- Academic Divisions
- Decision, Risk, and Operations
- Finance & Economics
- Cross-Disciplinary Areas
- Centers & Programs
The division's research and teaching typically involve the development and analysis of quantitative models of business problems. These models are used to support decision-making, to measure and manage risks, and to enhance understanding of business practices. Models are analyzed using tools from mathematical programming, game theory, probability, and statistics; the division is also active in advancing these underlying methodologies.
Operational Policies and Practices in the Health Care Sector
Performance Analysis and Control of Service Systems
Call Center Design and Analysis
Financial Engineering and Risk Management
Supply Chain Management
Yield and Revenue Management
Solution Methods for Decision Models
Health care costs and their containment have been a subject of intense political debate for decades and in particular over the last several years. Linda Green has been conducting an extensive project to identify the major drivers of increasing health care costs, both in the U.S. and other countries. A major objective has been to identify operational practices and policies that are candidates for substantial increases in efficiency and/or effectiveness. Current research efforts include analyzing the impact of hospital strategies and management practices on the utilization of beds, the resulting costs, and the quality of the health care delivered to the patients themselves.
Recent findings have illustrated that the standard approach to determining "optimal" hospital bed capacity ignore important factors such as the mix and size of clinical units, bed allocation practices, patient case mix, and variability of demand. Using empirical data in a variety of queueing models, she has shown that this simplistic approach can result in inefficiencies as well as excessive delays for appropriate beds for patients requiring immediate care. One recent study has used this approach to show that counter to the common wisdom that there are currently "too many" hospital beds in the U.S., there is compelling evidence that urgent care units such as intensive care and obstetrics may often be too small to assure bed availability in a timely fashion.
An open question is whether delays for appropriate beds can result in adverse medical consequences. The only published finding that relates delays for medical care to health outcomes has been in the area of heart attacks which showed that the probability of death is a direct function of the delay between the onset of the attack and the time that appropriate care is administered. Though the data requirements for trying to establish such relationships are extremely challenging, Professor Green is currently trying to examine the impact of ambulance diversions on mortality for those suffering heart attacks.
One result of the commonly used approach to determining bed capacity will be back-ups of patients into the emergency room and a consequent increase in the number of hours that the hospital will be "on diversion", i.e. turning away ambulances. A current project is looking at the current trend of increasing diversions and looking at both the major causes as well as financial and medical outcome effects. A related project examines the impact of emergency room physician staffing on delays and "walk-outs", particularly with regard to changing physician staffing to meet the time-varying demands over the day.
Another project is focused on policies regarding major diagnostic facilities, such as Magnetic Resonance Imaging (MRI) installations. In many cases, these imaging facilities are accessed by a wide range of patients from both inside and outside of the hospital: outpatients, inpatients, and emergency patients. Outpatient appointments are typically scheduled days or weeks in advance and sometimes result in cancellations and no-shows. On the other hand, inpatient demands are usually generated the same day as needed, while emergency patients must be served as soon as possible following the physician's request. The financial characteristics of these three classes are also generally quite different. Diagnostic imaging equipment is very expensive. For example, a new MRI costs approximately $2 million with a commensurate cost for building and preparing the space it will occupy. Therefore, hospital managers have every incentive to keep these machines fully utilized. This is often done by filling most, if not all, examination slots during the day with outpatient appointments. In particular, little or no slack is allocated for unanticipated inpatient demands or emergencies. This scheduling approach sometimes results in postponing an inpatient exam one or more days, potentially delaying the patients' discharge from the hospital and, therefore, increasing hospital costs. Outpatients, too, often experience significant delays. Our research focuses on identifying designing outpatient scheduling policies as well as real-time priority rules to improve the efficiency and effectiveness of these critical facilities.
Another important project (primarily Professors Green and Kolesar) deals with the performance analysis and control of customer waiting times and related measures in service systems. A major focus of the work is on the steady state performance of systems in which the parameters are non-stationary, i.e. fluctuate over time, e.g. customer arrival rates varying by the time of day or the day of the week. This part of the project has characterized how different types and degrees of non-stationarity impact on the system's congestion and customer delays as well as the resulting implications for the determination of flexible (time varying) capacity levels, e.g. the optimal structure of staffing schedules to adequately match time varying demand patterns. In two recent studies, Professors Green and Kolesar have shown that the most commonly used approach for determining staffing levels in such systems, particularly telephone call centers, will in most cases result in significant understaffing to meet desired service targets. They show that a simple modification of this approach will result in reliable staffing levels in most applications.
Stochastic networks are used as mathematical models of systems that arise in the manufacturing, services, and communications industries. The behavior of such systems is highly complex and difficult to analyze exactly. A major insight that has emerged over the past 10-15 years, uses a hierarchy of approximate models -and in particular, models with fluid and/or Brownian dynamics- as the basis for analysis and synthesis of such systems. This project of Professor Maglaras focuses on the development of a general framework for design, analysis, and performance optimization of stochastic networks based on such approximations.
A second project studies the impact of quality-of-service specifications, which are often quoted in service and communication networks, and analyzes the design of such systems both at the economic (product differentiation, dynamic pricing, etc.) and operations/tactical levels (capacity planning, control); this is joint work with Professor Van Mieghem of the Kellogg School of Management, NWU.
This project of Professor Maglaras studies modern contact centers that interact with customers through a variety of channels that offer different quality of service. How do the customers choose their desired service channel and how does this affect performance and system design? This work studies the interplay between customer preferences and the information available to them, and the resulting system equilibria. Based on this analysis we optimize system design and operation; this project is joint work with Professor Armony from the Stern School of Management, NYU.
