Optimal option purchase decision of a loss-averse retailer under emergent replenishment

Abstract

This paper studies the optimal option purchase of a loss-averse retailer under emergent replenishment. It is assumed that all or part of the excess demands in a stock-out situation can be replenished, and the loss-averse retailer's optimal option purchase quantity is investigated. It is found that the loss-averse retailer should not purchase options and only needs to replenish the inventory under certain conditions. When maximizing the expected utility without shortage cost, the loss-averse retailer's optimal option purchase quantity is decreasing in the loss aversion coefficient. To maximise the expected utility with shortage cost, a larger shortage cost implies a bigger option purchase quantity. If the shortage cost exists, there will be a loss on the expected profit and utility for the loss-averse retailer who selects an optimal option purchase quantity without shortage cost. Given the optimal option purchase quantity, it is proven that the loss-averse retailer's expected profit is decreasing in the loss aversion coefficient. Therefore the retailer should choose a proper loss aversion preference to balance between the two objectives of profit maximization and loss aversion preference. As a result of these findings, some management insights are recommended to the loss-averse retailer in selecting the option purchase quantity.