Appendix to “Managing Slow Moving Perishables in the Grocery Industry”

Abstract

Here, we characterize the distribution ψ ( β) � introduced in §3.1.2. Without information D sharing, the supplier only knows the batch size Q and the history of the number of periods since the retailer’s last order β. We follow the procedure outlined in Bai et al. (2007) to show how this information is used to determine the retailer’s order distribution. Let Xi be a random variable representing the usage of the product (sales and outdating) at the retailer on day i for i = 1, …, M. The Xi s are independent with the same mean and variance, but they may come from different distributions. Assuming the retailer uses a reorder point inventory control policy (a reasonable assumption in this industry), once the retailer’s approximate inventory position Ii is below the reorder point r, then an order quantity of size Q will be ordered at time ti. Thus, during the time interval [ti-1, ti) with length i D � = ti- ti-1, the relationship between accumulated usage and the retailer’s inventory position can be expressed a