International green supply chain with stochastic exchange rate involving refurbished products through interior point algorithm

In recent days supply chain management not only focusing on optimal polices, rather they concern on environmental effects also. The two level joint replenishment model has been considered in this paper, where the buyer and vendor are located in different countries. By keeping environmental concern in mind, the variable and fixed carbon emission cost during transportation have been considered. Since the entities belong to different countries, and their respective currencies with stochastic exchange rate have been considered. The holding cost at vendor side is larger than the buyer side, so they decided to transfer from vendor to buyer as soon as the lot-size reaches the particular level. Furthermore, to avoid transportation frequency, the unequal shipment size is incorporated. The produced items might have defective products, that will screened and they are sent to the second quality market as refurbished products. An interior point algorithm is used to find the all lot-sizes.