  We study the optimal design of a heterogeneous coded elastic computing (CEC)
network where machines have varying relative computation speeds. CEC introduced
by Yang {\it et al.} is a framework which mitigates the impact of elastic
events, where machines join and leave the network. A set of data is distributed
among storage constrained machines using a Maximum Distance Separable (MDS)
code such that any subset of machines of a specific size can perform the
desired computations. This design eliminates the need to re-distribute the data
after each elastic event. In this work, we develop a process for an arbitrary
heterogeneous computing network to minimize the overall computation time by
defining an optimal computation load, or number of computations assigned to
each machine. We then present an algorithm to define a specific computation
assignment among the machines that makes use of the MDS code and meets the
optimal computation load.
