Abstract: More and more retailers are willing to offer consumers money-back guarantees in regular seasons,which allows customers to return products that do not meet their expectation for a full refund. On the other hand,some consumers often wait to buy until the price mark down in clearance season, and this strategic behavior has a great impact on retailer's inventory and product returns strategies due to the uncertainty of demand. In the meantime, the strategic consumers have the risk of stockout in the clearance season, so they need to decide whether to buy in the regular season. In view of the complex behavior of the consumers, some retailers are attempting to reduce the loss by rationing the inventory reasonably. In this paper, the inventory rationing decisions and consumer return policies are examined in a two-period setting, where the first period is the regular selling season and the second is the clearance season.In this paper, it is assumed that consumers' valuations of products are heterogeneous and they are uncertain about their satisfaction until receiving the products. In addition, consumers' perceived fill rate is not always consistent with the actual fill rate, which reflects the cautious attitude of consumers. First, the base model without money-back guarantees is formulated and the retailer's optimal inventory rationing strategies are obtained. Then the scenario that the retailer offers money-back guarantees in the first period but not in the second period is analyzed. Through the comparison of these two scenarios, some thresholds for the retailer's money-back guarantees are identified.Our study shows that:markdown pricing is optimal when the range of consumers' valuations is large, otherwise uniform pricing is preferred; in the case of no-return, the number of consumers who purchase in regular season is increasing in consumers' satisfaction of products; in the case with money-back guarantees, the number of consumers who purchase inregular season is increasing in both retailer's and consumer's returns cost. Further more the profits under the cases of no-return and money-back guarantees are compared, and the conditions of implementing different returns policies are given.By comparing the case with myopic consumers and that with strategic consumer, it is found that the retailer suffers a loss due to consumers' strategic behavior. Finally, some numerical examples are present to investigate the impacts of consumers' satisfaction, return cost and price on the retailer's optimal decisions and profit. The results of this study can help managers develop better inventory rationingand product return policies.

Key words: strategic consumer, retailer, inventory rationing, money-back guarantees