In data centers, up to dozens of tasks are colocated on a single physical machine. Machines are used more efficiently, but the performance of the tasks deteriorates, as the colocated tasks compete for shared resources. Since the tasks are heterogeneous, the resulting performance dependencies are complex. In our previous work [26], [27] 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 other tasks allocated to the same machine. In this paper, we study the egalitarian optimization goal: the aim is to optimize the performance of the worst-off task. This problem generalizes the classic makespan minimization on multiple processors (P||C max). We prove that polynomially-solvable variants of P||C max are NP-hard for this generalization, and that the problem is 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. Compared with baseline algorithms solving P||C max , our proposed algorithms aware of the types of the jobs lead to significantly better tasks' performance. The notion of type enables us to extend standard combinatorial optimization methods to handle degradation of performance caused by colocation. Types add a layer of additional complexity. However, our results-approximation algorithms and good average-case performance-show that types can be handled efficiently.