Costis Maglaras

Dynamic Pricing and Lead-Time Quotation for a Multiclass Make-to-Order Queue

This paper considers a profit-maximizing make-to-order manufacturer that offers multiple products to a market of price and delay sensitive users, using a model that captures three aspects of particular interest: first, the joint use of dynamic pricing and lead-time quotation controls to manage demand; second, the presence of a dual sourcing mode that can expedite orders at a cost; and third, the interaction of the aforementioned demand controls with the operational decisions of sequencing and expediting that the firm must employ to optimize revenues and satisfy the quoted lead times. Using an approximating diffusion control problem we derive near-optimal dynamic pricing, lead-time quotation, sequencing, and expediting policies that provide structural insights and lead to practically implementable recommendations. A set of numerical results illustrates the value of joint pricing and lead-time control policies.

Monopoly Pricing in the Presence of Social Learning

A monopolist offers a product to a market of consumers with heterogeneous quality preferences. Although initially uninformed about the product quality, they learn by observing past purchase decisions and reviews of other consumers. Our goal is to analyze the social learning mechanism and its effect on the sellers pricing decision. Consumers follow an intuitive non-Bayesian decision rule and, under some conditions, eventually learn the products quality. We show how the learning trajectory can be approximated in settings with high demand intensity via a mean-field approximation that highlights the dynamics of this learning process, its dependence on the price, and the market heterogeneity with respect to quality preferences. Two pricing policies are studied: a static price, and one with a single price change. Finally, numerical experiments suggest that pricing policies that account for social learning may increase revenues considerably relative to policies that do not.

Monopoly Pricing with Limited Demand Information

Traditional monopoly pricing models assume that firms have full information about the market demand and consumer preferences. In this article, we study a prototypical monopoly pricing problem for a seller with limited market information and different levels of demand learning capability under relative performance criterion of the competitive ratio (CR). We provide closed-form solutions for the optimal pricing policies for each case and highlight several important structural insights. We note the following: (1) From the firms viewpoint the worst-case operating conditions are when it faces a homogeneous market where all customers value the product equally, but where the specific valuation is unknown. In cases with partial demand information, the worse case cumulative willingness-to-pay distribution becomes piecewise-uniform as opposed to a point mass. (2) Dynamic (skimming) pricing arises naturally as a hedging mechanism for the firm against the two principal risks that it faces: first, the risk of foregoing revenue from pricing too low, and second, the risk of foregoing sales from pricing too high. And, (3) even limited learning, for example market information at a few price points, leads to significant performance gains.

Dynamic Pricing with Financial Milestones: Feedback-Form Policies

We study a seller that starts with an initial inventory of goods, has a target horizon over which to sell the goods, and is subject to a set of financial milestone constraints on the revenues and sales that need to be achieved at different time points along the sales horizon. We characterize the revenue maximizing dynamic pricing policy for the seller and highlight the effect of revenue and sales milestones on its structure. The optimal policy can be written in feedback form, where the price at each point in time is selected so as to track the most stringent among all future milestones. Building on that observation, we propose a discrete-review policy that aims to dynamically track the appropriate milestone constraint and show that this simple and practical policy is near optimal in settings with large initial capacity and long sales horizons even in settings with no advance demand model information. One motivating application comes from the sales of new multiunit, residential real estate developments, where intermediate milestone constraints play an important role in their financing and construction. This paper was accepted by Gerard P. Cachon, stochastic models and simulation.

A Maximum Entropy Joint Demand Estimation and Capacity Control Policy

We propose a tractable, data-driven demand estimation procedure based on the use of maximum entropy (ME) distributions, and apply it to a stochastic capacity control problem motivated from airline revenue management. Specifically, we study the two fare class “Littlewood” problem in a setting where the firm has access to only potentially censored sales observations; this is also known as the repeated newsvendor problem. We propose a heuristic that iteratively fits an ME distribution to all observed sales data, and in each iteration selects a protection level based on the estimated distribution. When the underlying demand distribution is discrete, we show that the sequence of protection levels converges to the optimal one almost surely, and that the ME demand forecast converges to the true demand distribution for all values below the optimal protection level. That is, the proposed heuristic avoids the “spiral down” effect, making it attractive for problems of joint forecasting and revenue optimization problems in the presence of censored observations.

