We study a newsvendor who sells a perishable asset over repeated periods to consumers with a given consumption valuation for the product. The market size in each period is random, following a stationary distribution. Consumers are loss averse with stochastic reference points that represent their beliefs about possible price and product availability. Given the distribution of reference points, they choose purchase plans to maximize their expected total utility, including gain-loss utility, before visiting the store, and follow the plans in the store. In anticipation of consumers' purchase plans, in each period, before demand uncertainty resolves, the firm chooses an initial order quantity. After the uncertainty resolves, the firm chooses a contingent price depending on the demand realization, with the option of clearing inventory by charging a sale price, and otherwise, posting a full price. Over repeated periods, the interaction of the firm’s operational decisions about ordering and contingent pricing and the consumers' purchase actions results in a distribution of reference points, and, in equilibrium, this distribution is consistent with consumers' beliefs. Under this framework of endogenized reference points, we fully characterize the firm’s optimal inventory and contingent pricing policies. We identify conditions under which the firm’s expected price and profit are increasing in the consumer loss aversion level. We also show that the firm can prefer demand variability over no-demand uncertainty. We obtain a set of insights into how consumers' loss aversion affects the firm’s optimal operational policies that are in stark contrast to those obtained in classic newsvendor models. As examples, the optimal full price increases in the initial order quantity; and the optimal full price decreases, while the optimal sales frequency increases, in the procurement cost.

D isplay advertising is a $25 billion business with a promising upward revenue trend. In this paper, we consider an online display advertising setting in which a web publisher posts display ads on its website and charges based on the cost-per-click pricing scheme while promising to deliver a certain number of clicks to the ads posted. The publisher is faced with uncertain demand for advertising slots and uncertain traffic to its website as well as uncertain click behavior of visitors. We formulate the problem as a novel queueing system, where the slots correspond to service channels with the service rate of each server inversely related to the number of active servers. We obtain the closed-form solution for the steady-state probabilities of the number of ads in the publisher's system. We determine the publisher's optimal price to charge per click and show that it can increase in the number of advertising slots and the number of promised clicks. We show that the common heuristic used by many web publishers to convert between the cost-per-click and cost-per-impression pricing schemes using the so-called click-through-rate can be misleading because it may incur substantial revenue loss to web publishers. We provide an alternative explanation for the phenomenon observed by several publishers that the click-through-rate tends to drop when they switch from the cost-per-click to cost-per-impression pricing scheme.

Display advertising has a 39% share of the online advertising market and is its fastest-growing category. In this paper, we consider an online display advertising setting in which a web publisher posts display ads on its website and charges based on the cost-per-impression (CPM) pricing scheme while promising to deliver a certain number of impressions on the ads posted. The publisher faces uncertain demand for advertising slots and uncertain supply of visits from viewers. We formulate the problem as a queueing system, where the advertising slots correspond to service channels with the service rate of each server synchronized with other active servers. We determine the publisher’s optimal price to charge per impression and show that it can increase in the number of impressions made of each ad, which is in contrast to the quantity discount commonly offered in practice. We show that the optimal CPM price may increase in the number of ads rotating among slots. This result is typically not expected because an increase in the number of rotating ads in the system can be interpreted as an increase in the service capacity. However, the capacity increase leads to an increase in the fill rate of the demand (the portion of demand satisfied by the publisher). Hence, the publisher can afford to optimally decrease the arrival rate by increasing the price. The electronic companion is available at https://doi.org/10.1287/opre.2017.1697 .

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Problem definition: Managers in ad agencies are responsible for delivering digital ads to viewers on behalf of advertisers, subject to the terms specified in the ad campaigns. They need to develop bidding policies to obtain viewers on an ad exchange and allocate them to the campaigns to maximize the agency’s profits, subject to the goals of the ad campaigns. Academic/practical relevance: Determining a rigorous solution methodology is complicated by uncertainties in the arrival rates of viewers and campaigns, as well as uncertainty in the outcomes of bids on the ad exchange. In practice, ad hoc strategies are often deployed. Our methodology jointly determines optimal bidding and viewer-allocation strategies and obtains insights about the characteristics of the optimal policies. Methodology: New ad campaigns and viewers are treated as Poisson arrivals, and the resulting model is a Markov decision process, where the state of the system is the number of undelivered impressions in queue for each campaign type in each period. We develop solution methods for bid optimization and viewer allocation and perform a sensitivity analysis with respect to the key problem parameters. Results: We solve for the optimal dynamic, state-dependent bidding and allocation policies as a function of the number of ad impressions in queue, for both the finite horizon and steady-state cases. We show that the resulting optimization problems are strictly concave in the decision variables and develop and evaluate a heuristic method that can be applied to large problems. Managerial implications: Numerical analysis of our heuristic solution shows that its errors are generally small and that the optimal dynamic, state-dependent bidding policies obtained by our model are significantly better than optimal static policies. Our proposed approach is managerially attractive because it is easy to implement in practice. We identify the capacity of the impression queue as an important managerial control lever and show that it can be more effective than using higher bids to reduce delay penalties. We quantify potential operational benefits from the consolidation of ad campaigns, as well as merging ad exchanges. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.1142 .