Revenue Optimization for a Make-to-Order Queue in an Uncertain Market Environment

We consider a revenue-maximizing make-to-order manufacturer that serves a market of price- and delay-sensitive customers and operates in an environment in which the market size varies stochastically over time. A key feature of our analysis is that no model is assumed for the evolution of the market size. We analyze two main settings: (i) the size of the market is observable at any point in time; and (ii) the size of the market is not observable and hence cannot be used for decision making. We focus on high-volume systems that are characterized by large processing capacities and market sizes, and where the latter fluctuate on a slower timescale than that of the underlying production system dynamics. We develop an approach to tackle such problems that is based on an asymptotic analysis and that yields near-optimal policy recommendations for the original system via the solution of a stochastic fluid model

Optimal Price and Delay Differentiation in Large-Scale Queueing Systems

We study a multiserver queueing model of a revenue-maximizing firm providing a service to a market of heterogeneous price- and delay-sensitive customers with private individual preferences. The firm may offer a selection of service classes that are differentiated in prices and delays. Using a deterministic relaxation, which simplifies the problem by preserving the economic aspects of price-and-delay differentiation while ignoring queueing delays, we construct a solution to the fully stochastic problem that is incentive compatible and near optimal in systems with large capacity and market potential. Our approach provides several new insights for large-scale systems: (i) the deterministic analysis captures all pricing, differentiation, and delay characteristics of the stochastic solution that are nonnegligible at large scale; (ii) service differentiation is optimal when the less delay-sensitive market segment is sufficiently elastic; (iii) the use of “strategic delay” depends on system capacity and market heterogeneity—and it contributes significant delay when the system capacity is underutilized or when the firm offers three or more service classes; and (iv) connecting economic optimization to queueing theory, the revenue-optimized system has the premium class operating in a “quality-driven” regime and the lower-tier service classes operating with noticeable delays that arise either endogenously (“efficiency-driven” regime) or with the addition of strategic delay by the service provider. This paper was accepted by Gérard Cachon, stochastic models and simulation. </jats:p

Monopoly Pricing in the Presence of Social Learning

To be submitted on November 2011 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 seller’s pricing decision. This analysis borrows from the literature on social learning and on pricing and revenue management. Consumers follow a naive decision rule and, under some conditions, eventually learn the product’s quality. Using mean-field approximation, the dynamics of this learning process are characterized for markets with high demand intensity. The relationship between the price and the speed of learning depends on the heterogeneity of quality preferences. Two pricing strategies are studied: a static price and a single price change. Properties of the optimal prices are derived. Numerical experiments suggest that pricing strategies that account for social learning may increase revenues considerably relative to strategies that do not

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

Cross-Selling in a Call Center with a Heterogeneous Customer Population

This is the technical appendix accompanying the paper, “Cross-Selling in a Call Center with a Heterogeneous Customer Population, ” [3]. The organization of this appendix is as follows: we begin in §B with the completion of the proof of Proposition 1, whose sketch was given in §A of [3]. We continue in §C with some preliminaries required for the performance analysis of (S)-(C)