Optimal Dynamic Auctions for Revenue Management

We analyze a dynamic auction, in which a seller with C units to sell faces a sequence of buyers separated into T time periods. Each group of buyers has independent, private values for a single unit. Buyers compete directly against each other within a period, as in a traditional auction, and indirectly with buyers in other periods through the opportunity cost of capacity assessed by the seller. The number of buyers in each period, as well as the individual buyers’ valuations, are random. The model is a variation of the traditional singleleg, multiperiod revenue management problem, in which consumers act strategically and bid for units of a fixed capacity over time. For this setting, we prove that dynamic variants of the first-price and second-price auction mechanisms maximize the seller’s expected revenue. We also show explicitly how to compute and implement these optimal auctions. The optimal auctions are then compared to a traditional revenue management mechanism—in which list prices are used in each period together with capacity controls—and to a simple auction heuristic that consists of allocating units to each period and running a sequence of standard, multiunit auctions with fixed reserve prices in each period. The traditional revenue management mechanism is proven to be optimal in the limiting cases when there is at most one buyer per period, when capacity is not constraining, and asymptotically when the number of buyers and the capacity increases. The optimal auction significantly outperforms both suboptimal mechanisms when there are a moderate number of periods, capacity is constrained, and the total volume of sales is not too large. The benefit also increases when variability in the dispersion in buyers’ valuations or in the number of buyers per period increases. (Optimal Auction; Strategic Behavior; Revenue Management; Dynamic Programming; Mechanism Design)

Bayesian social learning with consumer reviews

We study a market of heterogeneous customers who rationally learn the mean quality of an offered product by observing the reviews of customers who purchased the product earlier in time. The seller, who is equally uniformed about the quality, prices dynamically to maximize her revenue. We find that social learning is successful|agents eventually learning the mean quality of the product. This result holds for an information structure when the sequence of past re- views and prices is observed, and, under some assumptions, even when only aggregate reviews are observed. The latter result hinges on the observation that earlier reviews are more inuential than later one. In addition, we find that under general conditions the seller benefits from social learning ex ante|before knowing the quality of her product. Finally, we draw conclusions on the sellers pricing problem when accounting for social learning. Under some assumptions, we find that lowering the price speeds social learning, in contrast with earlier results on social learning from privately observed signals.

Design of an Aggregated Marketplace Under Congestion Effects: Asymptotic Analysis and Equilibrium Characterization

We study an aggregated marketplace where potential buyers arrive and submit requests-for-quotes (RFQs). There are n independent suppliers modelled as M=GI=1 queues that compete for these requests. Each supplier submits a bid that comprises of a fixed price and a dynamic target leadtime, and the cheapest supplier wins the order as long as the quote meets the buyer’s willingness to pay. We characterize the asymptotic performance of this system, and subsequently extract insights about the equilibrium behavior of the suppliers and the efficiency of this market. We show that supplier competition results into a mixed-strategy equilibrium phenomenon and is significantly different from the centralized solution. We propose a compensation-while-idling mechanism that coordinates the system: each supplier gets monetary compensation from other suppliers during his idle periods. This mechanism alters suppliers’ objectives and implements the centralized solution at their own will.

Revenue Maximization for Cloud Computing Services

We study a stylized revenue maximization problem for a provider of cloud computing services, where the service provider (SP) operates an infinite capacity system in a market with heterogeneous customers with respect to their valuation and congestion sensitivity. The SP offers two service options: one with guaranteed service availability, and one where users bid for resource availability and only the “winning” bids at any point in time get access to the service. We show that even though capacity is unlimited, in several settings, depending on the relation between valuation and congestion sensitivity, the revenue maximizing service provider will choose to make the spot service option stochastically unavailable. This form of intentional service degradation is optimal in settings where user valuation per unit time increases sub-linearly with respect to their congestion sensitivity (i.e., their disutility per unit time when the service is unavailable) – this is a form of “damaged goods.” We provide some data evidence based on the analysis of price traces from the biggest cloud service provider, Amazon Web Services.

Product Design in a Market with Satisficing Customers

We study the product design problem of a revenue-maximizing firm that serves a market where customers are heterogeneous with respect to their valuations and desire for a quality attribute and are characterized by a perhaps novel model of customer choice behavior. Specifically, instead of optimizing the net utility that results from an appropriate combination of prices and quality levels, customers are “satisficers” in that they seek to buy the cheapest product with quality above a certain customer-specific threshold. This model dates back to Simon’s work in the 1950s and can be thought of as a model of bounded rationality for customer choice. We characterize the structural properties of the optimal product menu for this model and explore several examples where such preferences may arise.