The newsboy problem with resalable returns and emergency order

We study a newsboy problem with product returns and two-order opportunity. The returned products arriving before the end of the selling season can be resold if there is sufficient demand. The first order is placed before the season starts. During the selling season, if the retailer predicts that the first order quantity are not enough to meet customerspsila demands, an emergency order is placed. Excess inventory at the end of the season is salvaged and all demands not met directly are lost. Therefore, we respectively analyse the newsboy problem with single order opportunity and resalable returns, and the newsboy problem with two order opportunities and resalable returns. We drive a simple formula to determine order quantity for the newsboy problem with single order opportunity and resalable returns. Computational experiments show the profitability of the emergency order option.