  In high performance computing, scheduling of tasks and allocation to machines
is very critical especially when we are dealing with heterogeneous execution
costs. Simulations can be performed with a large variety of environments and
application models. However, this technique is sensitive to bias when it relies
on random instances with an uncontrolled distribution. We use methods from the
literature to provide formal guarantee on the distribution of the instance. In
particular, it is desirable to ensure a uniform distribution among the
instances with a given task and machine heterogeneity. In this article, we
propose a method that generates instances (cost matrices) with a known
distribution where tasks are scheduled on machines with heterogeneous execution
costs.
