This paper presents a new approach to address target setting in mergers by utilizing two complementary techniques: Goal Programming (GP) and Inverse Data Envelopment Analysis (InvDEA). Traditional DEA models assess the relative efficiency of decision-making units (DMUs) based on multiple inputs and outputs. However, InvDEA focuses on determining the input and output quantities required to achieve a specific efficiency score target. These models face limitations when deviations from the frontier occur due to noise and random errors in the data. To overcome this issue, this paper introduces a novel stochastic method that estimates the input/output levels of the merged unit needed to attain the predetermined efficiency score at a specified level of significance (α ∈ [0, 1]). Our models proposed are applied to the banking industry, demonstrating their effectiveness. The study provides decision makers with a valuable method to incorporate their preferences when setting merger targets, enabling them to optimize savings in specific inputs or maximize the production of desired outputs. To validate the proposed method, an illustrative application is conducted within the banking industry.