ is a set of Jobs and $\mathcal M$ is a set of Machines.
$c_{ij}$ is a vector and describes the cost of the job $i$ on the machine $j$.
So the cost has multiple dimension.


The Aim of the programm is to find a schedule so that each job is scheduled on a machine and the biggest dimension of the add up cost vector is minimized. 

The problem is described here:

http://arxiv.org/pdf/1211.5729v2.pdf (Page 2 left column bottom) as Generalized load balancing

and here:

http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=A8FEB960E21CA0361066CD5200C02718?doi=10.1.1.380.8241&amp;rep=rep1&amp;type=pdf (Page 4 left column) as  generalized AP association
problem

EDIT

load balancing can be generalized in several ways, i.e. restrict that each job can only run on a specific set of machines. 
This is also a generalization of the scheduling problem.

I'm interested in the case where the scheduling is restricted and multidimensional.
I'm looking for more literature for this problem.

Thank you
Appreciable literature is available in this standard book on Approximation Algo by Vazirani
http://www.cc.gatech.edu/fac/Vijay.Vazirani/book.pdf

Refer to chapter 10 for details.