the newsvendor problem with different delivery time, resalable returns, and an additional order

In a B2C scenario, the retailer is confronted with two kinds of demand. One requires an immediate delivery after placing an order, while the other prefers a delayed shipment due to some personal reasons. Considering demands for different delivery time, we explore a newsvendor model with resalable returns and an additional order to optimize the procurement decision under a stochastic demand distribution. The impact of the proportion of the instant delivery needs and the return rate on the order quantity and the expected profit is illustrated through numerical tests. It is shown that the expected profit decreases as the ratios of immediate delivery needs and returned products increase. Besides, if the sum of the percentage of the instant delivery needs and the return rate is less than 1, the expected profit is always greater than the result if the sum of them is equal to or greater than 1. Management implications are also discussed.