Production scale expansion and congestion in two-stage network systems

In managerial practice, decision-makers usually confront the problem of whether an organization (or decision-making unit, DMU) could expand its production to increase output. This paper develops new approaches for production scale expansion analysis and target setting of two-stage network systems based on data envelopment analysis. First, the technique of fixing the strongly efficient frontier is adopted to ensure that the analysis proceeds on the efficient frontier. Second, a model is proposed to obtain the maximum aggregated output for each DMU. A two-step procedure is then developed for production scale expansion analysis to check if expanding a DMU's production scale (i.e., increasing the inputs and intermediate measures) would increase, maintain, or decrease its outputs (due to congestion). Further, we build a model to set appropriate production scale expansion targets for DMUs capable of increasing outputs through production scale expansion, considering their limited ability to increase inputs. Our approach always proceeds with production scale expansion analysis on the production efficient frontier. It also provides a simple sufficient and necessary condition to judge the congestion situation of a DMU in production scale expansion. Finally, we illustrate the proposed approach using a simple numerical example and a case study of China's agricultural industry.