Data envelopment analysis (DEA) is a common nonparametric technique to measure the relative efficiency scores of the individual homogenous decision making units (DMUs). One aspect of the DEA literature has recently been introduced as a centralized resource allocation (CRA) which aims at optimizing the combined resource consumption by all DMUs in an organization rather than considering the consumption individually through DMUs. Conventional DEA models and CRA model have been basically formulated on desirable inputs and outputs. The objective of this paper is to present new CRA models to assess the overall efficiency of a system consisting of DMUs by using directional distance function when DMUs produce desirable and undesirable outputs. This paper initially reviewed a couple of DEA approaches for measuring the efficiency scores of DMUs when some outputs are undesirable. Then, based upon these theoretical foundations, we develop the CRA model when undesirable outputs are considered in the evaluation. Finally, we apply a short numerical illustration to show how our proposed model can be applied.