An Integrated Single Vendor-Buyer Stochastic Inventory Model with Partial Backordering under Imperfect Production and Carbon Emissions

This paper develops an integrated single vendor single buyer inventory model with imperfect quality and environmental impact. The demand during lead time is assumed to be stochastic and follows the normal distribution. An integrated system with controllable lead time and logarithmic investment to reduce the defective percentage is discussed in this model.100% error-free screening process is adopted by the buyer to separate defective and non-defective items. We assume that shortages are allowed and are partially backordered at the buyer’s end. Logistics management is the component of supply chain management that focusses on how and when to get raw materials, intermediate products and finished goods from their respective origins to their destinations.Thus, transportation play a major role in supply chain. As transportation increases, it affects the weather by the matter of carbon emission.The fixed and variable carbon emission cost for both vendor and buyer is considered. The prime motive is to determine the optimal policies regarding optimal order quantity, reorder point, lead time and the number of lots delivered in a production run by minimizing the expected total cost of the system. Finally, a numerical example is provided to demonstrate the model