1. Tradeoffs between discounting and averaging in discrete time stochastic, dynamic optimisation models over an infinite time horizon
2. Hamiltonian Cycle and Travelling Salesman problems as singularly perturbed controlled Markov chains
3. Stationary distributions of singularly perturbed Markov chains
4. Time scales and singularly perturbed systems
5. An integrated model of the enhanced greenhouse effect; stabilisation at equilibrium and uncertainty propagation.

In this talk, we re-examine these issues and provide some new insights. In particular, we show that such heavy tail distributions are not the most appropriate for characterizing traffic of many Web servers. Instead, light tail and subexponential tail distributions are frequently observed which can not cause long range dependence, yet coexist with the long range dependence in the observation. Though there are results in the literature for self-similar arrival process with constant service rates, or for subexponential service times with i.i.d. arrival process, how the server performance would
be influenced by the coexistence of long range dependent arrival process and subexponential service times is an open question. We present asymptotic queueing analysis of such systems and show the different dominant components that influence server performance under different conditions. Simulation resutls are then presented for comparison.

This is joint work with Zhen Liu, Mark S. Squillante, Li Zhang and Naceur Malouch.

The goal of this project is to automate the treatment planning
process. For each patient, an optimization seeks to produce
a homogeneous dose distribution that conforms closely to the
treatment volume, while avoiding overdosing nearby sensitive
structures. The variables in the optimization can include the number of shots of radiation along with the size, the location, and the weight assigned to each. Formulation of such problems using a variety of mathematical programming models is described, and the solution of several test and real-patient examples is demonstrated.

This represents joint work with:

David M. Shepard
Department of Radiation Oncology, University of Maryland School of
Medicine,
22 South Green Street, Baltimore, MD 21201
email: dshep001@umaryland.edu

In this talk we consider a service system with many identical servers and no waiting buffer (loss system). Customers are classified into two types. The arrivals of the two types follow independent Poisson processes and the service times are exponentially distributed with generally class dependent service rates. Each customer generates a profit depending on his or her type. Upon arrival, the system manager must decide whether to accept the incoming customer or deny service. Customers arriving to a full system are lost. The objective is to find a dynamic policy of admission that maximizes the long-run expected average profit per unit time.

We show that the optimal admission policy has a threshold structure. In addition we discuss the issue of existence and identification of a preferred customer class, i.e., a class that is always admitted when there are free servers. Finally we consider extensions of the basic model to situations of random service profits and batch customer arrivals.

In the first portion of this talk, we will introduce existing software tools that allow users to harness the computational power of the internet. The second portion of the talk will deal with optimization algorithms that have been adapted to metacomputing platforms by using these software tools. As one concrete example, we will describe an implementation of a state-of-the-art algorithm for the quadratic assignment problem (QAP). Using this implementation, and the computational power of the internet, we are able to report the solutions of QAP instances that had been unsolved for decades.

An alternative measure of loss with more attractive properties, is Conditional Value-at-Risk (CVaR), see [6,7,8]. CVaR coincides in many special cases with Upper CVaR which is the conditional expectation of losses exceeding VaR (also called Mean Excess Loss and Expected Shortfall), see [7]. However, Acerbi et al. [1,2] recently redefined Expected Shortfall in a manner consistent with the CVaR definition. Acerbi et al. [1,2] proved several important mathematical results on properties of CVaR, including asymptotic convergence of sample estimates to CVaR.

CVaR, is a coherent measure of risk [5,7] (sub-additive, convex, and other nice mathematical properties). CVaR can be represented as a weighted average of VaR and Upper CVaR. This seems surprising, in the face of neither VaR nor Upper CVaR being coherent. The weights arise from the particular way that CVaR "splits the atom" of probability at the VaR value, when one exists.

