Evaluating directional scale elasticity in the RAM model with undesirable outputs: an application in the horticultural industry

This paper advances the concept of scale elasticity by examining the impact of directional input changes on both desirable and undesirable outputs. We integrate two disposability concepts into a unified measure within the Range Adjusted Measure (RAM) model, enabling the computation of both directional scale elasticity and directional scale damage. This approach allows for a comprehensive analysis of scale effects in the presence of undesirable outputs. Grounded in Data Envelopment Analysis (DEA), our research enhances the understanding of managing undesirable outputs while accounting for directional scale changes, offering significant implications for both performance improvement and environmental sustainability. The paper includes theoretical foundations, numerical examples to illustrate the methodologies, and an empirical application in the Iranian horticulture industry, demonstrating the effectiveness and adaptability of our approach.