Security pricing, portfolio management, and risk management are three areas where computational methods are playing an increasingly crucial role. The growing complexity of derivative securities has led to a demand for more efficient pricing methods. The globalization of companies and markets requires corporations to devise more effective risk evaluation and risk management procedures. Several sub projects have been completed in these areas, in particular by Professors Broadie and Glasserman. These include:
- new numerical methods for pricing standard American options, more accurate and many times faster than standard methods.
- efficient computation of risk measures by Monte Carlo simulation; new methods were developed to assess the sensitivity of the measures with respect to the underlying security parameters. These avoid time-consuming resimulation procedures and increase the efficiency and accuracy of the risk calculations.
- valuation of complex American-style options, i.e. options involving multiple assets and flexible exercise dates: the work in this area includes the characterization of optimal exercise policies along with the development of efficient valuation methods.
- approximations for barrier options. Barrier options are among the most widely traded exotic options. The new methods developed under this project address the complication (specified by most contracts, though ignored by traditional analyses) that options can be exercised at discrete points in time only, a distinction resulting in significant price changes.
- new models to manage risk in portfolio optimization, resulting in important insights to portfolio managers.
Another important part of this project deals with the characterization of optimal investment policies for institutional investors, in particular under non traditional objectives as when maximizing the probability of remaining solvent over a given time horizon or minimizing the expected time to reach a target wealth level. Some of the work in this area deals with settings where the investor faces an unhedgeable random risk, e.g. an insurance company vis-a-vis the claims' process of its clients.
Mark Broadie and Paul Glasserman were awarded a grant from the National Science Foundation in 2000 together with Steve Kou of Columbia's IEOR Department. The project, titled "Computational Methods in Financial Engineering", is funded for three years by the NSF's program in Computational Mathematics. The grant supports research on the pricing of American options, numerical methods for term structure models, and asymptotic approximations for path-dependent options.
In collaboration with Phil Heidelberger of IBM Research and Perwez Shahabuddin of Columbia's IEOR Department, Paul Glasserman has been working on efficient Monte Carlo methods for pricing derivative securities and measuring portfolio risk. This collaboration has resulted in publications in Mathematical Finance, Journal of Derivatives, and Management Science and in two joint Columbia-IBM patent applications. Glasserman is a recipient of an IBM Faculty Partnership Award for his work on computational methods in finance.
Supply chain management is a major part of the division's research agenda; many faculty members and doctoral students conduct research in this area. The division has a long tradition of studying production-distribution systems in both deterministic and stochastic settings. The traditional approach to the study of these systems is to assume that there is a central decision maker, who is omniscient and whose objective is to optimize the system-wide performance. This approach continues to attract our research attention, leading to contributions on topics such as the characterization of optimal production/inventory control policies, and the development of efficient algorithms to compute these policies, for complex multi-echelon production-distribution systems. The division is also very active in studying mathematical models designed to examine operations decisions in the context of decentralized decision making. This approach differs from the traditional approach in that there are typically multiple decision makers, who may have access to different information and operate under potentially conflicting objectives. Recent research topics in this area include: the value of information sharing, supply chain coordination mechanisms, the impact of competition, supply chain contracting, procurement auctions, and various marketing-operations interface topics such as the coordination between a firm?s production-inventory decisions and its decisions on pricing, market segmentation, product-line design, sales-force compensation, etc. This line of research is highly interdisciplinary, making use of existing knowledge from fields such as economics, game theory, marketing, behavioral sciences, etc.
The areas of yield management and more generally revenue management are increasingly viewed as being of central importance in most service and merchandising industries. All major airlines, and many hotel chains, car rental companies, and cruise ship lines, e.g. use reservation data to dynamically allocate space (cars) to various market segments and price classes. The benefits of revenue management are often staggering. American Airlines reports a 5% increase in revenue, with approximately $1.4 billion dollars over a three year period, directly attributable to effective yield management. Professor Van Ryzin has made fundamental contributions to the development of revenue management strategies; an important part of his work (conducted with experts from the airline industry) deals with the integration of pricing and allocation decisions.
In the retailing world, an important part of yield management consists of the tactical pricing of merchandise, in particular managing promotional and mark down pricing. By its nature, tactical pricing decisions involve the choosing of prices for literally thousands of combinations of product types, markets, locations, and time periods, all of which must be updated continuously based on a barrage of inventory, sales, and price information. The advent of point-of-sales systems, already ubiquitous in the retail sector, provides a rich infrastructure capable of supporting these decisions. Professor Van Ryzin is one of the pioneering contributors to the development of tactical pricing strategies, the full potential of which remains largely untapped. His work in this area has been sponsored by the National Science Foundation and Federated Department Stores under the NSF Joint Industry Academic Research Initiative.
To enable the above projects in the area of operations management, it is essential that we contribute to the advancement of the state-of-the-art in several generic management science methodologies.
Dynamic programming is the framework via which general multi-period decision processes are analyzed. A major focus of the research in this area (Professor Federgruen) is the development of more powerful solution methods for general classes of dynamic programs along with simple quantitative methods to identify how much information about the future is required to ensure that recommended decisions for initial stages of the planning horizon are determined in a manner consistent with a long term planning approach. Professor Glasserman has addressed the development of approximations and efficient Monte Carlo methods for estimating probabilities of rare events. In many settings events having low probabilities may nevertheless be of critical importance to the performance or survival of a system. Examples arise in financial applications (credit risk), inventory models (stockouts), reliability (system failures), and telecommunications (packet loss), to name just a few. The analysis and estimation of rare-event probabilities require specialized tools from statistics; these are also useful in developing Monte Carlo methods. This part of the project has resulted in the development of Monte Carlo estimators that outperform straightforward estimation by several orders of magnitude. This work is funded, in part, by grants from the National Science Foundation and IBM.