Multi-period capacity utilization measurement using a TOPSIS-DEA approach: A case study of the forestry industry

Excess capacity has emerged as a global challenge, limiting resource allocation efficiency and hindering sustainable industrial development. Accurate measurement of capacity utilization (CU) is therefore essential. To meet this need, we propose a new multi-period CU measurement model that integrates the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) and DEA (Data Envelopment Analysis) approaches. The model first constructs positive and negative production possibility sets, integrating the best and worst production states of decision-making units (DMUs) across periods. Using duality theory and multi-objective programming theory, Pareto optimality is proven to be equivalent to DEA efficiency in these sets. This equivalence serves as a foundation for defining benchmarks and ensures their scientific validity. Building on this foundation, positive and negative CU measurement models are developed, integrating the TOPSIS concept of relative closeness to construct a composite CU indicator. To demonstrate its applicability, the model is implemented using forestry sector data from 31 Chinese provinces for the period 2011–2020 and benchmarked against traditional methods. The results show that the efficiency evaluation based on the benchmark improves ranking reliability and allows comparisons across periods. Furthermore, the new CU indicator captures both positive and negative adjustment needs of DMUs, providing a more comprehensive and objective assessment of CU. This study provides a more precise quantitative tool for capacity regulation, offering important theoretical and practical implications for promoting industrial restructuring and sustainable development.