Matrix chain multiplication is widely used in high-performance computing environments. Different parenthesis assignments, which determine the multiplication order, produce the same output but may significantly affect the runtime. Thus, finding the optimal parentheses assignment is crucial. Several algorithms, such as Godbole (1973) and Hu & Shing (1982), have been proposed to address this optimization problem. However, they only focus on minimizing arithmetic operations and disregard inter-processor communication. In many cases, the inter-processor communication cost dominates the total runtime, which makes existing algorithms sub-optimal. Schwartz and Weiss (2019) generalized Godbole’s algorithm to support fast (sub-cubic) matrix multiplication algorithms and demonstrated cases where optimizing arithmetic cost leads to sub-optimal communication cost and vice-versa. We extend their work and show that the runtime of a chain multiplication with a given parentheses assignment additionally depends on processor allocation and available resources. We present a parentheses assignment algorithm that minimizes the total runtime and outperforms previous techniques by a factor of \(\varOmega \left( t^{\frac{1}{3}} \right) \) (where t is the chain size). Moreover, our algorithm demonstrates up to 7.8x speedup in simulations. To the best of our knowledge, this is the first study that discusses resource allocation in the context of matrix chain multiplication.