Well adjusted: Using expediting and cancelation to manage store replenishment inventory for a seasonal good

We consider an inventory problem that can be translated into a two‐period newsvendor setting where the day prior to sales, the newsvendor places an initial preliminary order–a semi‐binding forecast–with the publisher. At the beginning of the actual day of sales, the newsvendor has a better forecast for the day’s demand: based on knowing the actual content of the paper, he knows whether it will be a high‐demand day due to breaking news or a low‐demand day due to slow news. He then can revise the preliminary order quantity by expediting additional papers or canceling all or part of the order, but each of these activities has an associated cost. We find closed‐form solutions for the optimal preliminary and revised orders in this two‐period newsvendor problem where demand is characterized as a binary random variable in the first period and one of two general distributions in the second. At the beginning of the second period, the binary random variable has been realized and the general distribution is known. At this point, the preliminary order may be adjusted upward or downward, with these changes incurring expediting or cancelation costs, respectively.