Joint pricing and lot sizing model with statistical inspection and stochastic lead time

In many real-world situations, there are a fraction of defective items in a received lot whose quality should be evaluated before storage. In this article, we address the joint ordering, pricing, and inspection planning problem for a retailer facing price-sensitive demand and stochastic supply lead-time. The fraction of nonconforming items in a received lot follows a beta distribution and the buyer considers different kinds of inspection policies that include no inspection, inspection and sampling. Moreover, a novel non-linear optimization model is developed in order to determine optimal ordering, pricing and inspection policies. An analytical solution procedure based on mathematical properties of the model is proposed to find optimal decision variables. Numerical studies are conducted in order to show the applicability of the developed model and effectiveness of the proposed algorithms.