EOQ models for a coordinated two-level international supply chain considering imperfect items and environmental impact

For a two-level supply chain, models are presented to determine the optimal production-shipment policy for items with imperfect quality in three different scenarios: (a) both the vendor and the buyer are in the same country, (b) the vendor and the buyer are in different countries where the stochastic behavior of the exchange rate between the two countries is modeled using a mean-reverting process, and (c) environmental impact is incorporated in determining the optimal production-shipment policy by taking into account the fixed and variable carbon emission costs. The objective is to minimize the total expected cost per unit time. For each scenario, considering equal shipment size, the total expected cost per unit time is derived and the solution procedure is proposed. Numerical examples are presented and the results are discussed.