In data centers, up to dozens of tasks are colocated on a single physical machine. Machines are used more efficiently, but tasks’ performance deteriorates, as colocated tasks compete for shared resources. As tasks are heterogeneous, the resulting performance dependencies are complex. In our previous work [18] we proposed a new combinatorial optimization model that uses two parameters of a task — its size and its type — to characterize how a task influences the performance of the other tasks allocated to the same machine. In this paper, we study the egalitarian optimization goal: maximizing the worstoff performance. This problem generalizes the classic makespan minimization on multiple processors (P||Cmax). We prove that polynomially-solvable variants of P||Cmax are NP-hard and hard to approximate when the number of types is not constant. For a constant number of types, we propose a PTAS, a fast approximation algorithm, and a series of heuristics.We simulate the algorithms on instances derived from a trace of one of Google clusters. Algorithms aware of jobs’ types lead to better performance compared with algorithms solving P||Cmax. The notion of type enables us to model degeneration of performance caused by colocation using standard combinatorial optimization methods. Types add a layer of additional complexity. However, our results — approximation algorithms and good average-case performance — show that types can be handled efficiently.