Not so Current Research
- Bike Sharing Logistics
I am part of a team, led by David Shmoys, analyzing bike sharing
logistics in partnership with CitiBike in NYC. Our goal is to help
CitiBike and other bike-sharing companies with their operational and
strategic questions, including how to achieve smooth functioning
through a mix of rebalancing, valets, and depots, where and how
much to expand their network of stations, and how to design
incentive schemes to help balance the flows of bikes in time. The work involves a mix of
stochastic modeling and convex optimization.
- Structured Simulation Optimization
The problem of simulation optimization is essentially that of
optimizing a function that can only be computed (estimated) through
simulation. We have developed techniques to (numerically) detect
convexity in a function evaluated only through simulation. Moreover,
we have developed a library of simulation-optimization test problems. 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.
- Parallel Simulation Optimization
Parallel computing is ubiquitous today, from laptops to cloud
computing to high-performance computing. Each of these environments
differs in important ways, but we should be able to exploit their
parallel natures in developing simulation optimization algorithms. We
are developing parallel ranking and selection algorithms that work in
such environments and scale to very large problems. We are also
exploring the interplay between search algorithms and ranking and
- Stochastic Root Finding
This is the problem of identifying a point at which a function equals
zero, i.e., a root, when the function or its gradient (in the case it
is differentiable) can only be observed with noise. This problem is
closely related to simulation optimization, in the sense that the
unconstrained minimum of a differentiable function is a root of the
gradient. We are developing theory and algorithms for a Bayesian
algorithm that updates a prior belief on the location of the
- Conjoint Analysis
I am part of a team exploring methods for learning a user's
preferences over a large set of items, for use in, e.g.,
recommendation systems. The algorithm updates a Bayesian prior as it
learns more about a user's preferences.
- 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.
- What are the tradeoffs in ambulance fleet design?
Ambulances can be roughly categorized into two types: Advanced Life Support (ALS) that are staffed by paramedics and deliver the highest level of care, and Basic Life Support (BLS) that deliver high-quality care, but not quite at the same level as paramedics. Some ambulance fleets consist entirely of ALS units, while others are a mix. Why? What are the tradeoffs from an operational perspective?
- 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.
- 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.
- 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
- 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.