Monitoring and Limiting Deceptive Counterfeiting: a Two-Stage Model

Abstract

Over past decades, deceptive counterfeits which cannot be recognized by ordinary consumers when purchasing, such as counterfeit cosmetics, have posed serious threats on consumers’ health and safety, and resulted in huge economic loss and inestimable brand damages to the genuine goods at the same time. Thus, how to effectively control and eliminate deceptive counterfeits in the market has become a critical problem to the local government. One of the principal challenges in combating the cheating action for the government is how to enhance the enforcement of relative quality inspection agencies like industrial administration office (IAO). In this paper, we formulate a two-stage counterfeit product model with a fixed checking rate from IAO and a penalty for holding counterfeits. To minimize the total expected cost over two stages, the retailer adopts optimal ordering policies which are correlated with the checking rate and penalty. Under certain circumstances, we find that the optimal expected cost function for the retailer is first-order continuous and convex. The optimal ordering policy in stage two depends closely on the inventory level after the first sales period. When the checking rate in stage one falls into a certain range, the optimal ordering policy for the retailer at each stage is to order both kinds of products. Knowing the retailer’s optimal ordering policy at each stage, IAO can modify the checking rate accordingly to keep the ratio of deceptive counterfeits on the market under a certain level.