How to measure bullwhip effect by network data envelopment analysis?

One of the most complicated decision making problems in supply chain management is performance assessment which involves diverse criteria. One of the main criteria for evaluating supply chain performance is bullwhip effect (BWE). For supply chains’ managers, measuring bullwhip effect is of critical importance. However, BWE is measured in classical series or parallel structures of supply chains. This network structure is rarely found in real-life (Dominguez, Cannella, & Framinan, 2014; Dominguez, Framinan, & Cannella, 2014). To present an insight of BWE measure in different supply chain networks (SCNs), a novel mathematical approach is proposed. To deal with this issue, a new network data envelopment analysis (NDEA) model is developed to measure relative BWE of non-serial SCNs and their divisions. Our proposed model is based on slacks-based measure (SBM) model. Since bullwhip effect is undesirable, worst-practice frontier (WPF) approach is considered. Accordingly, a new network worst practice SBM model with undesirable outputs is developed to calculate BWE of non-serial SCNs. In addition, BWE of each division is computed. Finally, a case study in pharmaceutical industry validates applicability of the proposed model.