Robert A. Shumsky

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 companys use of mid-sized cars to satisfy unexpectedly high demand for compact cars and an airlines 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.

Call Center Outsourcing Contracts Under Information Asymmetry

In this paper, we examine contracts to coordinate the capacity decision of a vendor who has been hired by a client to provide call center support. We consider a variety of contracts, all based on our observations of contracts used by one large vendor. We examine the role of different contract features such as pay-per-time, pay-per-call, service-level agreements, and constraints on service rates and abandonment. We show how different combinations of these contract features enable client firms to better manage vendors when there is information asymmetry about worker productivity. In particular, we focus on how different contracts can coordinate by yielding the system-optimal capacity decision by the vendor and consider how profits are allocated between the client and the vendor.

Dynamic Capacity Management with Substitution

We examine a multiperiod capacity allocation model with upgrading. There are multiple product types, corresponding to multiple classes of demand, and the firm purchases capacity of each product before the first period. Within each period, after demand arrives, products are allocated to customers. Customers who arrive to find that their product has been depleted can be upgraded by at most one level. We show that the optimal allocation policy is a simple two-step algorithm: First, use any available capacity to satisfy same-class demand, and then upgrade customers until capacity reaches a protection limit, so that in the second step the higher-level capacity is rationed. We show that these results hold both when all capacity is salvaged at the end of the last demand period as well as when capacity can be replenished (in the latter case, an order-up-to policy is optimal for replenishment). Although finding the optimal protection limits is computationally intensive, we describe bounds for the optimal protection limits that take little effort to compute and can be used to effectively solve large problems. Using these heuristics, we examine numerically the relative value of strictly optimal capacity and dynamic rationing, the value of perfect demand information, and the impact of demand and economic parameters on the value of optimal substitution.

Dynamic Revenue Management in Airline Alliances

Major airlines are selling increasing numbers of interline itineraries in which flights operated by two or more airlines are combined and sold together. One reason for this increase is the rapid growth of airline alliances, which promote the purchase of interline itineraries and, therefore, virtually extend the reach of each alliance members network. This practice, however, creates a difficult coordination problem: Each member of the alliance makes revenue management decisions to maximize its own revenue and the resulting behavior may produce suboptimal revenue for the alliance as a whole. Airline industry researchers and consultants have proposed a variety of static and dynamic mechanisms to control revenue management decisions across alliances (a dynamic mechanism adjusts its parameters as the number of available seats in the network changes and time passes). In this paper, we formulate a Markov game model of a two-partner alliance that can be used to analyze the effects of these mechanisms on each partners behavior. We begin by showing that no Markovian transfer pricing mechanism can coordinate an arbitrary alliance. Next, we examine three dynamic schemes as well as three forms of the static scheme widely used in practice. We derive the equilibrium acceptance policies under each scheme and use analytical techniques as well as numerical analyses of sample alliances to generate fundamental insights about partner behavior under each scheme. The analysis and numerical examples also illustrate how certain transfer price schemes are likely to perform in networks with particular characteristics.

OM Practice---Work Expands to Fill the Time Available: Capacity Estimation and Staffing Under Parkinson's Law

We develop a method to estimate the capacity of agents who answer e-mail in a contact center, given aggregate historical data that have been distorted both by constraints on work availability and by internal incentives to slow down when true capacity exceeds demand. We use the capacity estimate to find a contact centers optimal daily staffing levels. The implementation results, from an actual contact center, demonstrate that the method provides accurate staffing recommendations. We also examine and test models in which agents exhibit speed-up behavior and in which capacity varies over time. Finally, we use the capacity estimates to examine the implications of solving the staffing problem with two different model formulations, the service-level constraint formulation used by the contact center and an alternate profit-maximization formulation.

A Comparison of Retained and Appointed Counsel in Cases of Capital Murder

We examined the role of counsel as a source of arbitrary and capricious sentencing in cases of capital murder. The method is a reanalysis of the data of Baldus, Woodworth, & Pulaski (1990) on 606 cases of capital murder in Georgia in the 1970s. Controlling for variables describing the character of the defendant and the circumstances of the crime, a death sentence was more likely when defense counsel was appointed rather than retained privately. This was a consequence primarily of the prosecutors decision to seek a death sentence rather than jury bias in sentencing. Our data support the conclusion that sentencing under the Georgia statute was in the 1970s, and is today to some degree, arbitrary and capricious.

Queueing Models of Case Managers

Many service systems use case managers, servers who are assigned multiple customers and have frequent, repeated interactions with each customer until the customer’s service is completed. Examples may be found in healthcare (emergency department physicians), contact centers (agents handling multiple online chats simultaneously) and social welfare agencies (social workers with multiple clients). We propose a stochastic model of a baseline case-manager system, formulate models that provide performance bounds and stability conditions for the baseline system, and develop two approximations, one of which is based on a two-time-scale approach. Numerical experiments and analysis of the approximations show that increasing case throughput by increasing the probability of case completion can lead to much greater waiting-time reductions than increasing service speed. Many systems place an upper limit on the number of customers simultaneously handled by each case manager. We examine the impact of these caseload limits...

Call for Papers---Proposal for an M&SOM Special Issue on Practice-Focused Research

Co-Editors of the Special Issue: Jeremie Gallien, London Business School, Regents Park, London NW1 4SA, United Kingdom; and Alan Scheller-Wolf, Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213. Associate Editors of the Special Issue: Srinivas Bollapragada, Felipe Caro, Charles Corbett, Marshall Fisher, Ananth Iyer, Andrew Lim, Ananth Raman, Nicola Secomandi, Robert Shumsky, Lawrence Snyder, Jay Swaminathan, Geert-Jan van Houtum, Andres Weintraub, and Sean Willems.

Managing the Outsourcing of Two-Level Service Processes: Literature Review and Integration

The outsourcing of service processes presents several complex management challenges. Services typically have variability in both the pattern of customer arrivals and service times, which make capacity planning challenging. Workers also have discretion over the workflow, and therefore each worker can affect the workload passed to other parts of the system. When a service process is outsourced, this discretion may be in the hands of a vendor who then makes choices that influence the customer experience. A firm must decide upon the design of the process, which parts of the process to outsource, and how to contract with the vendor to overcome issues related to information asymmetry. This paper addresses these questions within the context of a two-level service process where the first level serves as a gatekeeper for experts in the second level. We integrate the results from several papers in the literature to give a comprehensive perspective on how to approach service outsourcing.

Case Article---Introductory Integrative Cases on Airline Revenue Management

This case article summarizes two case series. Each case series includes three subcases and has an associated teaching note. These six short cases introduce many of the concepts that underlie the practice of airline revenue management: protection levels, overbooking, customer buy-up and buy-down behavior, network controls, bid prices, and the spiral-down effect. The cases are integrative in the sense that they reinforce many of the fundamental concepts taught in business programs, such as the formulation of statistical models, customer segmentation, the meaning of shadow prices in optimization, and the impact of model errors on real-world decisions. The cases also use many of the basic skills and tools taught in business programs: data analysis and forecasting, simulation, and optimization. By applying these tools, the cases move students quickly beyond the standard newsvendor-style formulation of the revenue management problem. Because the cases require students to apply these tools to interesting and relatively complex revenue management problems, the tools themselves gain more credibility among the students. Case Teaching Note: Interested Instructors please see the Instructor Materials page for access to the restricted materials. To maintain the integrity and usefulness of cases published in ITE, unapproved distribution of the case teaching notes and other restricted materials to any other party is prohibited.