In recent years, several mixed integer linear programming (MILP) models have been proposed for finding the most efficient decision-making unit (DMU) in data envelopment analysis. This paper introduces a new linear programming (LP) model to determine the most BCC-efficient decision-making unit. Unlike previous models, which are not convex, the new model is linear programming and so that it can be solved efficiently to discover the most efficient DMU. Moreover, it is mathematically proved that the new model identifies only a single BCC-efficient DMU by a common set of optimal weights. To show the applicability of the proposed model, a numerical example which contains a real data set of nineteen facility layout designs (FLDs) is used.