The Efficiency Measurement of Parallel Production Systems: A Non-radial Data Envelopment Analysis Model

Abstract

Problem statement: Data Envelopment Analysis (DEA) is a non-parametric technique for measuring the relative efficiency of a set of production systems or Decision Making Units (DMU) that have multiple inputs and outputs. Sometimes, DMUs have a parallel structure, in which systems composed of parallel units work individually; the sum of their own inputs/outputs is the input/output of the system. For this type of system, conventional DEA models treat each DMU as a black box and ignore the performance of its units. Approach: This study introduces a DEA model in Slacks-Based Measure (SBM) formulation which considers the parallel relationship of the units within the system in measuring the efficiency of the system. Under this framework, the overall efficiency of the system is expressed as a weighted sum of the efficiencies of its units. Results: As an SBM model, the proposed model is non-radial and is suitable for measuring the efficiency when inputs and outputs may change non-proportionally. A theoretical result shows that if any unit of a parallel system is inefficient then the system is inefficient. Conclusion: This study introduces a non-radial DEA model, takes into account the operation of individual components within the parallel production system, to measure the overall efficiency as well as the efficiencies of sub-processes. This helps the decision makers recognize inefficient units and make later improvements.