Exact Algorithms for the Imbalanced Time Minimizing Assignment Problem

This paper studies the imbalanced time minimizing assignment problem (ITMAP) dealing with the allocation of n jobs to m (< n) machines. There are few works about this problem in the literature. In fact, only one lexi-shearch algorithm was found for the ITMAP, but it contain an slight error that was corrected here. Other algorithm by dynamic programming was found for the R∣Cmax problem and adapted for the ITMAP. A new approach through a linear model for this problem is introduced in this paper achieving considerables better results.