Measurement of productivity changes for general network production systems with stochastic data

Abstract

Performance evaluation of network production systems has been widely studied in recent Data Envelopment Analysis (DEA) literature where internal relations of sub-units are taken into consideration. Most of prior work assumes network systems to have simple series or parallel structures. Complexities of some practical production processes require development of DEA models for their effective analysis. However; input, intermediate products and/or output data are often stochastic and linked to exogenous random variables in most applications. The current study extends Malmquist Productivity Index (MPI) for investigating productivity changes of general network production units with stochastic data in a DEA framework. The proposed stochastic performance analysis models are then transformed into deterministic equivalent non-linear forms so they could be simplified to deterministic programming with quadratic constraints. Numerical examples including an application to productivity evaluation of branches of a university system are presented to illustrate the applicability of the proposed framework.