Sensitivity analysis of the bullwhip effect in supply chains with time delay

The bullwhip effect (BWE) is a major challenge engineers facing in the industry. From the time and economic point of view, it is important to determine stability regions, where the bullwhip effect does not occur. In this paper, we designed a structure for optimal regulation of the BWE with Network Inverse Data Envelopment Analysis (IDEA) approach. The results indicated that time can negatively affect the magnitude of the bullwhip effect. So, the effect of time and delays should be considered in the BWE score. There are two modes: (1) the RBWE occurs at this interval, where the proposed network was able to regulate and control the RBWE; (2) the RBWE does not occur at this interval, where the stability area was obtained to ensure that the manager can change the inputs or outputs according to his policies, in this area with no regard to the occurrence of the RBWE. Finally, two numerical examples indicated the method efficiency for managing the RBWE in the proposed network supply chain.