Add to ORKGMapReduce framework is established as the standard approach for parallel processing of massive amounts of data. In this work, we extend the model of MapReduce scheduling on unrelated processors (Moseley et al., SPAA 2011) and deal with the practically important case of jobs with any number of Map and Reduce tasks. We present a polynomial-time (32 + ✏)-approximation algorithm for minimizing the total weighted completion time in this setting. To the best of our knowledge, this is the most general setting of MapReduce scheduling for which an approximation guarantee is known. Moreover, this is the first time that a constant approximation ratio is obtained for minimizing the total weighted completion time on unrelated processors under a nontrivi...