Constantinos Maglaras

Dynamic Pricing Strategies for Multiproduct Revenue Management Problems

Consider a firm that owns a fixed capacity of a resource that is consumed in the production or delivery of multiple products. The firm strives to maximize its total expected revenues over a finite horizon, either by choosing a dynamic pricing strategy for each product or, if prices are fixed, by selecting a dynamic rule that controls the allocation of capacity to requests for the different products. This paper shows how these well-studied revenue management problems can be reduced to a common formulation in which the firm controls the aggregate rate at which all products jointly consume resource capacity, highlighting their common structure, and in some cases leading to algorithmic simplifications through the reduction in the control dimension of the associated optimization problems. In the context of their associated deterministic (fluid) formulations, this reduction leads to a closed-form characterization of the optimal controls, and suggests several natural static and dynamic pricing heuristics. These are analyzed asymptotically and through an extensive numerical study. In the context of the former, we show that resolving the fluid heuristic achieves asymptotically optimal performance under fluid scaling.

On Customer Contact Centers with a Call-Back Option: Customer Decisions, Routing Rules, and System Design

Organizations worldwide use contact centers as an important channel of communication and transaction with their customers. This paper describes a contact center with two channels, one for real-time telephone service, and another for a postponed call-back service offered with a guarantee on the maximum delay until a reply is received. Customers are sensitive to both real-time and call-back delay and their behavior is captured through a probabilistic choice model. The dynamics of the system are modeled as anM/M/N multiclass system. We rigorously justify that as the number of agents increases, the systems load approaches its maximum processing capacity. Based on this observation, we perform an asymptotic analysis in the many-server, heavy traffic regime to find an asymptotically optimal routing rule, characterize the unique equilibrium regime of the system, approximate the system performance, and finally, propose a staffing rule that picks the minimum number of agents that satisfies a set of operational constraints on the performance of the system.

Dynamic scheduling in multiclass queueing networks: Stability under discrete-review policies

This paper describes a family of discrete-review policies for scheduling open multiclass queueing networks. Each of the policies in the family is derived from what we call a dynamic reward function: such a function associates with each queue length vector q and each job class k a positive value rk(q), which is treated as a reward rate for time devoted to processing class k jobs. Assuming that each station has a traffic intensity parameter less than one, all policies in the family considered are shown to be stable. In such a policy, system status is reviewed at discrete points in time, and at each such point the controller formulates a processing plan for the next review period, based on the queue length vector observed. Stability is proved by combining elementary large deviations theory with an analysis of an associated fluid control problem. These results are extended to systems with class dependent setup times as well as systems with alternate routing and admission control capabilities.

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.

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

Cross-selling is becoming an increasingly prevalent practice in call centers, due, in part, to its unique capability to allow firms to dynamically segment their callers and customize their product offerings accordingly. This paper considers a call center with cross-selling capability that serves a pool of customers that are differentiated in terms of their revenue potential and delay sensitivity. It studies the operational decisions of staffing, call routing, and cross-selling under various forms of customer segmentation. It derives near-optimal controls in each of the settings analyzed, and characterizes the impact of a more refined customer segmentation on the structure of these policies and the centers profitability.

Revenue Management for a Multiclass Single-Server Queue via a Fluid Model Analysis

Motivated by the recent adoption of tactical pricing strategies in manufacturing settings, this paper studies a problem of dynamic pricing for a multiproduct make-to-order system. Specifically, for a multiclass Mn/M/1 queue with controllable arrival rates, general demand curves, and linear holding costs, we study the problem of maximizing the expected revenues minus holding costs by selecting a pair of dynamic pricing and sequencing policies. Using a deterministic and continuous (fluid model) relaxation of this problem, which can be justified asymptotically as the capacity and the potential demand grow large, we show the following: (i) greedy sequencing (i.e., the cμ-rule) is optimal, (ii) the optimal pricing and sequencing decisions decouple in finite time, after which (iii) the system evolution and thus the optimal prices depend only on the total workload. Building on (i)--(iii), we propose a one-dimensional workload relaxation to the fluid pricing problem that is simpler to analyze, and leads to intuitive and implementable pricing heuristics. Numerical results illustrate the near-optimal performance of the fluid heuristics and the benefits from dynamic pricing.

Continuous-Review Tracking Policies for Dynamic Control of Stochastic Networks

This paper is concerned with dynamic control of stochastic processing networks. Specifically, it follows the so called “heavy traffic approach,” where a Brownian approximating model is formulated, an associated Brownian optimal control problem is solved, the solution of which is then used to define an implementable policy for the original system. A major challenge is the step of policy translation from the Brownian to the discrete network. This paper addresses this problem by defining a general and easily implementable family of continuous-review tracking policies. Each such policy has the following structure: at each point in time t, the controller observes the current vector of queue lengths q and chooses (i) a target position z(q) of where the system should be at some point in the near future, say at time t+l, and (ii) an allocation vector v(q) that describes how to split the servers processing capacity amongst job classes in order to steer the state from q to z(q). Implementation of such policies involves the enforcement of small safety stocks. In the context of the “heavy traffic” approach, the solution of the approximating Brownian control problem is used in selecting the target state z(q). The proposed tracking policy is shown to be asymptotically optimal in the heavy traffic limiting regime, where the Brownian model approximation becomes valid, for multiclass queueing networks that admit orthant Brownian optimal controls; this is a form of pathwise, or greedy, optimality. Several extensions are discussed.

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 h...