Risk-averse newsvendor models

Abstract

The multi(or single-) product newsvendor problem is a well-known classical problem in inventory management. The general setting analyzed is as follows. There are multiple (or single) perishable products with random demand in a single-selling season. Given a purchase cost and resale price, the decision maker (aka the newsvendor) chooses the optimal ordering quantity for each product at the beginning of the selling season. If the newsvendor orders too much of any product, all leftovers are sold at salvage value; if the newsvendor orders too little, it incurs lost opportunity of sales. Given uncertain demand, it is obvious that the final profit for the newsvendor is random. Thus prior researchers have focused on maximizing expected profits for the newsvendor in making the ordering decision. Unless there are resource constraints and/or demand substitution effects, most multiproduct newsvendor problems can be decomposed into multiple independent single-product problems. The general solution (for expected profit maximization) is a simple closed-form ratio of the overage and underage ”costs” for the newsvendor’s (cumulative) marginal demand distribution. Given such a straightforward result, this approach has been applied in numerous industry settings to address problems of revenue management and/or overbooking. From a decision-maker’s perspective, maximizing expected profits implies risk neutrality. However, risk neutrality guarantees the best decision only on average. Although the use of this model may be justified by the Law of Large Numbers, one cannot expect that a single realization will be sufficiently close to the expected value. In fact, when actual outcomes deviate greatly from their expected values due to their randomness, it may cause an unacceptably large loss to the newsvendor.