How accurate is the integrated vendor-buyer continuous model?

The classic single-item, deterministic-demand, integrated vendor-buyer model is revisited. The decision problem may also be viewed as that of one centralized firm, dealing with a two-level EOQ-like supply chain with finite production rates. It is sought to optimize the production lot-size and the integral number of its shipments, in equal batches, from the vendor to the buyer. While the problem calls for discrete optimization techniques, we introduced a continuous model where one can take derivatives with respect to both variables. In this short paper, we establish a 98.5% lower bound on the accuracy of this continuous model.