Enhancing Cost Efficiency Estimates with Trade-offs for Improved Reallocation Processes

Abstract This paper presents a novel approach to estimate and decompose cost efficiency within the framework of Data Envelopment Analysis (DEA). We introduce the estimation of cost efficiency scores using trade-offs, enabling the estimation of technical efficiency (TE) and allocative efficiency (AE) within a single model. Furthermore, by utilizing initial input quantities, the reformulation estimates the substitution necessary for cost-efficient reallocation. Through a multi-stage optimization process, it is possible to minimize the required substitution to derive optimal quantities that remain close to the initial values, thereby facilitating easier reallocation. The optimization also provides insights into reallocation strategies, offering decision-makers concrete substitution guidelines to achieve an optimal input mix. Furthermore, the reformulation allows for considering only specific reallocations that reduce the discriminatory power of AE, enabling economic, social, or regulatory considerations in reallocation. The methodology is illustrated with an empirical example of electric utilities in the US Mid-Atlantic region. Additionally, statistical software has been developed to facilitate the estimation method for reproducibility and application.