Developing trust among players in a vendor-managed inventory model for random demand under environmental impact

Retailers play a vital role in supply chain management because they deal directly with consumers. Occasionally, retailers may cover the entire system's statistics and not disclose these data to the manufacturer. Therefore, asymmetry is generated in the data throughout the system. The main motive of this research was to prevent unreliability throughout the system using a vendor-managed inventory policy. This research shows that by applying a cap and trade policy, the total carbon emitted from the production and transportation sectors can be controlled in the atmosphere. Finally, numerical and sensitivity analyses, along with pictorial representations of various parameters, are performed to examine the optimal results of this study. In addition, the retailer's lead time demand for items is assumed to be random rather than fixed and follows uniform and normal distribution functions. Under these two distribution functions, the optimal retailer lot size, service provided by the retailer to customers, and retailer reorder points are assessed. Furthermore, an evaluation of the total carbon released from an environmental viewpoint is illustrated using numerical findings. The numerical results show that this research is 50.24% more economically beneficial than the methods used in previous studies, whereas the mean value of demand follows a uniform distribution.