Estimating most productive scale size with stochastic data in data envelopment analysis

Abstract

This article estimates most productive scale size in stochastic data envelopment analysis (DEA). Jahanshahloo and Khodabakhshi [Jahanshahloo, G.R. and Khodabakhshi, M., Using input–output orientation model for determining most productive scale size in DEA. Applied Mathematics and Computation 2003, 146(2–3), 849–855.] studied most productive scale size in classic data envelopment analysis. The classic data envelopment analysis requires that the values for all inputs and outputs be known exactly. However, this assumption may not be true, because data in many real applications cannot be precisely measured. One of the important methods to deal with imprecise data is considering stochastic data in DEA. Therefore, this research studies most productive scale size with considering stochastic data in DEA. To that end, input–output orientation model introduced in Jahanshahloo and Khodabakhshi [Jahanshahloo, G.R. and Khodabakhshi, M., Using input–output orientation model for determining most productive scale size in DEA. Applied Mathematics and Computation 2003, 146(2–3), 849–855.] is extended in stochastic data envelopment analysis. To solve the stochastic model, a deterministic equivalent is obtained. Although the deterministic equivalent is non-linear, it can be converted to a quadratic program. Furthermore, data of software companies is used to apply the proposed approach. Performance of software companies are evaluated based on their scale sizes in classic and stochastic data envelopment analysis.