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The prevalent economic principle of weak disposability has been the foundation for studies in environmental assessment using Data Envelopment Analysis (DEA). Recently, a shift from classical free disposability to weak disposability has been observed as an emerging trend for treating undesirable factors in research. Weak disposability is perceived to have significant analytical power in measuring the efficiency of Decision-Making Units (DMUs). Addressing the increment of undesirable inputs, a non-radial model grounded on a non-uniform augment factor is presented. The application of this proposed model anticipates a suitable quantity for the increment of undesirable inputs. Concurrently, the model ensures a corresponding reduction in desirable inputs. Numerical instances illuminate the practicality and robustness of the proposed model and demonstrate its superior performance over its original counterpart.