This paper proposes single-supplier single-retailer production and inventory models for maximizing the supplier and retailer’s profits in non-cooperative and cooperative environments. The effect of defective items and inspection errors are considered in the proposed models. In addition, we consider that the supplier offers the retailer a quantity threshold to absorb transportation costs for promoting the economies of scale of transport. Mathematical analyses are conducted, and optimal equilibrium production and replenishment strategies for the supplier and retailer are derived under non-cooperative and cooperative situations. Subsequently, we establish two algorithms to explain the optimal equilibrium solutions for these cases. Finally, several numerical examples and a sensitivity analysis with respect to major parameters are presented to demonstrate the theoretical results, compare the distinct solutions, and derive managerial insights.