CVaR can be used in conjunction with VaR and is applicable to the estimation of risks with non-symmetric return-loss distributions. Although CVaR has not become a standard in the finance industry, it is likely to play a major role. CVaR is able to quantify dangers beyond value-at-risk, [1,6,7,8,10]. CVaR can be optimized using linear programming, which allows handling portfolios with very large numbers of instruments and scenarios. Numerical experiments indicate that for symmetric distributions the minimization of CVaR also leads to near optimal solutions in VaR terms because CVaR is always greater than or equal to VaR, [6]. Moreover, when the return-loss distribution is normal, these two measures are equivalent [6,7], i.e., they provide the same optimal portfolio. However, for skewed distributions, VaR optimal and CVaR optimal portfolios may be very different, [10]. Similar to the Markowitz mean-variance approach, CVaR can be used in return-risk analyses. For instance, we can calculate a portfolio with a specified return and minimal CVaR. Alternatively, we can constrain CVaR and find a portfolio with maximal return, see [4,7]. Also, we can specify several CVaR constraints simultaneously with various confidence levels (thereby shaping the loss distribution), which provides a flexible and powerful risk management tool.

Several case studies showed that risk optimization with the CVaR performance function and constraints can be done for large portfolios and a large number of scenarios with relatively small computational resources. For instance, a problem with 1,000 instruments and 20,000 scenarios can be optimized on a 700 MHz PC in less than one minute using the CPLEX LP solver. A case study on the hedging of a portfolio of options using CVaR is included in [6]. Also, the CVaR minimization approach was applied to the credit risk management of a portfolio of bonds, [3]. A case study on optimization of a portfolio of stocks with CVaR constraints is included in [4]. The numerical efficiency and stability of CVaR calculations are illustrated with an example of index tracking in [7]. Several related papers on probabilistic constrained optimization are included in [8].

REFERENCES

1. Acerbi, C., Nordio, C., Sirtori, C. Expected Shortfall as a Tool for Financial Risk Management, Working Paper. (Can be downloaded: www.gloriamundi.org/var/wps.html)

2. Acerbi, C., and Tasche, D. On the Coherence of Expected Shortfall. Working Paper. (Can be downloaded: www.gloriamundi.org/var/wps.html)

3. Andersson, F., Mausser, H., Rosen, D., and S. Uryasev (2001): Credit Risk Optimization with Conditional Value-At-Risk Criterion. Mathematical Programming, Series B 89, 2001, 273-291.
(Can be downloaded: www.ise.ufl.edu/uryasev/pubs.html#t)

4. Palmquist, J., Uryasev, S., and P. Krokhmal (1999): Portfolio Optimization with Conditional Value-At-Risk Objective and Constraints. The Journal of Risk, forthcoming. (Can be downloaded: www.ise.ufl.edu/uryasev/pal.pdf)

5. Pflug, G. (2000): Some Remarks on the Value-at-Risk and the Conditional Value at Risk. In Probabilistic Constrained Optimization: Methodology and Applications. Uryasev, S. (Ed.)
Kluwer Academic Publishers, 2000

6. Rockafellar R.T. and S. Uryasev (2000): Optimization of Conditional Value-at-Risk. The Journal of Risk, Vol. 2, # 3. (Can be downloaded: www.ise.ufl.edu/uryasev/cvar.pdf)

7. Rockafellar R.T. and S. Uryasev (2001): Conditional Value-at-Risk for General Loss Distributions. Research Report 2001-5. ISE Dept., University of Florida, April 2001. (Can be downloaded: www.ise.ufl.edu/uryasev/cvar2.pdf)

8. Uryasev, S. Conditional Value-at-Risk: Optimization Algorithms and Applications. Financial Engineering News, No. 14, February, 2000 (Can be downloaded: www.ise.ufl.edu/uryasev/pubs.html#t).

9. Uryasev, S. (Ed.) Probabilistic Constrained Optimization: Methodology and Applications. Kluwer Academic Publishers, 2000, 307 p.

