Current Research

• Dynamic Relocation of Ambulances
  When an ambulance is dispatched to a call it leaves a "hole." Should we try to fill that hole with an available ambulance? What moves should be considered? How can this be done without overly frustrating ambulance crews? We are tackling this question using approximate dynamic programming and simulation. Click here for some TV coverage.
• Statistical Analysis of Emergency Services Data
  The Operations Research models we are applying to try to help Emergency Medical Service (EMS) organizations require a number of input parameters, including call arrival rates in space and time, and travel speeds/times on road networks. We are applying advanced statistical methods to turn Computer-Aided Dispatch data and Automatic Vehicle Location data into reliable estimates of these quantities. See here for some TV coverage.
• Structured Simulation Optimization
  The problem of simulation optimization is essentially that of optimizing a function that can only be computed (estimated) through simulation. Applications: Ambulance deployment, call center staffing, control of stochastic processing networks, radiation treatment planning. See here for some TV coverage on ambulances that is related.
• The Game of Monopoly
  The game of Monopoly exhibits many complexities that are faced by real organizations. Specifically, a player has to make decisions in real time in the face of competition from other players and considerable uncertainty about the future. Luck plays a role, but so does strategy. Click here for information on our efforts to understand the game and identify effective strategies, and here for some press coverage.

Not so Current Research

• Low Rank Approximations in Optimization
  Representing complex constraints in high dimensions can require more storage than is currently possible. If one replaces complex constraints with simpler versions, then what is the impact on the optimization problem? This work was motivated through our work in radiation treatment planning where ellipsoidal constraints in 1000 dimensions were replaced with infinitely long cylinders, which could be stored in less than 1% of the memory needed for the ellipsoids.
• American Option Pricing and Stochastic Root Finding
  The problem of American option pricing includes a series of decisions: should I stop and exercise the option, or continue? In one dimension, these decisions come down to solving a stochastic root finding problem. We are working on methods to solve such root finding problems efficiently, and to determine how one should allocate computational effort across the different stages in the process to get as accurate an option price as possible.
• Variance Reduction Techniques
  Exploring the use of general variance reduction techniques. In particular, looking at the use of martingales to obtain variance reduction in simulations of Markov processes. Current work involves exploring adaptive methods to tune the variance reduction and extending the methods from the Markov setting to general discrete-event simulations.
• The Regenerative Method
  The regenerative method of simulation output analysis possesses qualities that make it preferable to other time-average variance constant estimation methods such as batch means. Therefore, it is of great interest to determine how to apply the method to general discrete-event simulations.
• Dependence Structures
  The primitive inputs to stochastic models are often assumed to be independent, even when they are known to be dependent in some way. This assumption is usually made to avoid the difficulties of modeling and generating dependent random variables. This work develops methods for modeling and generating dependent random variables.
• Input Uncertainty
  There is invariably some uncertainty about the "correct" values of input parameters for simulations, e.g., what is the "correct" arrival rate to a queue? Forecast errors are an example of input uncertainty. In this work we attempt to understand and quantify the impact of that uncertainty.