<p>Researchers have recently developed a model for international supply chains for transferring lots in equal-sizedbatches, taking environmental concerns into account. This scheme incorporated stochastic behaviour of the exchange rate between the vendor’s and buyer’s currencies as part of the process for making optimal decisions onthe supply chain. They demonstrated that their model leads to a decrease in the total cost. However, a lowertotal cost can be achieved by synchronizing the integrated production flow through generalization of the batchtransfer method used to deliver the lot. Furthermore, there seems to be a better fit from a new data set for comparing two currencies. With these developments in mind, we suggest an alternative model, considering transferringbatches of unequal sizes, transfer costs that may be fixed or variable, and with an eye on environmental issues.Numerical experiments are presented to demonstrate the proposed model and solution method. These numericalexperiments show the value of this integrated approach in the combined determination of optimal policies forproduction and shipment. Suggestions for further research are given in the conclusion.<br></p>