10. Yamai, Y. and T. Yoshiba. On the Validity of Value-at-Risk: Comparative Analyses with Expected Shortfall. Institute for Monetary and Economic Studies. Bank of Japan. IMES Discussion Paper 2001-E-4, 2001. (Can be downloaded: www.imes.boj.or.jp/english/publication/edps/fedps2001_index.html )

Personal Profile
Dr. Fugee Tsung is an assistant professor of Industrial Engineering and Engineering Management at the Hong Kong University of Science and Technology. He received both his PhD and MSc in Industrial and Operations Engineering from the University of Michigan, Ann Arbor, and his BSc in Mechanical Engineering from National Taiwan University. He worked for Ford Motor Company and Rockwell International and did his post-doctoral research with Chrysler Corporation. He serves as an elected Council Member for Institute for Operations Research and the Management Sciences (INFORMS) Quality, Statistics and Reliability (QSR) Section. He is also a member of IIE, ASQ, and ASQ Six Sigma Forum. His current research interests include quality engineering and management, process control, monitoring and diagnosis.

This year's event will feature:

I shall then walk you through my simplex algorithm for the solution of SCLP.

I will then discuss the form of the solution and how it can be
used for nearly optimal control of the wafer fab. This will lead to a general discussion of SCLP applications.

Presentation 2:
Lifted Inequalities for 0-1 Mixed Integer Programming
by Jean-Philippe Richard

Both these talks will be given at the INFORMS meeting in Miami as well.

Seminar title:
Measurement of Volatility in the Energy Markets

Speaker:
Dr. Vincent Kaminski
Managing Director and Head of Research, ENRON

Time: 11:00 am, Thursday, November 1, 2001
Room 215, Instructional Center Building

Outline of the talk:
1. Importance of volatility in financial engineering
a. option pricing
b. risk management
c. legacy software systems
2. Is volatility the right tool for energy markets?
3. The dynamics of energy prices in the US markets in recent years:
a few stylized facts
4. Alternative theoretical tools to represent price dynamics:
the importance of dialogue between academics and practitioners

Background:
The last few years have been characterized by exceptionally high volatility
of the power prices in the US markets. The market developments have
created a number of unique challenges for energy industry economists.
One immediate question is 'how should the volatility of energy prices be
measured. Although it is agreed upon that the prices in the power markets
are characterized by high variability, the traditional measures used in
financial economics (annualized standard deviation of log price
returns) may not fit well for electricity prices. The second challenge is to
explain the sources of high price volatility and to answer the question to
what extent can this high price volatility be attributed to problems
that can be addressed in the long run.' Such problems include flaws
in market design that allow some market participants to abuse market power,
limited availability and/or unequal access to transmission, and temporary
shortages of generation capacity. Some factors underlying high volatility of
electricity prices may be of a permanent nature and may be a necessary
price to pay for increased market efficiency and expanded customer choice.

The Speaker:
Vincent (Vince) Kaminski is Managing Director and Head of Research for
Enron. Vince joined Enron in June of 1992. Previously, Vince was a Vice
President in the research department of Salomon Brothers in New York (Bond
Portfolio Analysis Group) and a manager in AT&T Communications (Long
Lines) in Bedminster, New Jersey. In his current position, Vince is
responsible for development of analytical tools for pricing of commodity
options and other commodity transactions, hedging strategies, optimization
of financial and physical transactions, as well as development of
value-at-risk system. Enron Capital & Trade Resources manages the largest
portfolio of fixed-price and derivative natural gas contracts in the world
and has invested a lot of time and effort in the development of state-
of-art risk management systems.

Vince is a recipient of the 1999 James H. McGraw Award for Energy Risk
Management (Energy Risk Manager of the Year). Vince holds an M.S. degree in
international economics and a Ph.D. degree in mathematical economics from the
Main School of Planning and Statistics in Warsaw, Poland, and an MBA from
Fordham University in New York.

The window sizes and slow start thresholds of each TCP session evolves like independent dynamical systems coupled by the RED mechanism. Here we introduce a mean-field approximation to one such RED system as the number of flows tends to infinity. The
deterministic limiting system is described by a transport equation. The numerical solution of the limiting system is found to provide a good description of the of the evolution of the distribution of the window sizes, the average queue size, the average loss rate per connection and the total throughput. We see that TCP with RED or tail-drop may exhibit limit cycles and this causes unnecessary packet delay variation and variable loss rates. The root cause of these limit cycles is the hysteresis due to the round trip time delay in reacting to a packet loss.