Robust multiperiod inventory model with a new type of buy one get one promotion: “My Own Refrigerator”

Recently, one of the largest retail companies in Korea introduced a mobile application that enables customers to store buy-one-get-one (BOGO) products in their virtual storage for later use. That is, customers who store the extra freebies in their virtual storage can drop by the store to pick them up in the future. Consequently, the application was successful in attracting customers. However, this type of promotion has significant implications for inventory levels. Since customers who buy the product do not need to take both products on the day of purchase, the promotion involves a high degree of uncertainty regarding the revisiting date. To deal with this uncertainty, we propose a robust multiperiod inventory model by addressing the approximation of a multistage stochastic optimization model. Without full information on the distribution, the inventory policy can be derived with support and the first and second moments of uncertainty factors. The presented model is different from previous studies in that the sum of the uncertainty factors in a particular interval is constrained to less than or equal to 1. This part is reformulated as a robust counterpart that retains tractability under modest data sizes. The results of the comparative simulation experiments show that the presented model provides a robust and stable solution against the worst-case scenario. We also obtain managerial insights from the experiments by varying the expiry date according to three types of customers’ revisiting tendencies.