@techreport{TR-IC-05-15, number = {IC-05-15}, author = {E. C. Xavier and F. K. Miyazawa}, title = {An {APTAS} for the Variable-Sized Bin Packing Problem With Color Constraints}, month = {July}, year = {2005}, institution = {Institute of Computing, University of Campinas}, note = {In English, 7 pages. \par\selectlanguage{english}\textbf{Abstract} We consider the Variable-Sized Bin Packing Problem With Color Constraints (VBPCC). In this problem we have an unbounded number of bins, each one with size in $\{w_1,\ldots,w_k\}$, a list of items $L$, each item $e\in L$ with size $s_e$ and color $c_e$. The objective is to pack the items of $L$ into bins, such that no bin has items of more than $p$ colors, the total size of items packed in a bin is no more than the bin size and the total size of used bins is minimized. We present an asymptotic polynomial time approximation scheme when the number of different item colors is bounded by a constant $C$. } }