Revenue Management Games: Horizontal and Vertical Competition

A well-studied problem in the literature on airline revenue (or yield) management is the optimal allocation of seat inventory among fare classes, given a demand distribution for each class. In practice, the seat allocation decisions of one airline affect the passenger demands for seats on other airlines. In this paper, we examine the seat inventory control problem under both horizontal competition (two airlines compete for passengers on the same flight leg) and vertical competition (different airlines fly different legs on a multileg itinerary). Such vertical competition can be the outcome of a code-sharing agreement between airlines, because each airline sells seats on the partner airlines’ flights but the airlines are unwilling, or unable, to coordinate yield management decisions. We provide a general sufficient condition under which a pure-strategy Nash equilibrium exists in these revenue management games, and we also compare the total number of seats available in each fare class with, and without, competition. Analytical results as well as numerical examples demonstrate that more seats are protected for higher-fare passengers under horizontal competition than when a single airline acts as a monopoly. Under vertical competition the booking limit may be higher or lower, however, than the monopoly level, depending on the demand for connecting flights in each fare class. Finally, we discuss revenue-sharing contracts that coordinate the actions of both airlines

Flexible Service Capacity: Optimal Investment and the Impact of Demand Correlation

We consider a firm that provides multiple services using both specialized and flexible capacity. The problem is formulated as a two-stage, single-period stochastic program. The firm invests in capacity before the actual demand is known and optimally assigns capacity to customers when demand is realized. Sample applications include a car rental company\u27s use of mid-sized cars to satisfy unexpectedly high demand for compact cars and an airline\u27s use of business-class seats to satisfy economy-class demand. We obtain an analytical solution for a particular case, when services may be upgraded by one class. The simple form of the solution allows us to compare the optimal capacities explicitly with a solution that does not anticipate flexibility. Given that demand follows a multivariate normal distribution, we analytically characterize the effects of increasing demand correlation on the optimal solution. For the case with two customer classes, the effects of demand correlation are intuitive: Increasing correlation induces a shift from flexible to dedicated capacity. When there are three or more classes, there are also adjustments to the resources not directly affected by the correlation change. As correlation rises, these changes follow an alternating pattern (for example, if the optimal capacity of one resource rises, then the optimal capacity of the adjacent resource falls). These results make precise conjectures based on numerical experiments that have existed in the literature for some time

Optimal Updating of Forecasts for the Timing of Future Events

A major problem in forecasting is estimating the time of some future event. Traditionally, forecasts are designed to minimize an error cost function that is evaluated once, possibly when the event occurs and forecast accuracy can be determined. However, in many applications forecast error costs accumulate over time, and the forecasts themselves may be updated with information that is collected as the expected time of the event approaches. This paper examines one such application, in which flow control managers in the U.S. air traffic system depend on forecasts of aircraft departure times to predict and alleviate potential congestion. These forecasts are periodically updated until take-off occurs, although the number of updates may be limited by the cost of collecting, processing, and distributing information. The procedures developed in this paper balance the costs of accumulated forecast errors and the costs of forecast updates. The procedures are applied to the aircraft departure forecasting problem and are compared with methods currently used by the air traffic management system. Numerical examples demonstrate that the procedures increase forecast accuracy while reducing the costs associated with frequent forecast updates.Forecasting, Dynamic Programming Applications, Air Transportation

Gatekeepers and Referrals in Services

This paper examines services in which customers encounter a gatekeeper who makes an initial diagnosis of the customer's problem and then may refer the customer to a specialist. The gatekeeper may also attempt to solve the problem, but the probability of treatment success decreases as the problem's complexity increases. Given the costs of treatment by the gatekeeper and the specialist, we find the firm's optimal referral rate from a particular gatekeeper to the specialists. We then consider the principal--agent problem that arises when the gatekeeper, but not the firm, observes the gatekeeper's treatment ability as well as the complexity of each customer's problem. We examine the relative benefits of compensation systems designed to overcome the effects of this information asymmetry and show that bonuses based solely on referral rates do not always ensure first--best system performance and that an appropriate bonus based on customer volume may be necessary as well. We also consider the value of such output--based contracts when gatekeepers are heterogeneous in ability, so that two gatekeeper types face different probabilities of treatment success when given the same problem. We show that the firm may achieve first--best performance by either offering two contracts that separate the gatekeeper types or by offering a single contract that coordinates the treatment decisions of both gatekeepers.Stochastic Model Applications, Personnel, Principal--Agent Problems, Routing/Triage

The Efficiency-Quality Trade-Off of Cross-Trained Workers

Does cross-training workers allow a firm to achieve economies of scale when there is variability in the content of work, or does it create a workforce that performs many tasks with consistent mediocrity? To address this question we integrate a model of a stochastic service system with models for tenure- and experience-based service quality. When examined in isolation, the service system model confirms a well-known "rule of thumb" from the queueing literature: Flexible or cross-trained servers provide more throughput with fewer workers than specialized servers. However, in the integrated model these economies of scale are tempered by a loss in quality. Given multiple tasks, flexible workers may not gain sufficient experience to provide high-quality service to any one customer, and what is gained in efficiency is lost in quality. Through a series of numerical experiments we find that low utilization in an all-specialist system can also reduce quality, and therefore the optimal staff mix combines flexible and specialized workers. We also investigate when the performance of the system is sensitive to the staffing configuration choice. For small systems with high learning rates, the optimal staff mix provides significant benefits over either extreme case (a completely specialized or completely flexible workforce). If the system is small and the rate of learning is slow, flexible servers are preferred. For large systems with high learning rates, the model leans toward specialized servers. In a final set of experiments, the model analyzes the design options for an actual call center.queues: approximations, service quality, learning curves, crosstraining, worker turnover, personnel

Staffing and routing in a two-tier call centre

Abstract: This paper studies service systems with gatekeepers who diagnose a customer problem and then either refer the customer to an expert or attempt treatment. We determine the staffing levels and referral rates that minimise the sum of staffing, customer waiting, and mistreatment costs. We also compare the optimal gatekeeper system (a two-tier system) with a system staffed with only experts (a direct-access system). When waiting costs are high, a direct-access system is preferred unless the gatekeepers have a high skill level. We also show that an easily computed referral rate from a deterministic system closely approximates the optimal referral rate