Developing a new theory of integer-valued data envelopment analysis for supplier selection in the presence of stochastic data

Supplier selection has a strategic importance for every company. Hybrid integer data is one of the models in data envelopment analysis (DEA). In many real world applications, data are often stochastic. A successful approach to address uncertainty in data is to replace deterministic data via random variables, leading to chance-constrained DEA. In this paper, a chance-constrained hybrid integer data envelopment analysis (CCHIDEA) model is developed and also its deterministic equivalent which is a nonlinear program is derived. Furthermore, it is shown that the deterministic equivalent of the CCHIDEA model can be converted into a quadratic program. In addition, sensitivity analysis of the CCHIDEA model is discussed with respect to changes on parameters. Finally, a case study demonstrates the application of the proposed model.