Abstract: Markdown contract is prevalent in industries selling perishable goods with uncertain demand, e.g., fashion apparel, fresh products, and newspapers. It is a form that the fashion brand pays a rebate credit to the retailer for each unsold unit only based on reported sales at the end of the regular selling season. Since the retailer is closer to the market and may also have better expertise in observing the basic demand of the market than the fashion brand (i.e., the sales are the retailer’s private information), the fashion brand has to try to eliminate or curb underreporting of sales. A large percentage of the literature (e.g., screening model and traditional auditing) on dishonest reporting focuses on inducing truthful information revelation strictly. Rather than this, the “relaxed” auditing strategy is considered explicitly that leaves room for underreporting and optimal order quantity is investigated in a supply chain consisting of a fashion brand and a retailer. First, the benchmark scenario is considered where the fashion brand uses a comprehensive auditing strategy to encourage true reporting. Second, the retailer’s optimal order quantity and the fashion brand’s optimal threshold are analyzed under a threshold auditing strategy to allow underreporting. Finally, the supply chain expected profits are compared under comprehensive and threshold auditing strategy. Analyses reveal that the retailer is willing to increase the order quantity since the retailer gains an additional compensation under threshold auditing strategy. Hence, the incentives of underreporting are more consistent with that of the overall supply chain, which mitigates double marginalization. Additionally, the supply chain and fashion brand expected profits can be increased by threshold auditing strategy. Unlike the screening model and traditional auditing literature, which induce truthful sales reporting by the retailer, the threshold auditing strategy to allow underreporting can do better when the retailer has private information about its demand than when this information is public. The analyses provide some guidelines for the fashion brands as they design markdown contract in situations where they do not know the demand the retailer faces. Hence, the fashion brands can relax auditing strategy and allow the retailers to be free to report sales to some extent when work with them, which not only promotes close cooperation, but also improves the overall supply chain performance.

Key words: markdown contracts, audit, ordering strategy