Jayant Rajgopal
RESEARCH INTERESTS
My research interests are focused primarily on operations research and its applications. Although I am always open to working on interesting research problems that combine the use of quantitative/analytical techniques with computers, my current focus is on two broad (and interconnected) areas:
Applications of IE/OR to Healthcare
DeliveryIn the past, I have also worked on more focused topics including
My preference is for things
that are continuous (i.e., just let me differentiate it
...) and deterministic (uncertainty is
annoying...). But at the end of the day, it's more
important for the problem to (1) be interesting and (2)
be real.
Supply Chain Analysis
I have worked for many years in
the general area of supply chains, including topics such
as production and inventory control, scheduling,
logistics, and distribution. Some of my earlier work
in this area covered topics such as just-in-time systems,
multi-echelon distribution, parallel machine scheduling
with major and minor setups, optimal fixture selection for
machining rotational parts, and applications of RFID
systems.
Some years ago, I did some
interesting work with my colleague Andrew Schaefer (now
at Rice University) on designing and managing remnant
inventory supply chains, which are found in areas
including (but not limited to) steel, aluminum, paper,
textiles, fiber-optic cable and lumber, where remnants
from prior cutting operations are stored in inventory
and can be used to satisfy (stochastic) demand as it
comes in. We worked on combining both the design
aspect of where facilities should be optimally located
and the operational aspect of how they should service
demand. I also worked with Kim Needy at the University
of Arkansas and PhD student Natalie Scala (now a faculty
member at Towson University) on a data-driven,
engineering management approach to managing spare parts
inventories in the nuclear power sector. Finally,
I collaborated for a number of years with my
ex-colleague Bryan Norman (now
at Texas Tech) and several graduate students (Sheng-I
Chen, Nazanin Esmaili, Jung Lim and Yuwen Yang) on the
health care supply chain (more on some of this in the
section below...). I also worked briefly on the
so-called "unconventional" energy sector, with a focus
on fracking and the shale gas supply chain.
Here's a partial list of some of my relevant
publications in the broad area of operations, in
case you're interested.
Applications of IE/OR to
Healthcare
This is an area in which I have
been working for the last ten to twelve years. In
one initiative within the Veteran's Engineering Resource
Center (VERC,
funded by the Veteran's Administration), I worked with
my ex-IE colleague Bryan Norman on various
operational problems within the VA System, ranging from
improving Veterans' access to healthcare, to managing
inventories of medical supplies and pharmaceuticals, to
better matching of demand and capacity. Earlier I
was part of another VERC effort, working with another
ex-IE colleague, Andrew Schaefer, and a large team on a
project to more efficiently schedule the operating room
suite in the VA Pittsburgh hospital. The second area in
healthcare delivery that I have been involved with is
global health and the WHO-EPI vaccine distribution
chain. This began as the HERMES
project (funded by the Bill & Melinda Gates
Foundation) where Bryan and I worked with a team of people
from the Graduate School of Public Health (led by
Bruce Lee - now at CUNY) and the Pittsburgh Supercomputing
Center (led by Shawn Brown), on developing a detailed
simulation model of the WHO-EPI vaccine supply chain in
developing countries, with a focus on improving the
efficiency with which vaccines are delivered to the final
recipients. This eventually led to a couple of
different NSF funded grants (one with Bruce, Bryan and
another IE colleague, Lisa Maillart, and one a solo
effort) on improving clinic operations with the goal of
reducing vaccine waste and increasing coverage, and more
recently on redesigning the vaccine distribution chain and
its operation so as to increase coverage and reduce waste.
I am also currently working with a large team of people from
IE, Pitt's medical school, Strathmore University in Kenya
and several others on a project to improve the entire
blood transfusion continuum in Kenya, from collection to
delivery. Here is a partial list of some of relevant publications.
Geometric Programming
Geometric Programming (GP) is a
nonlinear optimization technique for problems with
polynomial objective and constraint functions, and has a
very elegant theory as well as attractive structural
properties. Unfortunately, there has been a misconception
that GP requires a very rigid format and that it has very
limited applicability in practice. I have been working on
a linear reformulation of the GP primal dual pair - this
was work that I did with Dennis
Bricker at the University of Iowa many years ago. In
the reformulation, the primal is stated as a semi-infinite
LP, while the dual is a generalized LP. The reformulation
leads to a very robust dual-based column generation
algorithm that works well on a wide variety of GP problems
with virtually no computational difficulties. If you are
interested, I have available a list
of references of some of my publications in this
area; you may also contact me directly if you can't locate
the papers, and I'll be happy to send you copies/reprints!
I also have the code for the algorithm if you have
posynomial GP problems that you need to solve, or if you'd
just like to play with the software - it runs on any
desktop computer. The whole system is stored in a
file called GPINSTAL.EXE
that you may download. This file is self extracting
and contains the object file along with instructions and a
couple of sample data files - just ftp the file (in binary
mode) and run it.Reliability
This is another area in which I
did a fair amount of work with my ex-colleague Dr. Mainak
Mazumdar, although I have not done much in the area for
quite a few years now. Our goal was to develop minimum
cost system-based component test plans for
demonstrating the reliability of a system of different
components in various configurations. There are numerous
advantages to testing the individual components of a
complex system in order to verify system reliability, as
opposed to assembling the entire system and then testing
it - cost and convenience are the most obvious. However,
it is not clear how best this can be done - both from the
perspective of the statistical properties of the system
and its components, as well as cost. There are lots of
challenging and interesting issues that arise from this
problem, and the solution techniques encompass a unique
blend of probability / statistics and mathematical
programming.
Another topic that I worked on with S.V. Majety, a former doctoral student of mine, is optimal reliability design. Here we try to allocate reliability (and as a special case, redundancy) among the various components and subsystems that make up an arbitrary system so that the total cost of the system is minimized while meeting a specified value for reliability (or reliability is maximized while costs are within some budget). In particular we looked at the case where cost is not necessarily some closed form function of reliability, but rather, cost and reliability appear as discrete data sets. We formulated the problem as an integer program and worked on developing suitable techniques to solve these.
Again, if you are interested here's a list of publications that I have in the reliability area.
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