Although resource allocation is a well studied problem in computer science, until the prevalence of distributed systems, such as computing clouds and data centres, the question had been addressed predominantly for single resource type scenarios. At the beginning of the last decade, with the introuction of Dominant Resource Fairness, the studies of the resource allocation problem has finally extended to the multiple resource type scenarios. Dominant Resource Fairness is a solution, addressing the problem of fair allocation of multiple resource types, among users with heterogeneous demands. Based on Max-min Fairness, which is a well established algorithm in the literature for allocating resources in the single resource type scenarios, Dominant Resource Fairness generalises the scheme to the multiple resource case. It has a number of desirable properties that makes it preferable over alternatives, such as Sharing Incentive, Envy-Freeness, Pareto Efficiency, and Strategy Proofness, and as such, it is widely adopted in distributed systems. In the present study, we revisit the original study, and analyse the structure of the algorithm in closer view, to come up with an alternative algorithm, which approximates the Dominant Resource Fairness allocation in fewer steps. We name the new algorithm Precomputed Dominant Resource Fairness, after its main working principle.